plots.R

library("ggplot2")
library(gridExtra)
library(grid)
library(ggpubr)
library(extrafont)
font_import()
loadfonts(device="win")       #Register fonts for Windows bitmap output


# Involuntariness subscales; p = .15 --------------------------------------
# MAMBAC ------------------------------------------------------------------

mambac.empcurve.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)
mambac.empcurve.y <- c(0.5905273,0.5689108,0.5612718,0.5588037,0.5452747,0.5431529,0.5368974,0.5290554,0.5216489,0.5120615,0.5069634,0.5002172,0.497582,0.4934917,0.4924358,0.4909373,0.4913425,0.4880423,0.4933784,0.49704,0.4996758,0.5033576,0.5027592,0.4986302,0.4967131,0.4956178,0.4942532,0.4928129,0.4904009,0.4900658,0.4850468,0.4870515,0.4920108,0.5029594,0.510751,0.5111621,0.5105589,0.5084409,0.5094427,0.5064202,0.5099179,0.5089331,0.5093905,0.5236789,0.5318987,0.5440125,0.5611064,0.5748894,0.5956134,0.6072795)
mambac.y.range <- c(0.2718427, 0.8855649)

#Duplicate empirical values to allow the simulated polygon to be more smooth
mambac.empcurve.x <- rep(mambac.empcurve.x, each = 2)
mambac.empcurve.y <- rep(mambac.empcurve.y, each = 2)

mambac.polygon.cat.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1)
mambac.polygon.cat.y <- c(0.4345879,0.4396825,0.4393294,0.4457419,0.4464244,0.4439076,0.4431523,0.4445873,0.4445944,0.4495505,0.4498675,0.4554126,0.4583472,0.4618437,0.4657364,0.4707589,0.4770924,0.4848118,0.4921624,0.4992761,0.5076971,0.515535,0.5214255,0.5281761,0.5368793,0.5459656,0.5489698,0.5557557,0.5589522,0.5654058,0.5694168,0.5725997,0.5822704,0.5911577,0.6019538,0.610985,0.6205434,0.6304271,0.6442946,0.6489191,0.6602313,0.6673185,0.6793918,0.6917884,0.6964019,0.7037769,0.718853,0.7302291,0.7369156,0.7342907,0.6229991,0.641645,0.6494667,0.6434296,0.6320777,0.6223268,0.61658,0.6129271,0.6040006,0.5986832,0.5909132,0.5794898,0.5647989,0.5564628,0.5480297,0.5417526,0.534098,0.5236353,0.5163228,0.5129617,0.5079737,0.4990797,0.4968302,0.4931796,0.486852,0.4807999,0.4756573,0.4699357,0.4607908,0.452025,0.4444576,0.4365369,0.4295372,0.4251383,0.4183799,0.4181474,0.4180545,0.4156846,0.4096755,0.4048854,0.3992506,0.3913734,0.3911607,0.3922187,0.3941644,0.3931346,0.3939559,0.3863608,0.3789572,0.3767143)

mambac.polygon.dim.x <- mambac.polygon.cat.x
mambac.polygon.dim.y <- c(0.5021347,0.5006817,0.5054656,0.5054524,0.5018201,0.5024087,0.5019835,0.5027595,0.5044102,0.5042747,0.5016465,0.5023633,0.5049884,0.5053163,0.5074507,0.5102878,0.5140519,0.520138,0.5270833,0.5329517,0.5372523,0.5414721,0.545404,0.5518484,0.5579776,0.5619662,0.5672659,0.5730636,0.5779319,0.5772361,0.576077,0.5798486,0.5824322,0.5812126,0.5856955,0.593337,0.5968098,0.6020076,0.6116763,0.6180064,0.62515,0.6294086,0.6453816,0.6586515,0.6746658,0.686348,0.7114891,0.7325866,0.7529128,0.7867028,0.6933842,0.6682417,0.6489877,0.633879,0.6115795,0.6004882,0.588941,0.5795114,0.5693705,0.5631889,0.5580587,0.5492102,0.5447177,0.5373406,0.5302913,0.524798,0.5213008,0.5193179,0.5175872,0.5170775,0.5185418,0.5120616,0.507489,0.5045851,0.5007952,0.4961838,0.4947697,0.4929433,0.4904967,0.4841345,0.4787358,0.4737302,0.4688378,0.4635997,0.4596696,0.4556521,0.4533928,0.4476622,0.4464978,0.444039,0.4451088,0.445223,0.4433,0.4464725,0.4499136,0.4562083,0.454742,0.4559272,0.4517272,0.4472005)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line1.cat.y <- rep(c(0.2718427,0.3122596,0.3113556,0.3114312,0.3130189,0.3216311,0.3247512,0.3285967,0.3309657,0.3322935,0.3342199,0.3324489,0.3343235,0.3317962,0.3268092,0.3288002,0.3300116,0.3336744,0.3392427,0.346012,0.3529165,0.3618901,0.3730124,0.3782421,0.3840198,0.3894902,0.3967492,0.403657,0.4069006,0.413536,0.4167249,0.4185661,0.4260785,0.4314141,0.4421155,0.4567827,0.4615678,0.4731259,0.4821934,0.4949591,0.5058544,0.5083446,0.5077476,0.5231399,0.5187211,0.5162563,0.525558,0.5427385,0.5462243,0.5246679), each = 2)

mambac.line1.dim.y <- rep(c(0.3733642,0.3806356,0.3706405,0.36984,0.3605964,0.3587805,0.3639816,0.3673352,0.3752726,0.377718,0.3712056,0.3751287,0.3802738,0.3809657,0.37827,0.3755255,0.3783849,0.3838303,0.3901575,0.3989983,0.4061345,0.4181051,0.4275582,0.4341983,0.4388501,0.4466158,0.4529386,0.4554729,0.4601409,0.4588944,0.4575283,0.4593841,0.4646799,0.4707736,0.4675672,0.4651606,0.4602807,0.458672,0.4660598,0.4772513,0.4886924,0.495768,0.5015443,0.5128181,0.5035449,0.5179626,0.5350782,0.5595762,0.5787279,0.5644037), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line2.cat.y <- rep(c(0.5154164,0.5161081,0.5192732,0.5426953,0.5477749,0.5541421,0.5410229,0.5416836,0.5402955,0.5362344,0.5364107,0.5378858,0.5424783,0.5543158,0.5495014,0.5557261,0.5627964,0.5709525,0.5786083,0.5870007,0.5934546,0.5987044,0.6046,0.6060521,0.6191849,0.62549,0.6302146,0.635185,0.63696,0.6392182,0.6465292,0.6547897,0.6616211,0.672158,0.6746126,0.6835324,0.6981472,0.7142679,0.7271436,0.7374703,0.7488498,0.7702841,0.7910838,0.7767294,0.7685112,0.769408,0.7796452,0.8253494,0.8413658,0.8350243), each = 2)

mambac.line2.dim.y <- rep(c(0.5849409,0.581261,0.5751273,0.5705738,0.5601426,0.547331,0.5449705,0.5513569,0.5585108,0.570922,0.5731614,0.5756343,0.5778565,0.5784609,0.5849276,0.5845291,0.5860623,0.5895265,0.5921275,0.5995517,0.603304,0.6121976,0.6212086,0.6318055,0.6366125,0.6427046,0.6446681,0.6442837,0.6551835,0.6633276,0.6656423,0.6672865,0.6631866,0.6603505,0.6608992,0.6642783,0.6653852,0.6649748,0.667221,0.6833578,0.696626,0.7073915,0.717596,0.726196,0.7287452,0.7489868,0.7929227,0.8242488,0.8790799,0.8855649), each = 2)

mamb.emp <- data.frame(mambac.empcurve.x, mambac.empcurve.y)
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.x"] <- "xvalues"
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.y"] <- "yvalues"

  
# MAXEIG ------------------------------------------------------------------

maxeig.empcurve.x <- c(-1.220567,-1.159481,-1.106531,-1.059193,-1.007682,-0.9676817,-0.9228465,-0.8790472,-0.8377732,-0.8014703,-0.763786,-0.7277492,-0.6893742,-0.6520352,-0.6201997,-0.5899325,-0.5529389,-0.5132085,-0.4699934,-0.4260877,-0.3794577,-0.3239856,-0.2698157,-0.2151026,-0.1503212,-0.0862098,-0.01382554,0.04928242,0.1069129,0.1665648,0.2234418,0.2814481,0.3363178,0.3909897,0.4362839,0.4721325,0.5111764,0.5669777,0.6300344,0.6883068,0.7515653,0.815658,0.8800961,0.9434982,1.023205,1.102204,1.189964,1.275377,1.3676,1.494068)
maxeig.empcurve.y <- c(0.2224346,0.2225657,0.2231542,0.2188066,0.2170967,0.2140541,0.2061418,0.2083651,0.2121687,0.2194715,0.2154601,0.2205223,0.2202422,0.2135292,0.2096454,0.2120398,0.2280805,0.2339484,0.2333908,0.2319039,0.2288722,0.2183078,0.2136491,0.2168941,0.2129897,0.2059248,0.1952026,0.1957596,0.202493,0.2018495,0.2028629,0.2001022,0.2015095,0.1996306,0.1980543,0.1992681,0.1973259,0.2041509,0.2078057,0.2133449,0.2126256,0.2170325,0.2210214,0.2204843,0.2331605,0.2541142,0.2653541,0.2735543,0.2748692,0.284127)
maxeig.y.range <- c(0.09599888, 0.4263868)

#Duplicate empirical values to allow the simulated polygon to be more smooth
maxeig.empcurve.x <- rep(maxeig.empcurve.x, each = 2)
maxeig.empcurve.y <- rep(maxeig.empcurve.y, each = 2)

maxeig.polygon.cat.x <- c(-1.220567,-1.159481,-1.106531,-1.059193,-1.007682,-0.9676817,-0.9228465,-0.8790472,-0.8377732,-0.8014703,-0.763786,-0.7277492,-0.6893742,-0.6520352,-0.6201997,-0.5899325,-0.5529389,-0.5132085,-0.4699934,-0.4260877,-0.3794577,-0.3239856,-0.2698157,-0.2151026,-0.1503212,-0.0862098,-0.01382554,0.04928242,0.1069129,0.1665648,0.2234418,0.2814481,0.3363178,0.3909897,0.4362839,0.4721325,0.5111764,0.5669777,0.6300344,0.6883068,0.7515653,0.815658,0.8800961,0.9434982,1.023205,1.102204,1.189964,1.275377,1.3676,1.494068,1.494068,1.3676,1.275377,1.189964,1.102204,1.023205,0.9434982,0.8800961,0.815658,0.7515653,0.6883068,0.6300344,0.5669777,0.5111764,0.4721325,0.4362839,0.3909897,0.3363178,0.2814481,0.2234418,0.1665648,0.1069129,0.04928242,-0.01382554,-0.0862098,-0.1503212,-0.2151026,-0.2698157,-0.3239856,-0.3794577,-0.4260877,-0.4699934,-0.5132085,-0.5529389,-0.5899325,-0.6201997,-0.6520352,-0.6893742,-0.7277492,-0.763786,-0.8014703,-0.8377732,-0.8790472,-0.9228465,-0.9676817,-1.007682,-1.059193,-1.106531,-1.159481,-1.220567)
maxeig.polygon.cat.y <- c(0.1695548,0.1714214,0.172894,0.1748003,0.1746866,0.1754791,0.1752904,0.1793736,0.1800475,0.1822516,0.1844325,0.1873408,0.1916206,0.1943542,0.1977401,0.2014076,0.2000519,0.2001155,0.2010035,0.202137,0.2083226,0.2171887,0.2245942,0.2342767,0.2469285,0.2527871,0.2617353,0.2689543,0.2735039,0.2768894,0.2812221,0.2855092,0.2877465,0.2882812,0.2948188,0.2998703,0.306614,0.315753,0.3188633,0.3299335,0.3332489,0.3351743,0.3363515,0.3329691,0.3258358,0.3227406,0.3184058,0.3063518,0.294758,0.2782238,0.2257218,0.2358169,0.2490615,0.260548,0.2674143,0.2753245,0.2808322,0.2841806,0.286103,0.2891838,0.2844524,0.2788757,0.2727033,0.2638412,0.2581726,0.2523512,0.2468736,0.2462151,0.2405092,0.2347948,0.2296778,0.2243731,0.2220917,0.2153822,0.2111775,0.2040117,0.1972591,0.1885013,0.1823885,0.1759693,0.1729534,0.1707729,0.1704892,0.1690179,0.1641679,0.1624214,0.1604355,0.1581683,0.1554657,0.1557628,0.1546896,0.1534821,0.1485858,0.1454705,0.1436769,0.1408253,0.1401298,0.1406832,0.1403178,0.1386876)

maxeig.polygon.dim.x <- maxeig.polygon.cat.x
maxeig.polygon.dim.y <- c(0.2226518,0.2255432,0.2273007,0.2264566,0.2279142,0.2288565,0.2338877,0.2374796,0.2393177,0.2355839,0.2364753,0.2370163,0.235672,0.2361949,0.2353031,0.235632,0.2371916,0.2362934,0.23898,0.2420289,0.2407586,0.242997,0.2431419,0.2424913,0.245649,0.2462317,0.2463317,0.2452463,0.2469553,0.2486176,0.2499651,0.2471421,0.2472889,0.2425939,0.2445524,0.2471679,0.2464494,0.24539,0.2423781,0.2440951,0.2476027,0.2488878,0.2515021,0.2477207,0.2486041,0.2476365,0.2502964,0.2530529,0.2619322,0.2623059,0.1966641,0.1941265,0.1959173,0.1980228,0.1992296,0.204287,0.205314,0.2049828,0.2067181,0.2090753,0.2072334,0.2063114,0.1994029,0.1981999,0.2008361,0.1992245,0.1995871,0.2002852,0.1985067,0.2043412,0.2072023,0.208589,0.2107687,0.2120877,0.2123401,0.212417,0.2114683,0.2102895,0.2088407,0.2059758,0.2057399,0.2059253,0.2053793,0.2041693,0.1991912,0.1976088,0.1991998,0.1996365,0.1982136,0.196302,0.1948089,0.1966954,0.1989232,0.1995646,0.199516,0.1966314,0.194056,0.195946,0.1945278,0.1930233)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line1.cat.y <- rep(c(0.1089488,0.1070435,0.103423,0.1053092,0.1020757,0.1028349,0.09599888,0.1088278,0.1156357,0.1252374,0.1215356,0.1242622,0.1205303,0.1270093,0.1215164,0.1231973,0.1283405,0.1296638,0.1407186,0.1306437,0.1256473,0.1138408,0.1113093,0.1215216,0.1406967,0.160291,0.172924,0.1780444,0.1858937,0.1880356,0.1921997,0.1950975,0.1958033,0.1997965,0.2058667,0.2145215,0.2190981,0.2275224,0.2305619,0.2353959,0.2323636,0.2275077,0.227252,0.2297458,0.2341557,0.2297458,0.2132311,0.1911323,0.1824198,0.1723257), each = 2)

maxeig.line1.dim.y <- rep(c(0.1414888,0.1366263,0.1516102,0.1532913,0.1537354,0.1549244,0.147396,0.1551939,0.1532911,0.1561076,0.1548032,0.1608595,0.1563006,0.1509496,0.1514524,0.1524501,0.1555937,0.1588597,0.1585621,0.1470305,0.1491888,0.1550747,0.1577396,0.1617704,0.1674083,0.1761316,0.1787849,0.1810883,0.1724757,0.1765779,0.1755741,0.1733162,0.1699787,0.1639895,0.163521,0.1552296,0.1503906,0.1474447,0.1534191,0.1581234,0.1640124,0.1686424,0.1692662,0.1698573,0.1714603,0.1632062,0.1457233,0.1407206,0.132165,0.1219839), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line2.cat.y <- rep(c(0.2273831,0.2241193,0.2186804,0.216569,0.2170442,0.2217575,0.2189803,0.219433,0.225344,0.2305595,0.2301395,0.233531,0.2368188,0.2307718,0.2253007,0.2350114,0.2401376,0.2417803,0.2414751,0.2398547,0.2420921,0.2534539,0.2747194,0.2829018,0.3069987,0.3062041,0.3110057,0.3210294,0.3291834,0.3309805,0.3404453,0.3468032,0.3525323,0.3587479,0.3715343,0.3769241,0.3832685,0.3847044,0.3896588,0.3929091,0.4139065,0.4146428,0.4170158,0.4204397,0.4250757,0.4263868,0.4158476,0.3926891,0.3820011,0.345521), each = 2)

maxeig.line2.dim.y <- rep(c(0.255518,0.2658665,0.2652644,0.269991,0.2709395,0.2722919,0.2763783,0.274172,0.2785702,0.2806036,0.2761925,0.2753891,0.2799198,0.280307,0.2778145,0.2757085,0.2759498,0.282449,0.2795282,0.2841557,0.2716209,0.2825939,0.2842144,0.2852079,0.2851824,0.2880994,0.2917027,0.3092902,0.3136628,0.3181998,0.3136816,0.3095682,0.3075569,0.3026788,0.2953766,0.3008447,0.3036162,0.31048,0.312356,0.3070719,0.3113006,0.3088661,0.3013823,0.307748,0.3114448,0.3033088,0.3028608,0.3159532,0.3269873,0.3497722), each = 2)

maxe.emp <- data.frame(maxeig.empcurve.x, maxeig.empcurve.y)
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.x"] <- "xvalues"
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.y"] <- "yvalues"

# L-Mode ------------------------------------------------------------------
lmode.empcurve.x <-
  c(
    -3.169932,
    -3.157394,
    -3.144857,
    -3.132319,
    -3.119781,
    -3.107243,
    -3.094706,
    -3.082168,
    -3.06963,
    -3.057092,
    -3.044554,
    -3.032017,
    -3.019479,
    -3.006941,
    -2.994403,
    -2.981866,
    -2.969328,
    -2.95679,
    -2.944252,
    -2.931714,
    -2.919177,
    -2.906639,
    -2.894101,
    -2.881563,
    -2.869025,
    -2.856488,
    -2.84395,
    -2.831412,
    -2.818874,
    -2.806337,
    -2.793799,
    -2.781261,
    -2.768723,
    -2.756185,
    -2.743648,
    -2.73111,
    -2.718572,
    -2.706034,
    -2.693497,
    -2.680959,
    -2.668421,
    -2.655883,
    -2.643345,
    -2.630808,
    -2.61827,
    -2.605732,
    -2.593194,
    -2.580657,
    -2.568119,
    -2.555581,
    -2.543043,
    -2.530505,
    -2.517968,
    -2.50543,
    -2.492892,
    -2.480354,
    -2.467817,
    -2.455279,
    -2.442741,
    -2.430203,
    -2.417665,
    -2.405128,
    -2.39259,
    -2.380052,
    -2.367514,
    -2.354977,
    -2.342439,
    -2.329901,
    -2.317363,
    -2.304825,
    -2.292288,
    -2.27975,
    -2.267212,
    -2.254674,
    -2.242136,
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lmode.y.range <- c(3.058113e-05,0.4315346)

lmode.empcurve.x <- rep(lmode.empcurve.x, each = 2)
lmode.empcurve.y <- rep(lmode.empcurve.y, each = 2)

lmode.polygon.cat.x <-
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lmode.polygon.cat.y <-
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lmode.polygon.dim.x <- lmode.polygon.cat.x
lmode.polygon.dim.y <-
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    0.06274297,
    0.06431741,
    0.065887,
    0.06742094,
    0.06897741,
    0.0705573,
    0.07216146,
    0.07378934,
    0.07536163,
    0.07700804,
    0.07909086,
    0.08144256,
    0.08367333,
    0.08582521,
    0.08774492,
    0.08975467,
    0.09182737,
    0.09395341,
    0.09598554,
    0.09767645,
    0.09980073,
    0.1022182,
    0.1047102,
    0.1068796,
    0.1097706,
    0.1126889,
    0.1155047,
    0.1183082,
    0.1212274,
    0.1243678,
    0.1272632,
    0.1298557,
    0.1325584,
    0.1354375,
    0.1383557,
    0.1415304,
    0.1450171,
    0.1488259,
    0.1526817,
    0.1555818,
    0.1577691,
    0.160352,
    0.1631992,
    0.1660411,
    0.1684087,
    0.17029,
    0.1722313,
    0.1743117,
    0.176974,
    0.1799418,
    0.1829681,
    0.1860289,
    0.1890823,
    0.1915875,
    0.1946354,
    0.1974023,
    0.2002415,
    0.2032622,
    0.2061993,
    0.2090509,
    0.2116749,
    0.2146164,
    0.2174129,
    0.2196306,
    0.221272,
    0.2231372,
    0.225235,
    0.2274555,
    0.2296203,
    0.2317307,
    0.2340961,
    0.236847,
    0.2404107,
    0.242999,
    0.2450212,
    0.2470609,
    0.2504665,
    0.2530162,
    0.2551385,
    0.257205,
    0.2593547,
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    0.2649752,
    0.267612,
    0.2706873,
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    0.2767699,
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    0.2918935,
    0.293664,
    0.2956847,
    0.2981742,
    0.300823,
    0.3034198,
    0.3060136,
    0.307832,
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    0.3110497,
    0.3126356,
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    0.343,
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    0.3351783,
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    0.3347555,
    0.334021,
    0.3330826,
    0.3322749,
    0.33119,
    0.3299444,
    0.3289436,
    0.328288,
    0.3272211,
    0.3269502,
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    0.3229615,
    0.3214927,
    0.3196841,
    0.3186951,
    0.3171632,
    0.3161754,
    0.3143358,
    0.3130088,
    0.3114174,
    0.3100288,
    0.3087581,
    0.3065398,
    0.3050854,
    0.3036852,
    0.3023246,
    0.3010033,
    0.2997212,
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    0.2958435,
    0.2942348,
    0.2926871,
    0.2907747,
    0.2890712,
    0.2870053,
    0.2850906,
    0.283295,
    0.2817105,
    0.2805813,
    0.2792286,
    0.2771444,
    0.2752275,
    0.2740868,
    0.2728626,
    0.2716586,
    0.2692101,
    0.2667058,
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    0.2635487,
    0.2631075,
    0.2612851,
    0.2593209,
    0.2573269,
    0.2550057,
    0.2531311,
    0.2506478,
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    0.2470063,
    0.2455407,
    0.2438372,
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    0.2388947,
    0.2357719,
    0.2333211,
    0.2312621,
    0.2292605,
    0.2273981,
    0.2252158,
    0.2231412,
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    0.2183995,
    0.2158471,
    0.2138951,
    0.2120185,
    0.2096236,
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    0.2056065,
    0.2034159,
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    0.19926,
    0.1962422,
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    0.1914011,
    0.1893171,
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    0.1853178,
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    0.1782206,
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    0.1738853,
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    0.1696059,
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    0.1572965,
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    0.1030954,
    0.1009984,
    0.09894112,
    0.09672626,
    0.09453816,
    0.0924003,
    0.09033553,
    0.08853402,
    0.08639106,
    0.084217,
    0.08202555,
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    0.0675069,
    0.06534932,
    0.0633454,
    0.06167914,
    0.05958538,
    0.05744675,
    0.0556041,
    0.05426821,
    0.0528366,
    0.05154451,
    0.05026251,
    0.04898214,
    0.04770193,
    0.04635169,
    0.04488261,
    0.04302006,
    0.04112269,
    0.03940756,
    0.03774724,
    0.03628856,
    0.03498865,
    0.0338422,
    0.03242672,
    0.03108958,
    0.02951658,
    0.02838287,
    0.02730309,
    0.026267,
    0.02528364,
    0.02432042,
    0.02319635,
    0.02215761,
    0.02123461,
    0.02039224,
    0.01941671,
    0.01847258,
    0.01758549,
    0.01680546,
    0.01587937,
    0.0150146,
    0.01414723,
    0.01326149,
    0.01243562,
    0.0117015,
    0.01097325,
    0.01033715,
    0.009653832,
    0.009021172,
    0.008441434,
    0.007865508,
    0.007293863,
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    0.006259099,
    0.00579173,
    0.005324291,
    0.004898845,
    0.004499467,
    0.004111483,
    0.00375448,
    0.003428933,
    0.003134071,
    0.002867034,
    0.00260216,
    0.002354724,
    0.002135662,
    0.001922081,
    0.001726604,
    0.001549216,
    0.001389272,0.001243437,0.001109563,0.0009870284,0.0008778158,0.0007793954,0.0006899215,0.0006094626,0.0005383765,0.0004748516,0.0004173776,0.0003657356,0.0003191035,0.0002789134,0.0002434283,0.0002110495,0.0001822551,0.0001578444,0.0001363861,0.0001175216,0.0001012133,8.664203e-05,7.391705e-05,6.295508e-05,5.337873e-05,4.511105e-05)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line1.cat.y <-
  rep(
    c(
      3.133964e-05,
      3.650056e-05,
      4.226287e-05,
      4.873374e-05,
      5.587682e-05,
      6.416501e-05,
      7.340102e-05,
      8.365206e-05,
      9.510473e-05,
      0.000108285,
      0.0001228536,
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      0.0001990519,
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      0.0004762708,
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      0.0007054918,
      0.0007748132,
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      0.000930508,
      0.001017896,
      0.001111063,
      0.001210217,
      0.001318325,
      0.001433803,
      0.00155638,
      0.001686301,
      0.001826928,
      0.001976783,
      0.0021353,
      0.002302772,
      0.002482988,
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      0.002876993,
      0.003090173,
      0.003307463,
      0.003535092,
      0.003778961,
      0.004023528,
      0.004239935,
      0.004464694,
      0.004696741,
      0.004935719,
      0.005181918,
      0.005437364,
      0.00570314,
      0.005977992,
      0.006262456,
      0.006557943,
      0.006868923,
      0.007192479,
      0.007529398,
      0.007880484,
      0.008253138,
      0.008643973,
      0.009053117,
      0.009481549,
      0.009935938,
      0.01041699,
      0.01092192,
      0.01145172,
      0.01201078,
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      0.01323086,
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      0.01457056,
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      0.0160651,
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      0.1572113,
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      0.1752107,
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      0.1791623,
      0.181123,
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      0.2277759,
      0.2297917,
      0.2318462,
      0.2339604,
      0.2361259,
      0.2383415,
      0.2406094,
      0.2429492,
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      0.2478226,
      0.2503495,
      0.2529509,
      0.2556286,
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      0.2611657,
      0.264031,
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      0.2699608,
      0.2730012,
      0.2760902,
      0.2792352,
      0.282413,
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      0.00940052,
      0.008953788,
      0.008547665,
      0.008174751,
      0.007828413,
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      0.004517787,
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      0.003954185,
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      0.003617583,
      0.003460007,
      0.003307718,
      0.003159838,
      0.003016033,
      0.00287663,
      0.002741336,
      0.002609149,
      0.002479955,
      0.002353789,
      0.00222475,
      0.002086336,
      0.001953996,
      0.001827491,
      0.001706645,
      0.001593421,
      0.001485176,
      0.00138178,
      0.001283106,
      0.001190706,
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      0.0001915868,
      0.0001708194,
      0.0001518022,
      0.0001344442,
      0.0001188723,
      0.0001051293,
      9.264389e-05,
      8.134234e-05,
      7.126366e-05,
      6.25054e-05,
      5.461249e-05,
      4.752843e-05,
      4.120906e-05,
      3.555477e-05,
      3.058484e-05
    ),
    each = 2
  )

lmode.line1.dim.y <-
  rep(
    c(
      3.146678e-05,
      3.69346e-05,
      4.281236e-05,
      4.958955e-05,
      5.72044e-05,
      6.572347e-05,
      7.530995e-05,
      8.644686e-05,
      9.885201e-05,
      0.000112616,
      0.0001278477,
      0.0001454597,
      0.0001649108,
      0.0001863181,
      0.0002097996,
      0.0002361779,
      0.000265588,
      0.0002977312,
      0.0003327569,
      0.0003713641,
      0.0004144494,
      0.0004612101,
      0.0005115974,
      0.0005668799,
      0.000627461,
      0.0006926758,
      0.0007627205,
      0.0008387481,
      0.0009218411,
      0.001010754,
      0.001105713,
      0.001207619,
      0.001318748,
      0.001437071,
      0.001562855,
      0.001696576,
      0.001842203,
      0.001996671,
      0.002160313,
      0.002333463,
      0.00252095,
      0.00271985,
      0.002930089,
      0.003152103,
      0.003390887,
      0.003644823,
      0.003912919,
      0.004195747,
      0.004498331,
      0.004821132,
      0.005161775,
      0.005521007,
      0.005903585,
      0.006313153,
      0.006745266,
      0.007200858,
      0.007683906,
      0.008202727,
      0.008733565,
      0.009266333,
      0.009827021,
      0.01041665,
      0.0110303,
      0.0116684,
      0.0123366,
      0.01303788,
      0.01376565,
      0.0145203,
      0.01530675,
      0.01613026,
      0.01698244,
      0.01786363,
      0.01877781,
      0.01973279,
      0.02071833,
      0.0217347,
      0.02278478,
      0.02387923,
      0.02500589,
      0.02616503,
      0.0273583,
      0.02859947,
      0.02987445,
      0.03118352,
      0.03252698,
      0.03392207,
      0.03535263,
      0.03681894,
      0.0383213,
      0.0398764,
      0.0414701,
      0.04310127,
      0.04477018,
      0.04649265,
      0.04825687,
      0.05006003,
      0.05190233,
      0.05379829,
      0.0557386,
      0.05771859,
      0.05945049,
      0.06057889,
      0.0617055,
      0.06283021,
      0.06395285,
      0.0650725,
      0.06619006,
      0.06730557,
      0.06841911,
      0.06953018,
      0.07063968,
      0.07174796,
      0.07285526,
      0.07396188,
      0.07506862,
      0.07617602,
      0.07728452,
      0.07839517,
      0.07950939,
      0.08062744,
      0.08175007,
      0.08287875,
      0.08401702,
      0.08516403,
      0.08632088,
      0.08748878,
      0.08867583,
      0.08987864,
      0.09109871,
      0.09233757,
      0.09360578,
      0.09490085,
      0.09622278,
      0.09757344,
      0.09896427,
      0.1003968,
      0.1018674,
      0.1033781,
      0.104939,
      0.1065593,
      0.1082292,
      0.1099504,
      0.1117294,
      0.1135864,
      0.1155027,
      0.1174799,
      0.1195193,
      0.1216508,
      0.1238492,
      0.126114,
      0.1284455,
      0.1308672,
      0.1333634,
      0.1359261,
      0.1385546,
      0.141264,
      0.1440489,
      0.1468944,
      0.1497991,
      0.1527691,
      0.1558081,
      0.1588966,
      0.162032,
      0.1652142,
      0.1684512,
      0.1717226,
      0.1750255,
      0.1783569,
      0.1817212,
      0.1839501,
      0.1849845,
      0.18605,
      0.1871504,
      0.1882967,
      0.1895015,
      0.1907579,
      0.1920696,
      0.1934402,
      0.1949032,
      0.1964372,
      0.1980453,
      0.199731,
      0.2015214,
      0.2034124,
      0.2053945,
      0.2074703,
      0.2096547,
      0.2119708,
      0.2143911,
      0.2169174,
      0.2195514,
      0.2223383,
      0.2252404,
      0.2282543,
      0.2313804,
      0.234645,
      0.2380409,
      0.2415456,
      0.2451573,
      0.2488826,
      0.2527417,
      0.2566953,
      0.2607392,
      0.2625593,
      0.2633255,
      0.2640909,
      0.2648653,
      0.2656536,
      0.2664606,
      0.2672978,
      0.2681772,
      0.2690972,
      0.2700621,
      0.2710807,
      0.2721771,
      0.2733363,
      0.2745614,
      0.2758552,
      0.277251,
      0.2787258,
      0.2802775,
      0.281907,
      0.2836366,
      0.2854557,
      0.2873506,
      0.2893197,
      0.2912182,
      0.292042,
      0.2929302,
      0.2938673,
      0.2948546,
      0.2958956,
      0.2970117,
      0.2981812,
      0.2994043,
      0.3006814,
      0.3020373,
      0.3034458,
      0.3049063,
      0.306418,
      0.3080002,
      0.3096314,
      0.3113078,
      0.3116883,
      0.3115704,
      0.3115578,
      0.3116514,
      0.3118523,
      0.3122091,
      0.3126735,
      0.3132448,
      0.3139219,
      0.3147376,
      0.3156649,
      0.3163064,
      0.3155614,
      0.3148623,
      0.3142149,
      0.3136123,
      0.3130561,
      0.3125579,
      0.3121255,
      0.3117456,
      0.3114187,
      0.3111525,
      0.3109579,
      0.310816,
      0.310726,
      0.3106911,
      0.3088382,
      0.3068289,
      0.304884,
      0.3017629,
      0.2985775,
      0.2953888,
      0.292199,
      0.2890089,
      0.2858196,
      0.2826328,
      0.2794513,
      0.2762763,
      0.2731094,
      0.2699529,
      0.2668153,
      0.2636952,
      0.2605953,
      0.2575182,
      0.2544762,
      0.2514708,
      0.2485018,
      0.2455726,
      0.2426926,
      0.2398768,
      0.2371157,
      0.2344125,
      0.2317705,
      0.229219,
      0.2267417,
      0.2243376,
      0.2220091,
      0.2197746,
      0.2176376,
      0.2155822,
      0.2136087,
      0.2117203,
      0.2099438,
      0.2082465,
      0.2066266,
      0.2050818,
      0.2036289,
      0.2022505,
      0.2009333,
      0.1996733,
      0.1984715,
      0.1973268,
      0.1962183,
      0.1951409,
      0.1940892,
      0.1930608,
      0.1920406,
      0.1910225,
      0.1900012,
      0.1889682,
      0.1860477,
      0.1830765,
      0.1801645,
      0.1773114,
      0.1745245,
      0.1718131,
      0.1691574,
      0.1665565,
      0.1640121,
      0.1615401,
      0.1591175,
      0.1567429,
      0.1544149,
      0.1521494,
      0.1499268,
      0.147744,
      0.1450148,
      0.1412932,
      0.1377627,
      0.1343723,
      0.1311194,
      0.1280041,
      0.1250706,
      0.1222907,
      0.1196451,
      0.1171323,
      0.1147778,
      0.1125775,
      0.1104982,
      0.1085368,
      0.1067023,
      0.1050104,
      0.103419,
      0.1019241,
      0.1005227,
      0.0992423,
      0.09803859,
      0.09690717,
      0.09456125,
      0.09194236,
      0.08867093,
      0.08553342,
      0.08250867,
      0.07958704,
      0.07676807,
      0.07406235,
      0.07148457,
      0.06900315,
      0.06661573,
      0.06431982,
      0.0621389,
      0.06004676,
      0.05803285,
      0.05609382,
      0.05423423,
      0.05245787,
      0.05074162,
      0.04908222,
      0.04747648,
      0.04593573,
      0.04444251,
      0.04299076,
      0.0415781,
      0.04020666,
      0.03887755,
      0.03757957,
      0.03631149,
      0.03507216,
      0.03386954,
      0.0326952,
      0.03154714,
      0.03042522,
      0.02933311,
      0.02827438,
      0.02724265,
      0.02623837,
      0.02526204,
      0.02432454,
      0.02341855,
      0.02254306,
      0.02169866,
      0.02089078,
      0.0201237,
      0.01938974,
      0.01868919,
      0.0180223,
      0.01740128,
      0.01681563,
      0.01626357,
      0.01574484,
      0.01526423,
      0.01482346,
      0.01441384,
      0.0140346,
      0.01368496,
      0.01337369,
      0.01308983,
      0.01283121,
      0.01259667,
      0.01238848,
      0.01220553,
      0.01199275,
      0.01172898,
      0.01126749,
      0.01070543,
      0.01018463,
      0.00970364,
      0.009253035,
      0.008831424,
      0.008437783,
      0.008079594,
      0.007744549,
      0.007431413,
      0.007138963,
      0.006870388,
      0.00662153,
      0.006388349,
      0.006169794,
      0.005900776,
      0.005645747,
      0.005407849,
      0.005186215,
      0.004981368,
      0.00479447,
      0.004619819,
      0.004456503,
      0.004303612,
      0.004162889,
      0.004030194,
      0.003904153,
      0.003783992,
      0.003669648,
      0.003559946,
      0.003453194,
      0.003348863,
      0.003246468,
      0.003145735,
      0.003045632,
      0.002945909,
      0.002846341,
      0.00274666,
      0.002646693,
      0.002546447,
      0.002445927,
      0.002345151,
      0.002244259,
      0.002143473,
      0.002042944,
      0.001942833,
      0.001843672,
      0.001745617,
      0.001648817,
      0.001553472,
      0.001460149,
      0.001369332,
      0.001280787,
      0.001194674,
      0.001111188,
      0.001031645,
      0.0009491343,
      0.0008721326,
      0.0007995411,
      0.0007310231,
      0.0006664992,
      0.0006068409,
      0.0005515594,
      0.0004991801,
      0.0004502192,
      0.0004048676,
      0.000364147,
      0.0003267461,
      0.0002922802,
      0.0002606113,
      0.0002322752,
      0.0002066932,
      0.0001833105,
      0.0001620082,
      0.0001429981,
      0.0001261664,
      0.000110911,
      9.713498e-05,
      8.485973e-05,
      7.422483e-05,
      6.466762e-05,
      5.611412e-05,
      4.849095e-05,
      4.187728e-05,
      3.58823e-05,
      3.058113e-05
    ),
    each = 2
  )

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line2.cat.y <-
  rep(
    c(
      0.0001940719,
      0.0002243474,
      0.000259935,
      0.000299932,
      0.0003446828,
      0.000395086,
      0.0004537837,
      0.0005191942,
      0.000591788,
      0.0006726663,
      0.0007659515,
      0.0008690209,
      0.0009824797,
      0.001107561,
      0.001250401,
      0.001406879,
      0.001577722,
      0.001764151,
      0.001974874,
      0.002203745,
      0.002451576,
      0.002719355,
      0.003018839,
      0.003341336,
      0.003687669,
      0.00405866,
      0.004468344,
      0.004906108,
      0.005372338,
      0.005867757,
      0.006407487,
      0.006979924,
      0.007584528,
      0.008221799,
      0.008907,
      0.009628104,
      0.01038342,
      0.01117309,
      0.01201141,
      0.01288659,
      0.01379572,
      0.01473851,
      0.01572715,
      0.01675076,
      0.01780537,
      0.01889023,
      0.02001452,
      0.0211688,
      0.02251988,
      0.02413467,
      0.02583239,
      0.02759875,
      0.02943381,
      0.03135424,
      0.03335929,
      0.03543172,
      0.0375709,
      0.03978982,
      0.04208972,
      0.04445142,
      0.04687349,
      0.04936469,
      0.05192731,
      0.05454173,
      0.05720582,
      0.059924,
      0.06269822,
      0.06551034,
      0.06835769,
      0.0712409,
      0.0741598,
      0.07709995,
      0.08005833,
      0.0830328,
      0.08601935,
      0.08900926,
      0.09199949,
      0.09498643,
      0.09796087,
      0.1009213,
      0.1038651,
      0.1067885,
      0.1096764,
      0.1125353,
      0.1153631,
      0.1181572,
      0.1208967,
      0.1235961,
      0.1262538,
      0.1288686,
      0.1314172,
      0.1339181,
      0.1363717,
      0.1387773,
      0.1411134,
      0.1433985,
      0.1456354,
      0.1478243,
      0.1499468,
      0.1520199,
      0.1540483,
      0.1560329,
      0.1579598,
      0.1598431,
      0.1616889,
      0.1634985,
      0.165263,
      0.1669934,
      0.168696,
      0.1703726,
      0.172019,
      0.1736433,
      0.1752513,
      0.1768449,
      0.1784243,
      0.1799952,
      0.1815619,
      0.1831265,
      0.1846922,
      0.1862639,
      0.1878433,
      0.1894322,
      0.1910363,
      0.1926602,
      0.195928,
      0.1994579,
      0.2029516,
      0.2064061,
      0.2097989,
      0.213137,
      0.2164229,
      0.2196543,
      0.2228123,
      0.2261993,
      0.2294988,
      0.2326694,
      0.2357389,
      0.2387133,
      0.2415919,
      0.2443364,
      0.2469761,
      0.2495212,
      0.2519728,
      0.2542998,
      0.2565296,
      0.2586756,
      0.2607403,
      0.2627022,
      0.2645846,
      0.266402,
      0.2681582,
      0.2703004,
      0.2728015,
      0.2752337,
      0.2776162,
      0.2799486,
      0.2822306,
      0.2844383,
      0.2865949,
      0.2890126,
      0.2918274,
      0.2945513,
      0.2972084,
      0.2997982,
      0.3023193,
      0.3047425,
      0.30735,
      0.3102877,
      0.3131687,
      0.3159659,
      0.3186897,
      0.3213432,
      0.3239237,
      0.3264038,
      0.328787,
      0.3310839,
      0.3332918,
      0.3353869,
      0.3373618,
      0.339237,
      0.3410107,
      0.3426654,
      0.3441805,
      0.3459293,
      0.3486774,
      0.3512523,
      0.3536514,
      0.3558436,
      0.3578062,
      0.3595884,
      0.3611909,
      0.3629135,
      0.3650203,
      0.3670639,
      0.3690274,
      0.3709008,
      0.3726997,
      0.3744223,
      0.3760547,
      0.377578,
      0.3790167,
      0.3806737,
      0.3835771,
      0.3863296,
      0.3888929,
      0.3913062,
      0.3935651,
      0.3956448,
      0.3974968,
      0.3991768,
      0.4006823,
      0.4019945,
      0.4030553,
      0.4039341,
      0.4046306,
      0.4053972,
      0.4064466,
      0.4073634,
      0.4081254,
      0.408708,
      0.4091523,
      0.4094581,
      0.4096179,
      0.4095858,
      0.4094192,
      0.4091201,
      0.4096165,
      0.4104908,
      0.4112109,
      0.4117999,
      0.4122559,
      0.4125506,
      0.4126688,
      0.4126469,
      0.4124839,
      0.4121619,
      0.4126437,
      0.4142658,
      0.415779,
      0.4171539,
      0.4183746,
      0.4194653,
      0.4204215,
      0.4212252,
      0.4218305,
      0.4222831,
      0.4225797,
      0.4227173,
      0.4226198,
      0.4223526,
      0.4219161,
      0.4213091,
      0.4204737,
      0.4194457,
      0.4182462,
      0.4168759,
      0.4152987,
      0.4135187,
      0.4115764,
      0.4094747,
      0.407199,
      0.4047251,
      0.4021088,
      0.3997429,
      0.3985729,
      0.3972252,
      0.3957453,
      0.3941362,
      0.3923824,
      0.3904713,
      0.388448,
      0.387018,
      0.3862896,
      0.3853839,
      0.3843416,
      0.3831713,
      0.3825695,
      0.3825877,
      0.3824088,
      0.3820848,
      0.3816161,
      0.3810032,
      0.3801904,
      0.3792333,
      0.3781396,
      0.3769119,
      0.3769053,
      0.3772575,
      0.3775478,
      0.3777695,
      0.3778842,
      0.3779171,
      0.3778647,
      0.3777236,
      0.3774506,
      0.3770741,
      0.3765975,
      0.3760191,
      0.3753038,
      0.3744698,
      0.3735315,
      0.3724891,
      0.3713189,
      0.370026,
      0.3686347,
      0.367147,
      0.3655511,
      0.3638396,
      0.3620438,
      0.3601667,
      0.3582061,
      0.3561463,
      0.3540208,
      0.3518329,
      0.3495861,
      0.3472629,
      0.3448929,
      0.3424798,
      0.3400266,
      0.3375257,
      0.3349924,
      0.3324325,
      0.3298484,
      0.3272379,
      0.3246078,
      0.3219633,
      0.3193062,
      0.3166364,
      0.3142465,
      0.3136675,
      0.3130437,
      0.3123633,
      0.3116181,
      0.3108207,
      0.3099697,
      0.30905,
      0.3080556,
      0.3070007,
      0.3058841,
      0.3046873,
      0.303408,
      0.3020614,
      0.3006466,
      0.2991426,
      0.2975518,
      0.2958897,
      0.294156,
      0.2923283,
      0.2904142,
      0.2884287,
      0.2863723,
      0.2850106,
      0.2851961,
      0.2852948,
      0.2852832,
      0.2851453,
      0.2849037,
      0.2845553,
      0.2840787,
      0.28345,
      0.2827028,
      0.2818352,
      0.2808311,
      0.2796578,
      0.2783594,
      0.2769357,
      0.2753771,
      0.2736441,
      0.2717885,
      0.2698118,
      0.2677115,
      0.265444,
      0.2630652,
      0.260578,
      0.257985,
      0.2552453,
      0.2524117,
      0.2494886,
      0.2464796,
      0.2433576,
      0.2401607,
      0.2368965,
      0.233569,
      0.2301628,
      0.226703,
      0.2231983,
      0.2196522,
      0.2160583,
      0.2124315,
      0.2087793,
      0.2051049,
      0.2024216,
      0.2001774,
      0.1978238,
      0.1954611,
      0.1934743,
      0.1913812,
      0.1891838,
      0.1868639,
      0.1844213,
      0.1818872,
      0.1792647,
      0.1769602,
      0.1750163,
      0.1729382,
      0.1707618,
      0.1684878,
      0.1661092,
      0.1635998,
      0.1609996,
      0.1583108,
      0.155532,
      0.1526361,
      0.149664,
      0.146619,
      0.1435043,
      0.1402965,
      0.1370332,
      0.1337183,
      0.1303559,
      0.1269366,
      0.1234847,
      0.1200063,
      0.116506,
      0.1129861,
      0.1094603,
      0.1059342,
      0.1024123,
      0.09890572,
      0.09542099,
      0.09196058,
      0.08852839,
      0.08514077,
      0.08180105,
      0.07850639,
      0.07605825,
      0.0737447,
      0.07144741,
      0.06916658,
      0.06690463,
      0.06466679,
      0.0624473,
      0.06024673,
      0.05806852,
      0.05591929,
      0.05379266,
      0.05168952,
      0.04961457,
      0.04757589,
      0.04556566,
      0.04358492,
      0.04163973,
      0.03973928,
      0.03787371,
      0.03604406,
      0.03425762,
      0.03252397,
      0.0308311,
      0.02917984,
      0.02757844,
      0.02603603,
      0.02453874,
      0.02308708,
      0.02168979,
      0.02035484,
      0.01906713,
      0.01782675,
      0.01664249,
      0.0155206,
      0.01444558,
      0.01341714,
      0.01244363,
      0.01152936,
      0.01065929,
      0.009832785,
      0.009057423,
      0.008335605,
      0.007653498,
      0.007010226,
      0.006412338,
      0.005860621,
      0.005342968,
      0.004858379,
      0.004412259,
      0.004004192,
      0.003624074,
      0.003270891,
      0.002948907,
      0.002656947,
      0.002386956,
      0.002137989,
      0.001913268,
      0.001711255,
      0.001525805,
      0.001356099,
      0.001204467,
      0.001069317,
      0.0009461571,
      0.000834318,
      0.0007354168,
      0.0006480059,
      0.0005689353,
      0.0004976881,
      0.0004353404,
      0.0003806918,
      0.0003316222,
      0.0002877517,
      0.0002497678,
      0.0002167451,
      0.000187313,
      0.0001612056,
      0.0001388439
    ),
    each = 2
  )

lmode.line2.dim.y <-
  rep(
    c(
      0.0002241237,
      0.0002618229,
      0.0003045245,
      0.0003526631,
      0.0004085638,
      0.0004729058,
      0.000545138,
      0.0006258797,
      0.0007176161,
      0.0008230243,
      0.0009402926,
      0.001070248,
      0.00121499,
      0.001380771,
      0.001563529,
      0.001764289,
      0.001984087,
      0.002234254,
      0.002507727,
      0.002805489,
      0.003128716,
      0.003489091,
      0.003882124,
      0.004306268,
      0.004762736,
      0.005262247,
      0.005804975,
      0.006385473,
      0.007004833,
      0.00767131,
      0.008391741,
      0.009155527,
      0.009963456,
      0.01081995,
      0.01173986,
      0.01270666,
      0.01372067,
      0.01478218,
      0.01591247,
      0.0170909,
      0.01831663,
      0.01958935,
      0.02092449,
      0.02230934,
      0.02373821,
      0.02521019,
      0.02673454,
      0.02830599,
      0.029915,
      0.03156016,
      0.03324524,
      0.03497052,
      0.03672446,
      0.03850528,
      0.04031287,
      0.04238008,
      0.04470865,
      0.04708885,
      0.04951871,
      0.05200314,
      0.05454308,
      0.05712218,
      0.05973794,
      0.06239006,
      0.06508223,
      0.06779882,
      0.07053714,
      0.07329448,
      0.07607219,
      0.07885916,
      0.08165265,
      0.08445007,
      0.08724718,
      0.09003926,
      0.09282416,
      0.09559971,
      0.09835948,
      0.1011006,
      0.1038239,
      0.1065279,
      0.1092067,
      0.111856,
      0.1144808,
      0.1170804,
      0.1196514,
      0.1221865,
      0.1246947,
      0.1271762,
      0.1296306,
      0.1320475,
      0.1344392,
      0.1368065,
      0.1391499,
      0.1414623,
      0.1437524,
      0.1460229,
      0.1482748,
      0.1505047,
      0.1527172,
      0.154916,
      0.1571024,
      0.1592752,
      0.1614365,
      0.1635898,
      0.165736,
      0.1678753,
      0.1700081,
      0.1721368,
      0.1742621,
      0.1763841,
      0.1785025,
      0.1806184,
      0.1827319,
      0.1848428,
      0.1869498,
      0.1890531,
      0.1911525,
      0.1932473,
      0.195335,
      0.1974151,
      0.200278,
      0.2035508,
      0.2067356,
      0.2098275,
      0.2127869,
      0.2156504,
      0.2184174,
      0.2210872,
      0.2236263,
      0.2260601,
      0.2283989,
      0.2306441,
      0.2327774,
      0.2348042,
      0.2367469,
      0.2386083,
      0.2403839,
      0.2420634,
      0.2436767,
      0.2452276,
      0.24672,
      0.2481394,
      0.2495138,
      0.2513362,
      0.2535561,
      0.2557099,
      0.2578128,
      0.2598664,
      0.2618697,
      0.2642133,
      0.2674348,
      0.2706297,
      0.2737962,
      0.276932,
      0.2800203,
      0.2830675,
      0.2860731,
      0.2890345,
      0.2919351,
      0.2947732,
      0.2975549,
      0.3002773,
      0.3029279,
      0.3054916,
      0.3079845,
      0.3104044,
      0.3127467,
      0.314978,
      0.3171278,
      0.3191947,
      0.3211777,
      0.3230449,
      0.3248184,
      0.3265055,
      0.3281062,
      0.3296006,
      0.3309934,
      0.3323031,
      0.3335312,
      0.3346698,
      0.3357073,
      0.3366713,
      0.3375643,
      0.3383881,
      0.3391192,
      0.3397904,
      0.3404041,
      0.3418078,
      0.3435798,
      0.3452318,
      0.3467646,
      0.3481397,
      0.3493939,
      0.350539,
      0.3515782,
      0.3524962,
      0.3532995,
      0.3540153,
      0.3546484,
      0.3552,
      0.3556566,
      0.3560521,
      0.3563913,
      0.3579864,
      0.3595943,
      0.3610923,
      0.3624933,
      0.3638094,
      0.3650408,
      0.3661726,
      0.3675529,
      0.3698525,
      0.3721161,
      0.3743308,
      0.3764962,
      0.3786058,
      0.3806495,
      0.3825919,
      0.3844498,
      0.386217,
      0.3878873,
      0.3894205,
      0.3908244,
      0.3921065,
      0.3932621,
      0.3942685,
      0.3950954,
      0.395778,
      0.3963132,
      0.3966985,
      0.3968725,
      0.3968851,
      0.3967418,
      0.3964423,
      0.39645,
      0.3972847,
      0.3980183,
      0.398649,
      0.3991621,
      0.3995376,
      0.399805,
      0.3999639,
      0.4000143,
      0.3999187,
      0.399709,
      0.399393,
      0.3989717,
      0.3984299,
      0.3977625,
      0.398252,
      0.3986653,
      0.3989961,
      0.3992128,
      0.3993435,
      0.3996259,
      0.399779,
      0.3997684,
      0.3995861,
      0.3992572,
      0.3987788,
      0.3981378,
      0.397282,
      0.3962654,
      0.3958976,
      0.395874,
      0.3963234,
      0.3972833,
      0.398087,
      0.3987312,
      0.3991574,
      0.3993966,
      0.3994663,
      0.399365,
      0.399054,
      0.398532,
      0.3978386,
      0.3969749,
      0.3959246,
      0.394654,
      0.3946048,
      0.3954769,
      0.3962306,
      0.3968581,
      0.3972967,
      0.3975909,
      0.3977355,
      0.3977253,
      0.397512,
      0.3971027,
      0.3965196,
      0.3957593,
      0.3948029,
      0.393601,
      0.392212,
      0.3912862,
      0.3905814,
      0.3897509,
      0.3887924,
      0.3877038,
      0.3864335,
      0.3850178,
      0.3834662,
      0.3817782,
      0.37992,
      0.3778999,
      0.3757458,
      0.3734591,
      0.371025,
      0.3684249,
      0.3657025,
      0.3628609,
      0.3599021,
      0.3567869,
      0.3535692,
      0.3506218,
      0.3478519,
      0.3454672,
      0.3435605,
      0.3415967,
      0.3395634,
      0.3374622,
      0.3353063,
      0.3330961,
      0.330825,
      0.3284853,
      0.3260945,
      0.3236533,
      0.3211601,
      0.3185996,
      0.3159926,
      0.3133402,
      0.3106432,
      0.3078858,
      0.305174,
      0.3040739,
      0.3028608,
      0.3015458,
      0.3001384,
      0.2986366,
      0.2970123,
      0.2952678,
      0.2934221,
      0.2914744,
      0.2894042,
      0.2872027,
      0.2848986,
      0.2824925,
      0.2799725,
      0.2773197,
      0.2745704,
      0.2717265,
      0.2687849,
      0.2657191,
      0.2625699,
      0.2593401,
      0.2560329,
      0.2526217,
      0.2491448,
      0.2456065,
      0.2420106,
      0.238344,
      0.2346301,
      0.2308769,
      0.2271647,
      0.2252983,
      0.2233931,
      0.2214451,
      0.2194476,
      0.2174157,
      0.2153511,
      0.2132528,
      0.2111159,
      0.2089547,
      0.2067714,
      0.2045675,
      0.2023408,
      0.2001024,
      0.1978545,
      0.1955991,
      0.1933387,
      0.1910785,
      0.1888203,
      0.186566,
      0.1843213,
      0.1820861,
      0.1798614,
      0.177648,
      0.1754526,
      0.1732721,
      0.1711056,
      0.1689535,
      0.1668207,
      0.1647032,
      0.1625988,
      0.1605069,
      0.1584299,
      0.1563641,
      0.1543066,
      0.1522563,
      0.150213,
      0.1481735,
      0.1461355,
      0.1440979,
      0.1420584,
      0.1400143,
      0.137965,
      0.1359095,
      0.1338448,
      0.1317683,
      0.1296815,
      0.1275839,
      0.1254729,
      0.1233457,
      0.1212061,
      0.1190539,
      0.1168877,
      0.1147048,
      0.1125102,
      0.1103044,
      0.1080871,
      0.1058564,
      0.1036175,
      0.101371,
      0.09911772,
      0.09685737,
      0.09459387,
      0.0923282,
      0.09006136,
      0.08779567,
      0.08553272,
      0.08327355,
      0.08101919,
      0.07877446,
      0.07653872,
      0.07431267,
      0.0720973,
      0.06989928,
      0.06771662,
      0.06554926,
      0.0633981,
      0.06127105,
      0.05916582,
      0.05708112,
      0.05501784,
      0.05298464,
      0.05097984,
      0.04900061,
      0.04704779,
      0.04513039,
      0.04324817,
      0.04139638,
      0.03957582,
      0.03779537,
      0.03605698,
      0.03435356,
      0.03268583,
      0.03106204,
      0.02948686,
      0.02795053,
      0.02645362,
      0.02500321,
      0.02360699,
      0.02225241,
      0.0209398,
      0.01967452,
      0.01846737,
      0.0173031,
      0.01618172,
      0.01510659,
      0.01409126,
      0.01311823,
      0.0121872,
      0.01129942,
      0.01047053,
      0.009681556,
      0.008931899,
      0.008220964,
      0.00756536,
      0.006945798,
      0.006361416,
      0.005811401,
      0.005308551,
      0.004838057,
      0.004397629,
      0.003986341,
      0.003613473,
      0.003268346,
      0.00294777,
      0.002650801,
      0.002383748,
      0.002139419,
      0.00191425,
      0.00170736,
      0.001522745,
      0.001355924,
      0.001203399,
      0.001064411,
      0.000941288,
      0.0008314918,
      0.0007319013,
      0.0006419018,
      0.0005627157,
      0.0004930826,
      0.0004304221,
      0.0003742668,
      0.0003251682,
      0.0002826267,
      0.0002446466,
      0.0002108924,
      0.0001815488,
      0.0001565174,
      0.0001343445
    ),
    each = 2
  )

lmode.vline1.cat.x <- c(-0.01041169, -0.01041169)
lmode.vline1.cat.y <- c(0.0001, 0.4128646)

lmode.vline2.cat.x <- c(0.177655, 0.177655)
lmode.vline2.cat.y <- c(0.0001, 0.4315346)

lmo.emp <- data.frame(lmode.empcurve.x, lmode.empcurve.y)
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.x"] <- "xvalues"
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.y"] <- "yvalues"


# Plots ---------------------------------------------------------

#MAMBAC

mambac.plot.cat <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.cat.x,
                                        y = mambac.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = mambac.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = mambac.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Categorical comparison data",
          subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  scale_y_continuous(breaks=seq(round(mambac.y.range[1], digits = 1),
                                round(mambac.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

mambac.plot.dim <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.dim.x,
                                        y = mambac.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = mambac.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = mambac.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Dimensional comparison data", subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#MAXEIG

maxeig.plot.cat <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.cat.x,
                                        y = maxeig.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = maxeig.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = maxeig.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  scale_y_continuous(breaks=seq(round(maxeig.y.range[1], digits = 1),
                                round(maxeig.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

maxeig.plot.dim <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.dim.x,
                                        y = maxeig.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = maxeig.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = maxeig.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  ) 
#L-Mode

lmode.plot.cat <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.cat.x, y = lmode.polygon.cat.y), fill = "#0b5db5") +
  geom_line(aes(y = lmode.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = lmode.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  scale_y_continuous(breaks=seq(round(lmode.y.range[1], digits = 1),
                                round(lmode.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

lmode.plot.dim <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.dim.x, y = lmode.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = lmode.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = lmode.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#Grid

grid.title <- textGrob(expression(bold("Involuntariness subscales ("~bolditalic("a priori")~"base rate: .15 )")), gp = gpar(fontsize = 14, fontfamily = "Arial"))
grid.arrange(mambac.plot.cat, mambac.plot.dim, maxeig.plot.cat, maxeig.plot.dim, lmode.plot.cat, lmode.plot.dim,
             nrow = 3,
             top=grid.title)



# Involuntariness subscales; p = .10 --------------------------------------
# MAMBAC ------------------------------------------------------------------

mambac.empcurve.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)
mambac.empcurve.y <- c(0.5857005,0.5592266,0.553367,0.5591243,0.5524368,0.5480382,0.5391065,0.5334334,0.5227267,0.5118497,0.5073839,0.5049048,0.503873,0.5055384,0.5045905,0.5032134,0.5002561,0.4991239,0.5015369,0.5054869,0.5053019,0.5064008,0.5049068,0.5004818,0.4970019,0.4977254,0.4955773,0.4926132,0.4902931,0.489726,0.4932472,0.4941454,0.4984032,0.5023331,0.5101294,0.508052,0.5030973,0.504424,0.5069876,0.5104285,0.5101471,0.5107538,0.5121451,0.5266274,0.5341734,0.541844,0.5668245,0.5754629,0.5932539,0.6242576)
mambac.y.range <- c(0.3161692,0.9052683)

#Duplicate empirical values to allow the simulated polygon to be more smooth
mambac.empcurve.x <- rep(mambac.empcurve.x, each = 2)
mambac.empcurve.y <- rep(mambac.empcurve.y, each = 2)

mambac.polygon.cat.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1)
mambac.polygon.cat.y <- c(0.4625103,0.4591922,0.4564237,0.456781,0.4534946,0.4530184,0.4577304,0.4575526,0.4562612,0.4570183,0.4612685,0.4630935,0.4691182,0.4702917,0.4735449,0.4782086,0.480808,0.4865013,0.4923039,0.4981088,0.5040912,0.5129975,0.5189792,0.5261963,0.5315941,0.5384375,0.5466746,0.5485729,0.5548267,0.5628533,0.56679,0.5696269,0.5747191,0.5807082,0.5895201,0.600098,0.614252,0.6252172,0.6409627,0.6517165,0.6644035,0.6752172,0.6841609,0.6957163,0.70489,0.7152527,0.7319674,0.7534758,0.7671485,0.7822793,0.6865124,0.6839382,0.6800228,0.6679094,0.6495526,0.6360093,0.6353461,0.6280704,0.6199134,0.6126844,0.5993939,0.5849946,0.5702247,0.5577715,0.5425304,0.5325404,0.5236432,0.5162066,0.5135768,0.5058359,0.5020248,0.4971124,0.4914889,0.4876087,0.4820683,0.4759204,0.4692761,0.4648265,0.4549715,0.4508597,0.4464814,0.4432494,0.4359261,0.4302451,0.4274621,0.4230185,0.419004,0.4135928,0.4114904,0.4083301,0.407195,0.4069716,0.4050418,0.4052669,0.405154,0.4043337,0.4016213,0.3996454,0.3924466,0.3946057)

mambac.polygon.dim.x <- mambac.polygon.cat.x
mambac.polygon.dim.y <- c(0.493162,0.4889562,0.4976923,0.4954293,0.4978425,0.497183,0.4916271,0.4891756,0.4923678,0.4912122,0.4921248,0.4945415,0.4964147,0.4988683,0.5005357,0.5039046,0.507525,0.513869,0.5194021,0.5245597,0.5295462,0.537392,0.5388528,0.5429871,0.5467531,0.5502108,0.5547858,0.5589522,0.5613135,0.5667688,0.5668445,0.569062,0.5711126,0.5734754,0.5753305,0.5816312,0.5849537,0.588835,0.5956674,0.6046018,0.6098468,0.6182849,0.627831,0.6363212,0.6560621,0.6795252,0.6982587,0.7200437,0.7424476,0.7688834,0.6804433,0.6487507,0.6308011,0.6103769,0.5934862,0.5804102,0.5676649,0.5578622,0.5517915,0.5450123,0.5398493,0.5346023,0.5281584,0.5252093,0.5238759,0.5210219,0.5188647,0.5151404,0.5120377,0.5127234,0.5122085,0.5119465,0.509748,0.5068439,0.5032814,0.5000917,0.4957559,0.4900663,0.4866717,0.4792453,0.4742835,0.468922,0.4622374,0.4583639,0.4554223,0.4474695,0.44302,0.4388817,0.4366098,0.4337773,0.4369923,0.4369623,0.4361187,0.4343579,0.4360493,0.4411396,0.4376323,0.4388367,0.4373304,0.4391831)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line1.cat.y <- rep(c(0.333037,0.320633,0.3161692,0.3241729,0.3329037,0.328621,0.3280635,0.337069,0.3430821,0.3445405,0.3471847,0.3450875,0.3489954,0.3455027,0.3412552,0.3445163,0.3509594,0.3558592,0.3643286,0.370437,0.3785313,0.3891032,0.3890535,0.3919261,0.3902097,0.3923712,0.3949162,0.4005309,0.4037805,0.4071002,0.410802,0.4151641,0.4222961,0.4307083,0.4427172,0.4532943,0.4633224,0.4735201,0.4839049,0.4963825,0.5017286,0.5014896,0.5037583,0.5194047,0.5232567,0.5263005,0.5370793,0.5435236,0.5437916,0.5298414), each = 2)

mambac.line1.dim.y <- rep(c(0.3641631,0.3672368,0.3668586,0.376322,0.3837611,0.3838811,0.377725,0.3597011,0.3532761,0.3525738,0.3528853,0.3460557,0.3514152,0.3570383,0.3680451,0.3770489,0.381018,0.3868459,0.3939718,0.4020549,0.4063872,0.4127314,0.4162276,0.4218431,0.4290454,0.4310031,0.4312619,0.4325009,0.4362953,0.4394343,0.4472676,0.4427941,0.436286,0.4410047,0.4452296,0.4495023,0.4523796,0.4592748,0.4714485,0.4797113,0.489122,0.4958553,0.4934071,0.4940395,0.4997589,0.5182983,0.5225678,0.5216829,0.5373425,0.5450861), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line2.cat.y <- rep(c(0.5494726,0.5572922,0.5477741,0.5373346,0.5520786,0.5494349,0.5433814,0.5289843,0.5334075,0.5351227,0.5312928,0.5299741,0.5327349,0.5354307,0.5409429,0.5484733,0.5556066,0.5591902,0.5640029,0.5746813,0.586253,0.6057763,0.6189124,0.6320789,0.6439618,0.6562447,0.6617329,0.6672263,0.6718008,0.6721576,0.6683967,0.6681896,0.6706922,0.6739957,0.6807241,0.6916267,0.7070184,0.7156596,0.7221051,0.7375464,0.7518886,0.7519,0.754289,0.7678388,0.7804719,0.7912198,0.8190541,0.8373263,0.8656715,0.9052683), each = 2)

mambac.line2.dim.y <- rep(c(0.6058893,0.5877781,0.577196,0.5686434,0.5556931,0.5512696,0.5499435,0.5505164,0.5494857,0.5545638,0.5521723,0.5562086,0.5616548,0.5706754,0.583872,0.5923604,0.601343,0.6050586,0.6079637,0.6121536,0.6111488,0.6131383,0.6168384,0.6171888,0.618985,0.6226099,0.6234204,0.6272386,0.6266141,0.6316478,0.6357966,0.6378691,0.635217,0.6405596,0.6498651,0.6560125,0.6594685,0.6619394,0.6709402,0.6835459,0.6926401,0.7104101,0.7280574,0.7377675,0.7536458,0.7760726,0.7965557,0.8269678,0.8631891,0.8919756), each = 2)

mamb.emp <- data.frame(mambac.empcurve.x, mambac.empcurve.y)
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.x"] <- "xvalues"
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.y"] <- "yvalues"


# MAXEIG ------------------------------------------------------------------

maxeig.empcurve.x <- c(-1.220567,-1.159481,-1.106531,-1.059193,-1.007682,-0.9676817,-0.9228465,-0.8790472,-0.8377732,-0.8014703,-0.763786,-0.7277492,-0.6893742,-0.6520352,-0.6201997,-0.5899325,-0.5529389,-0.5132085,-0.4699934,-0.4260877,-0.3794577,-0.3239856,-0.2698157,-0.2151026,-0.1503212,-0.0862098,-0.01382554,0.04928242,0.1069129,0.1665648,0.2234418,0.2814481,0.3363178,0.3909897,0.4362839,0.4721325,0.5111764,0.5669777,0.6300344,0.6883068,0.7515653,0.815658,0.8800961,0.9434982,1.023205,1.102204,1.189964,1.275377,1.3676,1.494068)
maxeig.empcurve.y <- c(0.2134713,0.21761,0.2170736,0.2095368,0.2061814,0.205265,0.20829,0.2052118,0.2095524,0.2150303,0.217339,0.2199207,0.2220058,0.2225551,0.216687,0.2199306,0.2251497,0.2342846,0.2405336,0.23696,0.232924,0.2231354,0.2240907,0.2229414,0.2198765,0.2121363,0.2061732,0.2063665,0.2099113,0.2078928,0.1999824,0.1995743,0.1967098,0.1970207,0.1928227,0.1915862,0.1906288,0.1971627,0.1985072,0.211443,0.2161114,0.2228673,0.2227735,0.2243355,0.2365466,0.2483131,0.262388,0.2776868,0.2782508,0.2829619)
maxeig.y.range <- c(0.105936,0.4109276)

#Duplicate empirical values to allow the simulated polygon to be more smooth
maxeig.empcurve.x <- rep(maxeig.empcurve.x, each = 2)
maxeig.empcurve.y <- rep(maxeig.empcurve.y, each = 2)

maxeig.polygon.cat.x <- c(-1.220567,-1.159481,-1.106531,-1.059193,-1.007682,-0.9676817,-0.9228465,-0.8790472,-0.8377732,-0.8014703,-0.763786,-0.7277492,-0.6893742,-0.6520352,-0.6201997,-0.5899325,-0.5529389,-0.5132085,-0.4699934,-0.4260877,-0.3794577,-0.3239856,-0.2698157,-0.2151026,-0.1503212,-0.0862098,-0.01382554,0.04928242,0.1069129,0.1665648,0.2234418,0.2814481,0.3363178,0.3909897,0.4362839,0.4721325,0.5111764,0.5669777,0.6300344,0.6883068,0.7515653,0.815658,0.8800961,0.9434982,1.023205,1.102204,1.189964,1.275377,1.3676,1.494068,1.494068,1.3676,1.275377,1.189964,1.102204,1.023205,0.9434982,0.8800961,0.815658,0.7515653,0.6883068,0.6300344,0.5669777,0.5111764,0.4721325,0.4362839,0.3909897,0.3363178,0.2814481,0.2234418,0.1665648,0.1069129,0.04928242,-0.01382554,-0.0862098,-0.1503212,-0.2151026,-0.2698157,-0.3239856,-0.3794577,-0.4260877,-0.4699934,-0.5132085,-0.5529389,-0.5899325,-0.6201997,-0.6520352,-0.6893742,-0.7277492,-0.763786,-0.8014703,-0.8377732,-0.8790472,-0.9228465,-0.9676817,-1.007682,-1.059193,-1.106531,-1.159481,-1.220567)
maxeig.polygon.cat.y <- c(0.1773597,0.1777632,0.1787939,0.1771752,0.178462,0.177416,0.1758769,0.1763711,0.179147,0.1813762,0.1827776,0.18618,0.1877663,0.1908992,0.1945607,0.1967989,0.197869,0.2006143,0.1977498,0.2001453,0.2025901,0.2080545,0.2114346,0.2171715,0.2227896,0.2271048,0.2345184,0.2386853,0.2483892,0.2547581,0.2646701,0.2660967,0.2682261,0.268673,0.2704856,0.2742437,0.2778543,0.287558,0.2988555,0.3093052,0.3173196,0.323118,0.3268708,0.3300414,0.3314436,0.334623,0.3318688,0.3319143,0.3196361,0.3102501,0.258475,0.2714289,0.2782152,0.2794998,0.2822102,0.2788824,0.2776866,0.278456,0.2742115,0.268628,0.2601119,0.2503813,0.2402277,0.2335055,0.2295017,0.2294204,0.2302434,0.2280793,0.2263321,0.2233596,0.2173796,0.2123234,0.207224,0.2023366,0.1955874,0.1898804,0.1856412,0.1783159,0.1726098,0.169428,0.1700293,0.1676095,0.1685099,0.1675079,0.1669659,0.1632478,0.1620038,0.1610277,0.1581987,0.1544882,0.1525731,0.1528374,0.1530897,0.1535221,0.1504434,0.1491079,0.1471908,0.1488012,0.1475915,0.1448794)

maxeig.polygon.dim.x <- maxeig.polygon.cat.x
maxeig.polygon.dim.y <- c(0.216695,0.2182206,0.2225483,0.2258507,0.2299544,0.2329036,0.2304659,0.2307512,0.2309987,0.2336995,0.2333651,0.234137,0.2354737,0.2346609,0.2368898,0.2374444,0.2414913,0.2428047,0.2433248,0.2403379,0.242725,0.243204,0.2448,0.2484506,0.2516159,0.2511663,0.2469166,0.2435431,0.2440899,0.2408573,0.2398632,0.2390882,0.2425546,0.2423247,0.2436457,0.2434973,0.24096,0.2369225,0.2364895,0.2383716,0.2392116,0.2424028,0.2440617,0.2442676,0.248413,0.2520663,0.2543554,0.2571501,0.2513826,0.2530106,0.2009872,0.2007615,0.1980167,0.1952484,0.1950769,0.1959161,0.1942216,0.1937935,0.1957688,0.1951071,0.1970677,0.198884,0.1994125,0.2009394,0.1977229,0.2007489,0.2005127,0.2011895,0.2029744,0.2043804,0.2092691,0.2085311,0.2074703,0.2072877,0.2070348,0.2107915,0.2106026,0.2104018,0.2113241,0.2096713,0.2062968,0.2038428,0.2047875,0.2047278,0.1991557,0.201065,0.1960528,0.1910605,0.1899109,0.1900278,0.191128,0.1889503,0.1887426,0.1888364,0.1893789,0.1881706,0.1863484,0.1857124,0.1862595,0.1874354)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line1.cat.y <- rep(c(0.1061844,0.1110112,0.1113123,0.1134549,0.1109356,0.109208,0.105936,0.1106027,0.1148638,0.112821,0.1188889,0.1188375,0.1177382,0.1265852,0.1295595,0.1327001,0.1367399,0.1404128,0.1454233,0.1408723,0.1405502,0.1389506,0.1428678,0.1496879,0.1565296,0.1637647,0.1668233,0.1640073,0.1550122,0.1537112,0.1584215,0.1548916,0.1590308,0.1669233,0.1757687,0.1810782,0.1809053,0.1852188,0.1900316,0.1984541,0.2035579,0.2044706,0.2088379,0.2130747,0.2012626,0.2008896,0.1967756,0.1997946,0.1982887,0.1887714), each = 2)

maxeig.line1.dim.y <- rep(c(0.1458296,0.152188,0.1491302,0.1502089,0.1530044,0.1503485,0.1469352,0.1466534,0.1508663,0.1559802,0.1601934,0.1604175,0.164028,0.1622235,0.1624875,0.1652999,0.1696998,0.1642974,0.1614434,0.1573065,0.1560733,0.153359,0.1528302,0.1459316,0.1372934,0.1308058,0.1355194,0.139013,0.1520206,0.1549423,0.1568714,0.1566128,0.1576375,0.1594931,0.1539747,0.1559389,0.1608389,0.1657805,0.1691469,0.1600165,0.1593553,0.1532864,0.1527061,0.1502426,0.1431475,0.1305893,0.1303838,0.1409044,0.1271009,0.125351), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line2.cat.y <- rep(c(0.2315749,0.2160796,0.2062395,0.2110194,0.2162192,0.2176028,0.2235733,0.2323925,0.2313034,0.2339517,0.2447164,0.2491331,0.245745,0.2413522,0.2553624,0.2584379,0.2655138,0.265261,0.2622812,0.256011,0.2549573,0.2710989,0.2820301,0.2881355,0.2800625,0.2824301,0.2837031,0.2883863,0.2877082,0.2918805,0.2982225,0.3020131,0.3130014,0.3281245,0.3438892,0.3444424,0.3433503,0.3415393,0.3644453,0.3746826,0.3894853,0.3842032,0.3862926,0.3956761,0.4059104,0.4106244,0.4029214,0.4109276,0.3968027,0.3898262), each = 2)

maxeig.line2.dim.y <- rep(c(0.2697736,0.2683682,0.2668921,0.2623394,0.2613843,0.2613052,0.270377,0.2681675,0.2685048,0.2685931,0.2734635,0.2763702,0.2779966,0.2828591,0.2847735,0.2874378,0.2823681,0.294729,0.3059027,0.3131851,0.3198202,0.3181958,0.3245594,0.3278124,0.3274576,0.3276087,0.3227256,0.3068638,0.3136331,0.3189911,0.3175208,0.3237838,0.313099,0.2979696,0.2887652,0.3003555,0.3049906,0.2968088,0.2968223,0.2944535,0.2902041,0.2879733,0.2872826,0.2865867,0.295296,0.3036145,0.3197387,0.3274531,0.3346137,0.3409845), each = 2)

maxe.emp <- data.frame(maxeig.empcurve.x, maxeig.empcurve.y)
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.x"] <- "xvalues"
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.y"] <- "yvalues"

# L-Mode ------------------------------------------------------------------
lmode.empcurve.x <-
  c(
    -3.169932,
    -3.157394,
    -3.144857,
    -3.132319,
    -3.119781,
    -3.107243,
    -3.094706,
    -3.082168,
    -3.06963,
    -3.057092,
    -3.044554,
    -3.032017,
    -3.019479,
    -3.006941,
    -2.994403,
    -2.981866,
    -2.969328,
    -2.95679,
    -2.944252,
    -2.931714,
    -2.919177,
    -2.906639,
    -2.894101,
    -2.881563,
    -2.869025,
    -2.856488,
    -2.84395,
    -2.831412,
    -2.818874,
    -2.806337,
    -2.793799,
    -2.781261,
    -2.768723,
    -2.756185,
    -2.743648,
    -2.73111,
    -2.718572,
    -2.706034,
    -2.693497,
    -2.680959,
    -2.668421,
    -2.655883,
    -2.643345,
    -2.630808,
    -2.61827,
    -2.605732,
    -2.593194,
    -2.580657,
    -2.568119,
    -2.555581,
    -2.543043,
    -2.530505,
    -2.517968,
    -2.50543,
    -2.492892,
    -2.480354,
    -2.467817,
    -2.455279,
    -2.442741,
    -2.430203,
    -2.417665,
    -2.405128,
    -2.39259,
    -2.380052,
    -2.367514,
    -2.354977,
    -2.342439,
    -2.329901,
    -2.317363,
    -2.304825,
    -2.292288,
    -2.27975,
    -2.267212,
    -2.254674,
    -2.242136,
    -2.229599,
    -2.217061,
    -2.204523,
    -2.191985,
    -2.179448,
    -2.16691,
    -2.154372,
    -2.141834,
    -2.129296,
    -2.116759,
    -2.104221,
    -2.091683,
    -2.079145,
    -2.066608,
    -2.05407,
    -2.041532,
    -2.028994,
    -2.016456,
    -2.003919,
    -1.991381,
    -1.978843,
    -1.966305,
    -1.953768,
    -1.94123,
    -1.928692,
    -1.916154,
    -1.903616,
    -1.891079,
    -1.878541,
    -1.866003,
    -1.853465,
    -1.840928,
    -1.82839,
    -1.815852,
    -1.803314,
    -1.790776,
    -1.778239,
    -1.765701,
    -1.753163,
    -1.740625,
    -1.728088,
    -1.71555,
    -1.703012,
    -1.690474,
    -1.677936,
    -1.665399,
    -1.652861,
    -1.640323,
    -1.627785,
    -1.615248,
    -1.60271,
    -1.590172,
    -1.577634,
    -1.565096,
    -1.552559,
    -1.540021,
    -1.527483,
    -1.514945,
    -1.502407,
    -1.48987,
    -1.477332,
    -1.464794,
    -1.452256,
    -1.439719,
    -1.427181,
    -1.414643,
    -1.402105,
    -1.389567,
    -1.37703,
    -1.364492,
    -1.351954,
    -1.339416,
    -1.326879,
    -1.314341,
    -1.301803,
    -1.289265,
    -1.276727,
    -1.26419,
    -1.251652,
    -1.239114,
    -1.226576,
    -1.214039,
    -1.201501,
    -1.188963,
    -1.176425,
    -1.163887,
    -1.15135,
    -1.138812,
    -1.126274,
    -1.113736,
    -1.101199,
    -1.088661,
    -1.076123,
    -1.063585,
    -1.051047,
    -1.03851,
    -1.025972,
    -1.013434,
    -1.000896,
    -0.9883585,
    -0.9758207,
    -0.963283,
    -0.9507452,
    -0.9382074,
    -0.9256696,
    -0.9131318,
    -0.9005941,
    -0.8880563,
    -0.8755185,
    -0.8629807,
    -0.8504429,
    -0.8379052,
    -0.8253674,
    -0.8128296,
    -0.8002918,
    -0.787754,
    -0.7752163,
    -0.7626785,
    -0.7501407,
    -0.7376029,
    -0.7250651,
    -0.7125274,
    -0.6999896,
    -0.6874518,
    -0.674914,
    -0.6623762,
    -0.6498385,
    -0.6373007,
    -0.6247629,
    -0.6122251,
    -0.5996873,
    -0.5871496,
    -0.5746118,
    -0.562074,
    -0.5495362,
    -0.5369984,
    -0.5244607,
    -0.5119229,
    -0.4993851,
    -0.4868473,
    -0.4743095,
    -0.4617718,
    -0.449234,
    -0.4366962,
    -0.4241584,
    -0.4116206,
    -0.3990829,
    -0.3865451,
    -0.3740073,
    -0.3614695,
    -0.3489317,
    -0.336394,
    -0.3238562,
    -0.3113184,
    -0.2987806,
    -0.2862428,
    -0.2737051,
    -0.2611673,
    -0.2486295,
    -0.2360917,
    -0.2235539,
    -0.2110162,
    -0.1984784,
    -0.1859406,
    -0.1734028,
    -0.1608651,
    -0.1483273,
    -0.1357895,
    -0.1232517,
    -0.1107139,
    -0.09817615,
    -0.08563837,
    -0.07310059,
    -0.06056281,
    -0.04802503,
    -0.03548725,
    -0.02294947,
    -0.01041169,
    0.002126087,
    0.01466387,
    0.02720165,
    0.03973943,
    0.05227721,
    0.06481499,
    0.07735277,
    0.08989055,
    0.1024283,
    0.1149661,
    0.1275039,
    0.1400417,
    0.1525794,
    0.1651172,
    0.177655,
    0.1901928,
    0.2027306,
    0.2152683,
    0.2278061,
    0.2403439,
    0.2528817,
    0.2654195,
    0.2779572,
    0.290495,
    0.3030328,
    0.3155706,
    0.3281084,
    0.3406461,
    0.3531839,
    0.3657217,
    0.3782595,
    0.3907973,
    0.403335,
    0.4158728,
    0.4284106,
    0.4409484,
    0.4534862,
    0.4660239,
    0.4785617,
    0.4910995,
    0.5036373,
    0.5161751,
    0.5287128,
    0.5412506,
    0.5537884,
    0.5663262,
    0.578864,
    0.5914017,
    0.6039395,
    0.6164773,
    0.6290151,
    0.6415529,
    0.6540906,
    0.6666284,
    0.6791662,
    0.691704,
    0.7042418,
    0.7167795,
    0.7293173,
    0.7418551,
    0.7543929,
    0.7669307,
    0.7794684,
    0.7920062,
    0.804544,
    0.8170818,
    0.8296196,
    0.8421573,
    0.8546951,
    0.8672329,
    0.8797707,
    0.8923085,
    0.9048462,
    0.917384,
    0.9299218,
    0.9424596,
    0.9549974,
    0.9675351,
    0.9800729,
    0.9926107,
    1.005148,
    1.017686,
    1.030224,
    1.042762,
    1.0553,
    1.067837,
    1.080375,
    1.092913,
    1.105451,
    1.117988,
    1.130526,
    1.143064,
    1.155602,
    1.16814,
    1.180677,
    1.193215,
    1.205753,
    1.218291,
    1.230829,
    1.243366,
    1.255904,
    1.268442,
    1.28098,
    1.293517,
    1.306055,
    1.318593,
    1.331131,
    1.343669,
    1.356206,
    1.368744,
    1.381282,
    1.39382,
    1.406357,
    1.418895,
    1.431433,
    1.443971,
    1.456509,
    1.469046,
    1.481584,
    1.494122,
    1.50666,
    1.519197,
    1.531735,
    1.544273,
    1.556811,
    1.569349,
    1.581886,
    1.594424,
    1.606962,
    1.6195,
    1.632037,
    1.644575,
    1.657113,
    1.669651,
    1.682189,
    1.694726,
    1.707264,
    1.719802,
    1.73234,
    1.744877,
    1.757415,
    1.769953,
    1.782491,
    1.795029,
    1.807566,
    1.820104,
    1.832642,
    1.84518,
    1.857717,
    1.870255,
    1.882793,
    1.895331,
    1.907869,
    1.920406,
    1.932944,
    1.945482,
    1.95802,
    1.970558,
    1.983095,
    1.995633,
    2.008171,
    2.020709,
    2.033246,
    2.045784,
    2.058322,
    2.07086,
    2.083398,
    2.095935,
    2.108473,
    2.121011,
    2.133549,
    2.146086,
    2.158624,
    2.171162,
    2.1837,
    2.196238,
    2.208775,
    2.221313,
    2.233851,
    2.246389,
    2.258926,
    2.271464,
    2.284002,
    2.29654,
    2.309078,
    2.321615,
    2.334153,
    2.346691,
    2.359229,
    2.371766,
    2.384304,
    2.396842,
    2.40938,
    2.421918,
    2.434455,
    2.446993,
    2.459531,
    2.472069,
    2.484606,
    2.497144,
    2.509682,
    2.52222,
    2.534758,
    2.547295,
    2.559833,
    2.572371,
    2.584909,
    2.597447,
    2.609984,
    2.622522,
    2.63506,
    2.647598,
    2.660135,
    2.672673,
    2.685211,
    2.697749,
    2.710287,
    2.722824,
    2.735362,
    2.7479,
    2.760438,
    2.772975,
    2.785513,
    2.798051,
    2.810589,
    2.823127,
    2.835664,
    2.848202,
    2.86074,
    2.873278,
    2.885815,
    2.898353,
    2.910891,
    2.923429,
    2.935967,
    2.948504,
    2.961042,
    2.97358,
    2.986118,
    2.998655,
    3.011193,
    3.023731,
    3.036269,
    3.048807,
    3.061344,
    3.073882,
    3.08642,
    3.098958,
    3.111495,
    3.124033,
    3.136571,
    3.149109,
    3.161647,
    3.174184,
    3.186722,
    3.19926,
    3.211798,
    3.224335,
    3.236873
  )
lmode.empcurve.y <-
  c(
    0.0001035517,
    0.0001212279,
    0.0001419102,
    0.0001660371,
    0.0001934052,
    0.0002243068,
    0.0002593228,
    0.0003003875,
    0.0003465138,
    0.0003981087,
    0.0004555894,
    0.0005217832,
    0.0005961156,
    0.000678477,
    0.0007694046,
    0.0008711327,
    0.0009858003,
    0.001111663,
    0.001249365,
    0.001399611,
    0.001569196,
    0.001753633,
    0.001953636,
    0.002169919,
    0.002408131,
    0.002667833,
    0.002947065,
    0.00324656,
    0.003569407,
    0.003921681,
    0.004297435,
    0.00469737,
    0.005122181,
    0.005582483,
    0.006071379,
    0.006588087,
    0.007133229,
    0.00771366,
    0.008330815,
    0.008978969,
    0.009658645,
    0.01037189,
    0.01113033,
    0.01192239,
    0.01274846,
    0.01360893,
    0.01451506,
    0.01546062,
    0.01644189,
    0.01745906,
    0.01851765,
    0.01962235,
    0.02076325,
    0.02194026,
    0.02315325,
    0.02441632,
    0.02571475,
    0.02704757,
    0.02841424,
    0.02982197,
    0.03126655,
    0.03274129,
    0.03424511,
    0.03577912,
    0.03734698,
    0.03893793,
    0.04055037,
    0.04218264,
    0.04383787,
    0.04550788,
    0.04718954,
    0.04888092,
    0.05058075,
    0.05228517,
    0.05399069,
    0.05569545,
    0.05739748,
    0.05909188,
    0.06077832,
    0.06245559,
    0.06412251,
    0.06577427,
    0.06741152,
    0.0690356,
    0.0706464,
    0.07224229,
    0.07382221,
    0.07539099,
    0.07694973,
    0.07849966,
    0.0800409,
    0.08157897,
    0.08311618,
    0.08465467,
    0.08619873,
    0.08775316,
    0.08931964,
    0.0909007,
    0.0925004,
    0.09412915,
    0.09578306,
    0.09746417,
    0.09917445,
    0.1009272,
    0.1027169,
    0.1045417,
    0.1064022,
    0.1083052,
    0.1102529,
    0.1122353,
    0.1142514,
    0.1163002,
    0.1183898,
    0.1205042,
    0.1226403,
    0.1247952,
    0.1269672,
    0.1291469,
    0.131328,
    0.1335058,
    0.1356738,
    0.1378195,
    0.1399405,
    0.1420318,
    0.1440883,
    0.1460857,
    0.1480296,
    0.1499173,
    0.1517443,
    0.1534905,
    0.1551489,
    0.1567298,
    0.1582302,
    0.1596426,
    0.1609365,
    0.1621411,
    0.1632559,
    0.1642804,
    0.1651862,
    0.1659944,
    0.1667162,
    0.1673536,
    0.1678972,
    0.1683455,
    0.1687242,
    0.1690378,
    0.169291,
    0.1694715,
    0.1696108,
    0.1697153,
    0.1697914,
    0.1698439,
    0.1698885,
    0.1699354,
    0.1699917,
    0.1700677,
    0.1701834,
    0.1703401,
    0.1705445,
    0.1708031,
    0.1711496,
    0.1715754,
    0.1720818,
    0.172674,
    0.1733767,
    0.1742006,
    0.1751283,
    0.1761627,
    0.1773112,
    0.1786152,
    0.1800338,
    0.1815673,
    0.1832159,
    0.1850135,
    0.1869368,
    0.1889703,
    0.1911119,
    0.1933734,
    0.1957624,
    0.1982458,
    0.2008198,
    0.2034804,
    0.2062519,
    0.2090958,
    0.2120059,
    0.2149771,
    0.2180157,
    0.2211077,
    0.2242385,
    0.2274034,
    0.2305988,
    0.2338213,
    0.2370568,
    0.2403012,
    0.2435503,
    0.2467977,
    0.2500373,
    0.2532664,
    0.2564822,
    0.2596785,
    0.2628502,
    0.266,
    0.2691268,
    0.2722291,
    0.2752969,
    0.2783401,
    0.2813593,
    0.2843549,
    0.2873222,
    0.2902667,
    0.2931933,
    0.2961034,
    0.2989976,
    0.3018777,
    0.3047499,
    0.3076164,
    0.3104791,
    0.3133411,
    0.3162059,
    0.3190751,
    0.3219503,
    0.3248352,
    0.3277319,
    0.3306395,
    0.3335587,
    0.3364906,
    0.339439,
    0.3423991,
    0.3453703,
    0.3483518,
    0.3513451,
    0.3543455,
    0.3573505,
    0.3603584,
    0.3633668,
    0.366371,
    0.3693685,
    0.3723567,
    0.3753328,
    0.3782854,
    0.3812163,
    0.3841224,
    0.3870005,
    0.3898372,
    0.3926295,
    0.3953788,
    0.3980814,
    0.4007275,
    0.4032978,
    0.4058042,
    0.4082424,
    0.4106081,
    0.4128646,
    0.4150291,
    0.4171006,
    0.4190746,
    0.4209222,
    0.4226331,
    0.4242241,
    0.4256901,
    0.4270191,
    0.4281575,
    0.429149,
    0.4299889,
    0.4306726,
    0.431143,
    0.4314255,
    0.4315346,
    0.4314672,
    0.4311926,
    0.430685,
    0.4299918,
    0.4291122,
    0.4280456,
    0.4267156,
    0.4251993,
    0.4235004,
    0.4216209,
    0.4195203,
    0.4172209,
    0.4147568,
    0.4121329,
    0.4093407,
    0.4063574,
    0.4032398,
    0.3999947,
    0.3966288,
    0.3931151,
    0.3894983,
    0.3857934,
    0.3820079,
    0.3781384,
    0.3741986,
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lmode.y.range <- c(3.058618e-05,0.4328031)

lmode.empcurve.x <- rep(lmode.empcurve.x, each = 2)
lmode.empcurve.y <- rep(lmode.empcurve.y, each = 2)

lmode.polygon.cat.x <-
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                         lmode.polygon.cat.y <-
                           c(
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lmode.polygon.dim.x <- lmode.polygon.cat.x
lmode.polygon.dim.y <-
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    0.001885125,
    0.001691707,
    0.001527178,
    0.001374861,0.001235667,0.001107169,0.0009839523,0.0008717214,0.0007731017,0.0006836251,0.0006049918,0.0005344144,0.0004713291,0.0004144254,0.000363287,0.0003184118,0.0002786014,0.000242854,0.0002108809,0.0001830085,0.0001587822,0.0001372077,0.0001180778,0.0001013358,8.726452e-05,7.489875e-05,6.408978e-05,5.461832e-05,4.666686e-05)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line1.cat.y <-
  rep(
    c(
      3.127718e-05,
      3.627454e-05,
      4.211681e-05,
      4.869391e-05,
      5.606531e-05,
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      0.0001100753,
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      0.0007287306,
      0.00080022,
      0.0008764859,
      0.00095768,
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      0.001138318,
      0.001238088,
      0.001343665,
      0.001455206,
      0.001575641,
      0.001702869,
      0.001836833,
      0.001977708,
      0.00212824,
      0.002287208,
      0.002453966,
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      0.002813934,
      0.003009621,
      0.003214372,
      0.003423418,
      0.003630618,
      0.003847291,
      0.004072966,
      0.004306507,
      0.004548096,
      0.004799751,
      0.005062379,
      0.005334156,
      0.005615375,
      0.005907739,
      0.006214012,
      0.006531383,
      0.00686027,
      0.007201859,
      0.007561501,
      0.007934891,
      0.008322566,
      0.008725064,
      0.009150509,
      0.009593187,
      0.01005345,
      0.01053192,
      0.01103678,
      0.0115639,
      0.01211215,
      0.01268214,
      0.01328153,
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      0.01456031,
      0.01523703,
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      0.1273002,
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      0.1319666,
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      0.1352337,
      0.1369232,
      0.1386544,
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      0.1422972,
      0.1442068,
      0.1461768,
      0.1482199,
      0.1503536,
      0.1525615,
      0.1548461,
      0.15721,
      0.1596935,
      0.1622639,
      0.1649231,
      0.1676726,
      0.1705418,
      0.1735176,
      0.1765879,
      0.1797528,
      0.183028,
      0.186422,
      0.1897997,
      0.1913807,
      0.1930151,
      0.1947206,
      0.1964778,
      0.198287,
      0.20015,
      0.2020863,
      0.2040719,
      0.2061055,
      0.2081859,
      0.2103309,
      0.212516,
      0.2147391,
      0.2169981,
      0.2193026,
      0.2214914,
      0.2229026,
      0.2243507,
      0.225838,
      0.2273863,
      0.2289825,
      0.230628,
      0.2323247,
      0.2340906,
      0.235923,
      0.2378154,
      0.2397694,
      0.241796,
      0.2439086,
      0.2460898,
      0.2483411,
      0.2506636,
      0.2530909,
      0.2555928,
      0.2581699,
      0.2608228,
      0.2635743,
      0.2664123,
      0.2693259,
      0.2723142,
      0.2753878,
      0.2781655,
      0.2790882,
      0.2800456,
      0.2810345,
      0.2820571,
      0.2831232,
      0.2842402,
      0.2853991,
      0.286601,
      0.2878532,
      0.2891665,
      0.290526,
      0.2919317,
      0.2933876,
      0.2949069,
      0.2964709,
      0.2980785,
      0.2997301,
      0.3014402,
      0.303188,
      0.3049719,
      0.3067904,
      0.3086538,
      0.3105452,
      0.3124615,
      0.3144006,
      0.3163661,
      0.3183005,
      0.3187584,
      0.3192551,
      0.3198023,
      0.3203872,
      0.3210044,
      0.321652,
      0.3223354,
      0.3230462,
      0.3237775,
      0.3245269,
      0.3252945,
      0.3260745,
      0.326861,
      0.3272773,
      0.3257493,
      0.3227932,
      0.3198091,
      0.3168005,
      0.3137703,
      0.310719,
      0.307659,
      0.3045938,
      0.3015269,
      0.2984658,
      0.2954161,
      0.292381,
      0.2893638,
      0.2863765,
      0.2834231,
      0.2805031,
      0.2776195,
      0.2747838,
      0.2720056,
      0.2692764,
      0.2665985,
      0.2639792,
      0.2614378,
      0.2589558,
      0.2565343,
      0.2541742,
      0.2519042,
      0.2496973,
      0.2475525,
      0.2454694,
      0.2434672,
      0.241529,
      0.2396465,
      0.2378179,
      0.2360524,
      0.2343426,
      0.2326751,
      0.231047,
      0.2294598,
      0.2279113,
      0.2263875,
      0.2248849,
      0.2234009,
      0.2219331,
      0.2204714,
      0.2190128,
      0.2175541,
      0.2160887,
      0.2133634,
      0.2104826,
      0.2077121,
      0.2044983,
      0.2012515,
      0.1980596,
      0.1949409,
      0.1918889,
      0.1889095,
      0.1860083,
      0.1832302,
      0.180547,
      0.1779624,
      0.17548,
      0.1731313,
      0.1709118,
      0.1688052,
      0.1668125,
      0.1649447,
      0.1632296,
      0.161628,
      0.1601383,
      0.158759,
      0.1575226,
      0.1563956,
      0.1553662,
      0.1544306,
      0.1535992,
      0.1528682,
      0.1522113,
      0.1516235,
      0.1508548,
      0.1491686,
      0.1472705,
      0.14484,
      0.1424958,
      0.140239,
      0.1381038,
      0.1360655,
      0.1341165,
      0.1322562,
      0.130507,
      0.1288587,
      0.1272934,
      0.125809,
      0.1244157,
      0.1231167,
      0.1218866,
      0.1207225,
      0.1196248,
      0.1186049,
      0.1176354,
      0.1167126,
      0.115833,
      0.1150056,
      0.1142099,
      0.1134411,
      0.112696,
      0.1119752,
      0.1112692,
      0.1105729,
      0.1098834,
      0.1091982,
      0.1085122,
      0.1078228,
      0.1071284,
      0.1064261,
      0.1057113,
      0.1049853,
      0.1042474,
      0.1034967,
      0.1027263,
      0.1019417,
      0.1006006,
      0.09873435,
      0.09687985,
      0.095039,
      0.09321364,
      0.09141231,
      0.08963331,
      0.0878758,
      0.08614062,
      0.08443311,
      0.08275505,
      0.08097322,
      0.07851525,
      0.07608756,
      0.07369355,
      0.07133649,
      0.06903718,
      0.06678547,
      0.06458192,
      0.06242839,
      0.06033847,
      0.05831346,
      0.05634351,
      0.05442905,
      0.05257342,
      0.05079359,
      0.04906861,
      0.04739774,
      0.04578015,
      0.04423019,
      0.04273522,
      0.04128809,
      0.03988735,
      0.03853744,
      0.03724062,
      0.03598305,
      0.0347631,
      0.03357913,
      0.03244172,
      0.03133568,
      0.03025894,
      0.02921015,
      0.02802342,
      0.02650803,
      0.02505084,
      0.02367534,
      0.0223567,
      0.02109396,
      0.01988645,
      0.0187478,
      0.01766982,
      0.01664325,
      0.01566711,
      0.0147463,
      0.01388694,
      0.01307304,
      0.01230338,
      0.01157671,
      0.01090733,
      0.01027728,
      0.009684296,
      0.009127002,
      0.008612021,
      0.008133595,
      0.007684602,
      0.007263654,
      0.006871971,
      0.006511956,
      0.006173928,
      0.005856611,
      0.005558742,
      0.00528505,
      0.005027414,
      0.004784106,
      0.004554099,
      0.004338875,
      0.004135991,
      0.003942468,
      0.003757576,
      0.003581235,
      0.003413961,
      0.003252684,
      0.003096973,
      0.002946419,
      0.002802173,
      0.002662308,
      0.002526377,
      0.002394206,
      0.0022664,
      0.002142709,
      0.002022373,
      0.001905365,
      0.001791918,
      0.001682967,
      0.001577384,
      0.001475203,
      0.001376456,
      0.001282439,
      0.001192235,
      0.001104882,
      0.00101766,
      0.0009351758,
      0.0008573087,
      0.0007839727,
      0.0007168024,
      0.0006537,
      0.0005945462,
      0.0005392219,
      0.0004888108,
      0.00044214,
      0.0003987406,
      0.0003584914,
      0.000321957,
      0.0002887287,
      0.0002580958,
      0.0002299412,
      0.0002044575,
      0.0001817465,
      0.0001609958,
      0.0001421006,
      0.0001250221,
      0.0001101464,
      9.667646e-05,
      8.452554e-05,
      7.360815e-05,
      6.421245e-05,
      5.584098e-05,
      4.83594e-05,
      4.17025e-05,
      3.583544e-05,
      3.063061e-05
    ),
    each = 2
  )

lmode.line1.dim.y <-
  rep(
    c(
      3.291719e-05,
      3.881437e-05,
      4.561939e-05,
      5.337762e-05,
      6.218083e-05,
      7.236113e-05,
      8.365042e-05,
      9.679173e-05,
      0.0001114821,
      0.0001278883,
      0.000146541,
      0.0001680134,
      0.0001915433,
      0.0002173099,
      0.0002470622,
      0.0002799409,
      0.0003161524,
      0.0003559058,
      0.00040117,
      0.0004510628,
      0.0005056215,
      0.0005651103,
      0.0006316764,
      0.0007049884,
      0.0007846102,
      0.0008708623,
      0.0009658844,
      0.001070388,
      0.001183157,
      0.001304565,
      0.00143648,
      0.001581293,
      0.001736622,
      0.001902894,
      0.002081366,
      0.002276874,
      0.002485427,
      0.002707497,
      0.00294356,
      0.003201089,
      0.003474677,
      0.003764605,
      0.00407139,
      0.004402279,
      0.004753759,
      0.005124626,
      0.005515434,
      0.005932764,
      0.006375934,
      0.006841734,
      0.007330749,
      0.007848397,
      0.008397852,
      0.008973331,
      0.009575442,
      0.01020789,
      0.01087879,
      0.01157917,
      0.01230966,
      0.01307167,
      0.01377679,
      0.01443808,
      0.01512512,
      0.01584618,
      0.01659298,
      0.01736579,
      0.01816482,
      0.01899844,
      0.0198611,
      0.02074973,
      0.02166398,
      0.02260692,
      0.02352237,
      0.02425645,
      0.02500109,
      0.02575682,
      0.02652484,
      0.02731051,
      0.0281104,
      0.02892542,
      0.02975654,
      0.03061089,
      0.03148718,
      0.03238482,
      0.03330514,
      0.03425362,
      0.03523651,
      0.03624882,
      0.03729219,
      0.03836826,
      0.03949446,
      0.04065949,
      0.04186461,
      0.04311144,
      0.04441322,
      0.04576935,
      0.04717363,
      0.04862728,
      0.05013618,
      0.0512709,
      0.05245222,
      0.05367512,
      0.05494217,
      0.05625591,
      0.05763916,
      0.05908232,
      0.06058353,
      0.06214509,
      0.06378695,
      0.06550855,
      0.06729976,
      0.06911941,
      0.07066606,
      0.07226802,
      0.07392782,
      0.07565698,
      0.07746874,
      0.07934803,
      0.08129658,
      0.08331601,
      0.08543695,
      0.08729305,
      0.08878219,
      0.09034416,
      0.09197967,
      0.09368032,
      0.0954485,
      0.09730157,
      0.09924911,
      0.1012744,
      0.1033794,
      0.1055766,
      0.1074684,
      0.1091969,
      0.1110014,
      0.112883,
      0.1148691,
      0.1169406,
      0.1190895,
      0.121315,
      0.1236316,
      0.1260365,
      0.1285105,
      0.1310511,
      0.1336603,
      0.1363474,
      0.1390859,
      0.1418718,
      0.1447009,
      0.1475793,
      0.1504857,
      0.1534134,
      0.1563572,
      0.1579841,
      0.1595992,
      0.1612743,
      0.163008,
      0.1648006,
      0.1666693,
      0.1686059,
      0.1706006,
      0.1726525,
      0.1747697,
      0.1769547,
      0.1791906,
      0.1814752,
      0.1838085,
      0.1862005,
      0.18863,
      0.1910942,
      0.1935901,
      0.1961224,
      0.1986769,
      0.2012483,
      0.2033437,
      0.2043621,
      0.2054441,
      0.2065906,
      0.2078022,
      0.2091114,
      0.2104867,
      0.2119274,
      0.2134331,
      0.2150302,
      0.2166907,
      0.2184106,
      0.220188,
      0.2220414,
      0.2239484,
      0.2259021,
      0.2278999,
      0.2299512,
      0.2320399,
      0.2332196,
      0.2343642,
      0.2355591,
      0.2368288,
      0.238177,
      0.2395993,
      0.2411005,
      0.2426988,
      0.2444146,
      0.2462267,
      0.2481379,
      0.2501531,
      0.2523168,
      0.2545873,
      0.2567849,
      0.2564093,
      0.2560954,
      0.2558625,
      0.2556936,
      0.2555911,
      0.2555572,
      0.2556276,
      0.2557748,
      0.2560004,
      0.2563065,
      0.2567238,
      0.2572386,
      0.2578428,
      0.2585384,
      0.2593482,
      0.2602769,
      0.2613046,
      0.2624325,
      0.2636732,
      0.2650528,
      0.2665376,
      0.268128,
      0.2698247,
      0.2716747,
      0.2736312,
      0.2756932,
      0.2778599,
      0.2801635,
      0.2825789,
      0.285092,
      0.2877007,
      0.2904216,
      0.2932486,
      0.2961575,
      0.2991442,
      0.3022123,
      0.3043111,
      0.3038523,
      0.303454,
      0.3031188,
      0.3028796,
      0.3027119,
      0.3026161,
      0.3025935,
      0.3026707,
      0.3028335,
      0.3030733,
      0.3033905,
      0.3038025,
      0.3043089,
      0.3048917,
      0.3055503,
      0.3062927,
      0.3071317,
      0.3080415,
      0.3090204,
      0.3085876,
      0.3067027,
      0.3048402,
      0.3030029,
      0.3011939,
      0.2994323,
      0.2977098,
      0.2960276,
      0.2943882,
      0.2928106,
      0.2912877,
      0.2898156,
      0.2880994,
      0.2862317,
      0.2844972,
      0.2829217,
      0.2814689,
      0.2801378,
      0.2789272,
      0.2774266,
      0.2753143,
      0.2732569,
      0.2712538,
      0.2693135,
      0.2674363,
      0.2656079,
      0.2638261,
      0.2620886,
      0.260407,
      0.2587595,
      0.2571423,
      0.2555518,
      0.2539868,
      0.2524375,
      0.2508951,
      0.2493549,
      0.2478111,
      0.2462508,
      0.24467,
      0.2423811,
      0.2393722,
      0.23642,
      0.233539,
      0.2307204,
      0.2279677,
      0.2252838,
      0.2226995,
      0.2201925,
      0.2177606,
      0.2154041,
      0.2131362,
      0.2109569,
      0.2088475,
      0.2063998,
      0.2034819,
      0.2006072,
      0.1977746,
      0.1949961,
      0.1922578,
      0.1895551,
      0.1868863,
      0.184256,
      0.1816606,
      0.1790915,
      0.1765472,
      0.1740279,
      0.171536,
      0.1690623,
      0.1660928,
      0.1626223,
      0.159163,
      0.1557206,
      0.1523092,
      0.1489363,
      0.1456025,
      0.1423121,
      0.1390733,
      0.1359061,
      0.1327969,
      0.1297477,
      0.1267606,
      0.1238571,
      0.1210259,
      0.1182601,
      0.1155595,
      0.1129318,
      0.1103852,
      0.1078996,
      0.1054735,
      0.103105,
      0.1008105,
      0.09856985,
      0.09637782,
      0.09423228,
      0.09213814,
      0.09009367,
      0.08765807,
      0.08503704,
      0.08250166,
      0.08004542,
      0.07766772,
      0.07538286,
      0.07319131,
      0.07107448,
      0.06903131,
      0.06706384,
      0.06519362,
      0.06339186,
      0.06165726,
      0.05998852,
      0.05840364,
      0.05688688,
      0.05542986,
      0.05403118,
      0.0526981,
      0.0514332,
      0.05022018,
      0.04905758,
      0.04794433,
      0.04689675,
      0.04589306,
      0.04493179,
      0.04401149,
      0.0431408,
      0.04231166,
      0.04151701,
      0.04075542,
      0.04002909,
      0.03934023,
      0.03865696,
      0.03765181,
      0.03668793,
      0.03542131,
      0.03402115,
      0.03266485,
      0.0313516,
      0.03008053,
      0.02886239,
      0.02768817,
      0.02655193,
      0.02545267,
      0.02439404,
      0.02337926,
      0.02239729,
      0.02144725,
      0.02052829,
      0.01965076,
      0.01880254,
      0.0179822,
      0.01718911,
      0.01642856,
      0.01569849,
      0.01499349,
      0.01431317,
      0.01365873,
      0.01303638,
      0.01243732,
      0.0118613,
      0.01130807,
      0.01078452,
      0.01028512,
      0.009807504,
      0.009351417,
      0.008919956,
      0.008514589,
      0.008129514,
      0.00755099,
      0.007005736,
      0.006506638,
      0.006051895,
      0.005639674,
      0.005281321,
      0.004960561,
      0.004673829,
      0.004419139,
      0.004199129,
      0.004011245,
      0.00384684,
      0.003704027,
      0.00358094,
      0.003481196,
      0.003395494,
      0.003322049,
      0.003259303,
      0.003207054,
      0.003162518,
      0.003122773,
      0.003086683,
      0.003053174,
      0.003020969,
      0.002988363,
      0.00295468,
      0.002919285,
      0.002870099,
      0.002801396,
      0.002731242,
      0.002659458,
      0.002585728,
      0.002509419,
      0.002431229,
      0.002351223,
      0.002269481,
      0.002185609,
      0.002100468,
      0.002014314,
      0.001927349,
      0.001839765,
      0.00175209,
      0.001664637,
      0.001577634,
      0.001491491,
      0.001406799,
      0.001323545,
      0.001241918,
      0.00116218,
      0.001085405,
      0.00101098,
      0.0009390182,
      0.0008696277,
      0.0008039069,
      0.0007412511,
      0.0006814591,
      0.000624559,
      0.0005712428,
      0.0005214275,
      0.000474474,
      0.0004303463,
      0.0003892966,
      0.0003518022,
      0.0003168729,
      0.0002844334,
      0.0002544064,
      0.000227611,
      0.0002029499,
      0.0001803045,
      0.0001595843,
      0.0001411931,
      0.0001246445,
      0.0001096119,
      9.600919e-05,
      8.396622e-05,
      7.34e-05,
      6.390023e-05,
      5.53954e-05,
      4.786441e-05,
      4.137746e-05,
      3.567189e-05,
      3.058618e-05
    ),
    each = 2
  )

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line2.cat.y <-
  rep(
    c(
      0.0002296568,
      0.0002671915,
      0.0003109315,
      0.0003602898,
      0.0004157294,
      0.0004790778,
      0.0005524996,
      0.0006346269,
      0.0007261045,
      0.0008289932,
      0.000947497,
      0.00107888,
      0.001223984,
      0.001384789,
      0.001568683,
      0.001770745,
      0.001992,
      0.002233824,
      0.002508169,
      0.002806912,
      0.0031312,
      0.003482181,
      0.00387453,
      0.004299092,
      0.004755925,
      0.005246178,
      0.005785299,
      0.006365227,
      0.006983728,
      0.007641781,
      0.008354362,
      0.009115656,
      0.009920362,
      0.01076909,
      0.01167498,
      0.01263532,
      0.01364134,
      0.01469308,
      0.0158006,
      0.01696459,
      0.01817296,
      0.01942506,
      0.02072714,
      0.02208256,
      0.02347695,
      0.02490894,
      0.02638089,
      0.0278972,
      0.02944302,
      0.03101635,
      0.03261646,
      0.03424621,
      0.03589281,
      0.03755384,
      0.03922692,
      0.04091056,
      0.04259668,
      0.04428279,
      0.0459664,
      0.04764011,
      0.04930196,
      0.05095007,
      0.0525823,
      0.05418791,
      0.05576856,
      0.05732462,
      0.05885463,
      0.0603475,
      0.06180595,
      0.06323366,
      0.06463014,
      0.06598643,
      0.06730469,
      0.06859195,
      0.06984879,
      0.07106995,
      0.07225684,
      0.07341862,
      0.0745569,
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  )

lmode.line2.dim.y <-
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      0.0234546,
      0.02209301,
      0.02077466,
      0.01949553,
      0.01825659,
      0.01707063,
      0.01593554,
      0.01484358,
      0.01379505,
      0.01280006,
      0.0118596,
      0.01096255,
      0.01010863,
      0.009304668,
      0.008554966,
      0.007845923,
      0.00717681,
      0.00655127,
      0.005976354,
      0.005437196,
      0.004932797,
      0.004464168,
      0.00404011,
      0.003645749,
      0.003279993,
      0.002941997,
      0.002641183,
      0.002363752,
      0.00210865,
      0.001874828,
      0.001668778,
      0.001481078,
      0.001309957,
      0.001154497,
      0.001018525,
      0.0008964062,
      0.0007860131,
      0.0006866068,
      0.0006002401,
      0.000523841,
      0.0004553544,
      0.0003942237,
      0.0003414211,
      0.0002954632,
      0.0002546046,
      0.0002184512,
      0.0001873792
    ),
    each = 2
  )

lmode.vline1.cat.x <- c(-0.01041169,-0.01041169)
lmode.vline1.cat.y <- c(0.0001,0.4128646)

lmode.vline2.cat.x <- c(0.177655,0.177655)
lmode.vline2.cat.y <- c(0.0001,0.4315346)

lmo.emp <- data.frame(lmode.empcurve.x, lmode.empcurve.y)
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.x"] <- "xvalues"
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.y"] <- "yvalues"




# Plots ---------------------------------------------------------

#MAMBAC

mambac.plot.cat <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.cat.x,
                                        y = mambac.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = mambac.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = mambac.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Categorical comparison data",
          subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  scale_y_continuous(breaks=seq(round(mambac.y.range[1], digits = 1),
                                round(mambac.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

mambac.plot.dim <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.dim.x,
                                        y = mambac.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = mambac.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = mambac.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Dimensional comparison data", subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#MAXEIG

maxeig.plot.cat <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.cat.x,
                                        y = maxeig.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = maxeig.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = maxeig.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  scale_y_continuous(breaks=seq(round(maxeig.y.range[1], digits = 1),
                                round(maxeig.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

maxeig.plot.dim <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.dim.x,
                                        y = maxeig.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = maxeig.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = maxeig.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  ) 
#L-Mode

lmode.plot.cat <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.cat.x, y = lmode.polygon.cat.y), fill = "#0b5db5") +
  geom_line(aes(y = lmode.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = lmode.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  scale_y_continuous(breaks=seq(round(lmode.y.range[1], digits = 1),
                                round(lmode.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

lmode.plot.dim <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.dim.x, y = lmode.polygon.dim.y), fill = "#5aa007") +
  geom_line(aes(y = lmode.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = lmode.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#Grid
grid.title <- textGrob(expression(bold("Involuntariness subscales ("~bolditalic("a priori")~"base rate: .10 )")), gp = gpar(fontsize = 14, fontfamily = "Arial"))
grid.arrange(mambac.plot.cat, mambac.plot.dim, maxeig.plot.cat, maxeig.plot.dim, lmode.plot.cat, lmode.plot.dim,
             nrow = 3,
             top=grid.title)



# Suggestibility subscales; p = .15 --------------------------------------
# MAMBAC ------------------------------------------------------------------

mambac.empcurve.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)
mambac.empcurve.y <- c(0.2086321,0.1969561,0.1959284,0.2040581,0.1997921,0.1999254,0.1970592,0.2016653,0.2070885,0.209458,0.2101162,0.210366,0.215851,0.213654,0.2057966,0.2039176,0.2006221,0.1994254,0.2016481,0.2013723,0.1986397,0.200449,0.2045067,0.2104505,0.2103934,0.2125541,0.2141681,0.2177834,0.2208925,0.2189793,0.22373,0.2286849,0.2304583,0.2346496,0.2391331,0.2420171,0.2468049,0.2456222,0.2496357,0.2540778,0.257835,0.2647294,0.2795737,0.2908588,0.3153515,0.3381021,0.3429644,0.3645467,0.3939522,0.3860164)
mambac.y.range <- c(0.05482831,0.5263492)

#Duplicate empirical values to allow the simulated polygon to be more smooth
mambac.empcurve.x <- rep(mambac.empcurve.x, each = 2)
mambac.empcurve.y <- rep(mambac.empcurve.y, each = 2)

mambac.polygon.cat.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1)
mambac.polygon.cat.y <- c(0.1670775,0.1726059,0.1711128,0.1762987,0.1765069,0.1781128,0.1791975,0.1815766,0.1852622,0.1862051,0.1889449,0.192497,0.1953231,0.1974271,0.1992812,0.2011743,0.2028513,0.2032341,0.2063855,0.2096819,0.2138127,0.2164439,0.219639,0.2231114,0.2285149,0.2336226,0.2423893,0.2493064,0.2566661,0.2643726,0.2728432,0.2824955,0.2937723,0.3038041,0.3106418,0.3139841,0.3174062,0.317446,0.3193666,0.3261309,0.3270297,0.3354829,0.3462096,0.3598042,0.3776976,0.3954731,0.4091647,0.4199657,0.4303766,0.4342306,0.3597207,0.3646506,0.3580118,0.3426642,0.3322842,0.3179301,0.3002798,0.2889048,0.2753439,0.2713937,0.2671889,0.2643751,0.2626358,0.2621628,0.2570911,0.2530659,0.2454629,0.2333537,0.2267132,0.2213563,0.2142413,0.2087725,0.2036435,0.1976371,0.1926304,0.1881566,0.1840526,0.1796703,0.1766047,0.1725385,0.1710672,0.1685811,0.1663302,0.1649971,0.162062,0.1618414,0.1599583,0.15726,0.1555142,0.1534109,0.1508865,0.1471969,0.1441508,0.1399384,0.1360567,0.1333886,0.1323571,0.1278566,0.1275514,0.119422)

mambac.polygon.dim.x <- mambac.polygon.cat.x
mambac.polygon.dim.y <- c(0.2133996,0.2132621,0.2120169,0.2134476,0.2093492,0.2109715,0.2125715,0.2134399,0.2160315,0.2186466,0.2186352,0.2187436,0.2215879,0.2244632,0.2272143,0.2248821,0.2243939,0.2244379,0.2260983,0.22564,0.2254407,0.2267528,0.2292145,0.2316553,0.2352261,0.2407056,0.2440052,0.2461438,0.2515644,0.2574403,0.2636145,0.2703514,0.2752763,0.2827397,0.2862843,0.289024,0.2932599,0.2924696,0.2934012,0.2966299,0.2985597,0.3058528,0.3146306,0.3301054,0.3419604,0.3574677,0.3610782,0.364778,0.3709214,0.3681659,0.2931975,0.3013917,0.3089268,0.3069652,0.3037549,0.294719,0.2811057,0.270041,0.2638278,0.2579279,0.2518752,0.251018,0.2511137,0.250478,0.2483248,0.2455259,0.2410719,0.2366928,0.2286581,0.2204503,0.215831,0.2115137,0.2087868,0.2047022,0.2015653,0.197257,0.1938165,0.1921007,0.1909351,0.1913754,0.1895129,0.1896367,0.1878757,0.1880855,0.1889565,0.1888184,0.189384,0.18836,0.1893885,0.1895332,0.1871134,0.185986,0.1862115,0.1835322,0.1793214,0.1787713,0.1808379,0.1772698,0.1749598,0.1722605)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line1.cat.y <- rep(c(0.05482831,0.07634818,0.06915473,0.08522333,0.08908939,0.09064096,0.09345925,0.09604733,0.09492773,0.1008598,0.1033051,0.1102554,0.1145046,0.1167478,0.1213774,0.1267845,0.1302042,0.1314314,0.1312563,0.1307418,0.1333214,0.1375206,0.1423095,0.1436724,0.150598,0.1563465,0.1629455,0.1686959,0.1748075,0.1803951,0.1838064,0.1874142,0.1959214,0.2029065,0.2107313,0.2174041,0.2234075,0.2236096,0.228679,0.2308957,0.2301554,0.2378384,0.2466182,0.2539978,0.2627812,0.2652678,0.2722174,0.2783514,0.3008835,0.2801638), each = 2)

mambac.line1.dim.y <- rep(c(0.1201988,0.1201503,0.1252871,0.1235974,0.1290192,0.1388564,0.1445861,0.144207,0.143083,0.1398308,0.1347735,0.1332145,0.1327998,0.1313359,0.129956,0.1295348,0.1283788,0.1262168,0.1268461,0.1257017,0.1243442,0.1254858,0.1270554,0.1270771,0.1313246,0.1347347,0.1366457,0.1409101,0.1424975,0.1417724,0.1447969,0.148018,0.1541501,0.1558936,0.1614269,0.1620622,0.1667554,0.1649742,0.1626287,0.1718913,0.1736562,0.1728692,0.1714358,0.1711256,0.1772416,0.1721512,0.1552669,0.142462,0.1184253,0.1202055), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line2.cat.y <- rep(c(0.2375411,0.2195178,0.2165679,0.2209744,0.2170017,0.2178289,0.222616,0.2353422,0.249298,0.2523305,0.2556515,0.2576531,0.2641997,0.2692648,0.2685203,0.2655461,0.2667946,0.2646808,0.2660749,0.2681777,0.2718786,0.275396,0.2757334,0.2775125,0.283048,0.2906605,0.2970419,0.3042889,0.3159456,0.326638,0.3387248,0.3507416,0.363028,0.3707036,0.3803323,0.3788757,0.3808302,0.3827815,0.3893185,0.3889189,0.3958319,0.4065915,0.4224595,0.4405852,0.4674625,0.4824498,0.4971588,0.5263492,0.5230965,0.5061542), each = 2)

mambac.line2.dim.y <- rep(c(0.2899342,0.2706757,0.2663231,0.2563475,0.2564982,0.2638913,0.2606693,0.2653411,0.2712759,0.271923,0.2705459,0.2701492,0.2683764,0.2669028,0.269423,0.2680449,0.2669725,0.2694097,0.2722558,0.277565,0.283012,0.2857413,0.2874521,0.2896112,0.2974124,0.3012334,0.3058449,0.3140101,0.3213263,0.3239226,0.3307146,0.3403656,0.3522816,0.3637515,0.3747482,0.3823464,0.3856578,0.3876891,0.3878994,0.3923531,0.3968274,0.4040556,0.4228698,0.4461118,0.4684873,0.4704827,0.4585101,0.4535409,0.4616872,0.4369181), each = 2)

mamb.emp <- data.frame(mambac.empcurve.x, mambac.empcurve.y)
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.x"] <- "xvalues"
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.y"] <- "yvalues"


# MAXEIG ------------------------------------------------------------------

maxeig.empcurve.x <- c(-0.9966096,-0.9469235,-0.9046903,-0.8754229,-0.8358321,-0.8002005,-0.7730312,-0.7557992,-0.7162084,-0.6766177,-0.6370269,-0.5974362,-0.5548959,-0.5049817,-0.4653909,-0.4297592,-0.3901685,-0.353062,-0.3383143,-0.3235666,-0.3088189,-0.2940712,-0.282273,-0.2719496,-0.2572019,-0.243929,-0.2291813,-0.2144336,-0.1996858,-0.1849381,-0.1231402,-0.04231268,0.04736342,0.1326152,0.2134427,0.2861874,0.3670149,0.4478424,0.5286699,0.6094974,0.6432746,0.6580223,0.6972679,0.7887596,0.8802513,0.9625938,1.091199,1.223927,1.356655,1.489384)
maxeig.empcurve.y <- c(0.1350406,0.137329,0.1402709,0.1355066,0.1303991,0.1356524,0.1384807,0.1385231,0.1417044,0.1427201,0.1428025,0.1383999,0.1331734,0.1317737,0.131827,0.131668,0.1294695,0.1222947,0.1219816,0.1249465,0.1282261,0.1297118,0.1330198,0.1249665,0.1218946,0.1198779,0.123987,0.1274461,0.1325097,0.1280879,0.1287592,0.1343842,0.1406155,0.1517946,0.1526662,0.1612255,0.1691266,0.1753704,0.175199,0.1747776,0.1775899,0.1721685,0.174453,0.1788085,0.1851174,0.1871707,0.1979448,0.1962308,0.1946726,0.196919)
maxeig.y.range <- c(0.0723201,0.3239922)

#Duplicate empirical values to allow the simulated polygon to be more smooth
maxeig.empcurve.x <- rep(maxeig.empcurve.x, each = 2)
maxeig.empcurve.y <- rep(maxeig.empcurve.y, each = 2)

maxeig.polygon.cat.x <- c(-0.9966096,-0.9469235,-0.9046903,-0.8754229,-0.8358321,-0.8002005,-0.7730312,-0.7557992,-0.7162084,-0.6766177,-0.6370269,-0.5974362,-0.5548959,-0.5049817,-0.4653909,-0.4297592,-0.3901685,-0.353062,-0.3383143,-0.3235666,-0.3088189,-0.2940712,-0.282273,-0.2719496,-0.2572019,-0.243929,-0.2291813,-0.2144336,-0.1996858,-0.1849381,-0.1231402,-0.04231268,0.04736342,0.1326152,0.2134427,0.2861874,0.3670149,0.4478424,0.5286699,0.6094974,0.6432746,0.6580223,0.6972679,0.7887596,0.8802513,0.9625938,1.091199,1.223927,1.356655,1.489384,1.489384,1.356655,1.223927,1.091199,0.9625938,0.8802513,0.7887596,0.6972679,0.6580223,0.6432746,0.6094974,0.5286699,0.4478424,0.3670149,0.2861874,0.2134427,0.1326152,0.04736342,-0.04231268,-0.1231402,-0.1849381,-0.1996858,-0.2144336,-0.2291813,-0.243929,-0.2572019,-0.2719496,-0.282273,-0.2940712,-0.3088189,-0.3235666,-0.3383143,-0.353062,-0.3901685,-0.4297592,-0.4653909,-0.5049817,-0.5548959,-0.5974362,-0.6370269,-0.6766177,-0.7162084,-0.7557992,-0.7730312,-0.8002005,-0.8358321,-0.8754229,-0.9046903,-0.9469235,-0.9966096)
maxeig.polygon.cat.y <- c(0.1254483,0.1260215,0.1282983,0.1261764,0.1250665,0.1232952,0.1251389,0.1244048,0.1258752,0.1285188,0.1309818,0.1339739,0.1378479,0.1405192,0.1440978,0.1459706,0.1523434,0.1565873,0.1553907,0.154098,0.1549832,0.1565188,0.1558217,0.155497,0.1543931,0.152992,0.1549712,0.1595449,0.1614943,0.1640175,0.1674763,0.1762746,0.1847347,0.1939707,0.19886,0.2068866,0.21338,0.2223051,0.2280187,0.2324769,0.2331171,0.2334526,0.2348582,0.2361339,0.2385895,0.235069,0.2341049,0.2333948,0.2340159,0.2374339,0.1847087,0.187016,0.1854961,0.1847036,0.1876661,0.1861414,0.1903037,0.1888906,0.1892532,0.1896352,0.1864488,0.1840148,0.1801929,0.1779369,0.171974,0.167359,0.161543,0.1561598,0.1479481,0.1425756,0.1383696,0.1392164,0.1382048,0.1378074,0.1356931,0.1339957,0.1328995,0.1339331,0.1330013,0.1321162,0.1334511,0.1330434,0.1313615,0.1293866,0.126572,0.1253561,0.123852,0.119614,0.116854,0.1140491,0.1105928,0.1090401,0.1073396,0.1055823,0.1060483,0.1062703,0.1063144,0.1063864,0.1065009,0.1060848)

maxeig.polygon.dim.x <- maxeig.polygon.cat.x
maxeig.polygon.dim.y <- c(0.1416605,0.1438339,0.1443334,0.1451031,0.1452494,0.1453868,0.1464032,0.1475526,0.1482296,0.1493182,0.1507925,0.1521934,0.1521332,0.1516541,0.1515693,0.15425,0.1540943,0.1561278,0.1554825,0.1555407,0.1571727,0.157292,0.1591359,0.1562543,0.158787,0.1577109,0.157385,0.1583716,0.1603957,0.1628185,0.1641909,0.1671612,0.1717589,0.173816,0.1731397,0.1724538,0.1728227,0.1729943,0.1737575,0.1740332,0.1742081,0.176808,0.1770609,0.1784391,0.1811286,0.1854644,0.1846734,0.1856582,0.188162,0.1858598,0.1443026,0.1483075,0.1510831,0.1535519,0.155122,0.1522304,0.1486529,0.1468808,0.1461609,0.1481326,0.1485504,0.1493707,0.149049,0.149147,0.1470348,0.1469762,0.1449345,0.1476717,0.1430661,0.1391758,0.138464,0.1390475,0.1345531,0.1354169,0.1362482,0.1367825,0.1357252,0.134495,0.1342379,0.1334344,0.1335025,0.1347494,0.1351376,0.1351828,0.1337113,0.1331604,0.1313996,0.1302074,0.1292965,0.1264899,0.1264822,0.1261054,0.1236496,0.1235067,0.1236947,0.1229319,0.1216729,0.1209077,0.1206132,0.1220654)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line1.cat.y <- rep(c(0.08241319,0.08498491,0.08358424,0.08088493,0.07490612,0.0723201,0.07247699,0.07404184,0.08145011,0.0825357,0.08581037,0.08976032,0.0949582,0.09937345,0.09365752,0.09410077,0.09449111,0.09695465,0.1011956,0.09504707,0.09748996,0.1005462,0.1036921,0.1062571,0.1062171,0.1084152,0.1085582,0.1069829,0.1078142,0.1137486,0.1194322,0.1150589,0.1181577,0.1224277,0.1245801,0.1343708,0.1439224,0.1454204,0.1445321,0.1563789,0.1528443,0.1561121,0.147402,0.156874,0.1578464,0.1500446,0.1491683,0.1460145,0.1439994,0.1353352), each = 2)

maxeig.line1.dim.y <- rep(c(0.09582627,0.09270217,0.09141731,0.09197144,0.09615827,0.09528445,0.09327487,0.09131264,0.09068222,0.09194018,0.09437603,0.09116877,0.09434252,0.09259677,0.09769005,0.1050354,0.1089814,0.1130032,0.1097787,0.1066411,0.1059576,0.1035229,0.1028616,0.0970563,0.1027154,0.1053851,0.1060463,0.1094912,0.1137989,0.1100593,0.1086776,0.106303,0.1057169,0.1072277,0.1133277,0.1194301,0.115231,0.1168623,0.1208653,0.11791,0.115595,0.1164442,0.1127433,0.1114174,0.107023,0.1034756,0.09560809,0.08774741,0.0866141,0.0762879), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line2.cat.y <- rep(c(0.1499917,0.1543703,0.1509774,0.1495204,0.1510748,0.1491061,0.1514339,0.155206,0.1542113,0.1604586,0.1603163,0.1659057,0.1698897,0.1785359,0.174587,0.176735,0.1764852,0.1805058,0.1896775,0.1886401,0.1969037,0.1988241,0.2008408,0.1874075,0.189666,0.1899737,0.193818,0.1925509,0.1926926,0.2004966,0.1990514,0.2177806,0.2377569,0.2491554,0.2627177,0.2735518,0.2841311,0.2936257,0.2965524,0.3124901,0.3239922,0.3197771,0.3105306,0.3084945,0.3044989,0.3100883,0.3073166,0.2998157,0.3027087,0.2993256), each = 2)

maxeig.line2.dim.y <- rep(c(0.1846593,0.1867202,0.1880104,0.1888477,0.1910517,0.1853206,0.1931347,0.192837,0.1891945,0.1876731,0.1871248,0.1819676,0.1879393,0.1916439,0.1860432,0.1885177,0.1900748,0.1886811,0.1850259,0.191055,0.197745,0.1970371,0.1972935,0.1967792,0.1957755,0.1907061,0.1899397,0.1880492,0.1938834,0.1939402,0.193254,0.1958141,0.1959864,0.204605,0.2089875,0.2168823,0.2294182,0.2364731,0.2411307,0.239273,0.2480075,0.2442176,0.2415306,0.2485986,0.2646829,0.274171,0.2776804,0.2760024,0.2766026,0.2736081), each = 2)

maxe.emp <- data.frame(maxeig.empcurve.x, maxeig.empcurve.y)
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.x"] <- "xvalues"
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.y"] <- "yvalues"

# L-Mode ------------------------------------------------------------------
lmode.empcurve.x <-
  c(
    -2.943166,
    -2.930532,
    -2.917898,
    -2.905265,
    -2.892631,
    -2.879997,
    -2.867364,
    -2.85473,
    -2.842096,
    -2.829463,
    -2.816829,
    -2.804195,
    -2.791562,
    -2.778928,
    -2.766294,
    -2.753661,
    -2.741027,
    -2.728394,
    -2.71576,
    -2.703126,
    -2.690493,
    -2.677859,
    -2.665225,
    -2.652592,
    -2.639958,
    -2.627324,
    -2.614691,
    -2.602057,
    -2.589423,
    -2.57679,
    -2.564156,
    -2.551522,
    -2.538889,
    -2.526255,
    -2.513622,
    -2.500988,
    -2.488354,
    -2.475721,
    -2.463087,
    -2.450453,
    -2.43782,
    -2.425186,
    -2.412552,
    -2.399919,
    -2.387285,
    -2.374651,
    -2.362018,
    -2.349384,
    -2.33675,
    -2.324117,
    -2.311483,
    -2.29885,
    -2.286216,
    -2.273582,
    -2.260949,
    -2.248315,
    -2.235681,
    -2.223048,
    -2.210414,
    -2.19778,
    -2.185147,
    -2.172513,
    -2.159879,
    -2.147246,
    -2.134612,
    -2.121978,
    -2.109345,
    -2.096711,
    -2.084077,
    -2.071444,
    -2.05881,
    -2.046177,
    -2.033543,
    -2.020909,
    -2.008276,
    -1.995642,
    -1.983008,
    -1.970375,
    -1.957741,
    -1.945107,
    -1.932474,
    -1.91984,
    -1.907206,
    -1.894573,
    -1.881939,
    -1.869305,
    -1.856672,
    -1.844038,
    -1.831405,
    -1.818771,
    -1.806137,
    -1.793504,
    -1.78087,
    -1.768236,
    -1.755603,
    -1.742969,
    -1.730335,
    -1.717702,
    -1.705068,
    -1.692434,
    -1.679801,
    -1.667167,
    -1.654533,
    -1.6419,
    -1.629266,
    -1.616633,
    -1.603999,
    -1.591365,
    -1.578732,
    -1.566098,
    -1.553464,
    -1.540831,
    -1.528197,
    -1.515563,
    -1.50293,
    -1.490296,
    -1.477662,
    -1.465029,
    -1.452395,
    -1.439761,
    -1.427128,
    -1.414494,
    -1.40186,
    -1.389227,
    -1.376593,
    -1.36396,
    -1.351326,
    -1.338692,
    -1.326059,
    -1.313425,
    -1.300791,
    -1.288158,
    -1.275524,
    -1.26289,
    -1.250257,
    -1.237623,
    -1.224989,
    -1.212356,
    -1.199722,
    -1.187088,
    -1.174455,
    -1.161821,
    -1.149188,
    -1.136554,
    -1.12392,
    -1.111287,
    -1.098653,
    -1.086019,
    -1.073386,
    -1.060752,
    -1.048118,
    -1.035485,
    -1.022851,
    -1.010217,
    -0.9975838,
    -0.9849501,
    -0.9723165,
    -0.9596828,
    -0.9470492,
    -0.9344155,
    -0.9217819,
    -0.9091482,
    -0.8965146,
    -0.8838809,
    -0.8712473,
    -0.8586136,
    -0.84598,
    -0.8333463,
    -0.8207127,
    -0.808079,
    -0.7954454,
    -0.7828117,
    -0.7701781,
    -0.7575444,
    -0.7449108,
    -0.7322772,
    -0.7196435,
    -0.7070099,
    -0.6943762,
    -0.6817426,
    -0.6691089,
    -0.6564753,
    -0.6438416,
    -0.631208,
    -0.6185743,
    -0.6059407,
    -0.593307,
    -0.5806734,
    -0.5680397,
    -0.5554061,
    -0.5427724,
    -0.5301388,
    -0.5175051,
    -0.5048715,
    -0.4922378,
    -0.4796042,
    -0.4669705,
    -0.4543369,
    -0.4417032,
    -0.4290696,
    -0.416436,
    -0.4038023,
    -0.3911687,
    -0.378535,
    -0.3659014,
    -0.3532677,
    -0.3406341,
    -0.3280004,
    -0.3153668,
    -0.3027331,
    -0.2900995,
    -0.2774658,
    -0.2648322,
    -0.2521985,
    -0.2395649,
    -0.2269312,
    -0.2142976,
    -0.2016639,
    -0.1890303,
    -0.1763966,
    -0.163763,
    -0.1511293,
    -0.1384957,
    -0.125862,
    -0.1132284,
    -0.1005948,
    -0.0879611,
    -0.07532745,
    -0.06269381,
    -0.05006016,
    -0.03742651,
    -0.02479286,
    -0.01215921,
    0.000474433,
    0.01310808,
    0.02574173,
    0.03837538,
    0.05100903,
    0.06364267,
    0.07627632,
    0.08890997,
    0.1015436,
    0.1141773,
    0.1268109,
    0.1394446,
    0.1520782,
    0.1647119,
    0.1773455,
    0.1899792,
    0.2026128,
    0.2152464,
    0.2278801,
    0.2405137,
    0.2531474,
    0.265781,
    0.2784147,
    0.2910483,
    0.303682,
    0.3163156,
    0.3289493,
    0.3415829,
    0.3542166,
    0.3668502,
    0.3794839,
    0.3921175,
    0.4047512,
    0.4173848,
    0.4300185,
    0.4426521,
    0.4552858,
    0.4679194,
    0.4805531,
    0.4931867,
    0.5058204,
    0.518454,
    0.5310876,
    0.5437213,
    0.5563549,
    0.5689886,
    0.5816222,
    0.5942559,
    0.6068895,
    0.6195232,
    0.6321568,
    0.6447905,
    0.6574241,
    0.6700578,
    0.6826914,
    0.6953251,
    0.7079587,
    0.7205924,
    0.733226,
    0.7458597,
    0.7584933,
    0.771127,
    0.7837606,
    0.7963943,
    0.8090279,
    0.8216616,
    0.8342952,
    0.8469288,
    0.8595625,
    0.8721961,
    0.8848298,
    0.8974634,
    0.9100971,
    0.9227307,
    0.9353644,
    0.947998,
    0.9606317,
    0.9732653,
    0.985899,
    0.9985326,
    1.011166,
    1.0238,
    1.036434,
    1.049067,
    1.061701,
    1.074335,
    1.086968,
    1.099602,
    1.112235,
    1.124869,
    1.137503,
    1.150136,
    1.16277,
    1.175404,
    1.188037,
    1.200671,
    1.213305,
    1.225938,
    1.238572,
    1.251206,
    1.263839,
    1.276473,
    1.289107,
    1.30174,
    1.314374,
    1.327007,
    1.339641,
    1.352275,
    1.364908,
    1.377542,
    1.390176,
    1.402809,
    1.415443,
    1.428077,
    1.44071,
    1.453344,
    1.465978,
    1.478611,
    1.491245,
    1.503879,
    1.516512,
    1.529146,
    1.541779,
    1.554413,
    1.567047,
    1.57968,
    1.592314,
    1.604948,
    1.617581,
    1.630215,
    1.642849,
    1.655482,
    1.668116,
    1.68075,
    1.693383,
    1.706017,
    1.718651,
    1.731284,
    1.743918,
    1.756552,
    1.769185,
    1.781819,
    1.794452,
    1.807086,
    1.81972,
    1.832353,
    1.844987,
    1.857621,
    1.870254,
    1.882888,
    1.895522,
    1.908155,
    1.920789,
    1.933423,
    1.946056,
    1.95869,
    1.971324,
    1.983957,
    1.996591,
    2.009224,
    2.021858,
    2.034492,
    2.047125,
    2.059759,
    2.072393,
    2.085026,
    2.09766,
    2.110294,
    2.122927,
    2.135561,
    2.148195,
    2.160828,
    2.173462,
    2.186096,
    2.198729,
    2.211363,
    2.223996,
    2.23663,
    2.249264,
    2.261897,
    2.274531,
    2.287165,
    2.299798,
    2.312432,
    2.325066,
    2.337699,
    2.350333,
    2.362967,
    2.3756,
    2.388234,
    2.400868,
    2.413501,
    2.426135,
    2.438768,
    2.451402,
    2.464036,
    2.476669,
    2.489303,
    2.501937,
    2.51457,
    2.527204,
    2.539838,
    2.552471,
    2.565105,
    2.577739,
    2.590372,
    2.603006,
    2.61564,
    2.628273,
    2.640907,
    2.653541,
    2.666174,
    2.678808,
    2.691441,
    2.704075,
    2.716709,
    2.729342,
    2.741976,
    2.75461,
    2.767243,
    2.779877,
    2.792511,
    2.805144,
    2.817778,
    2.830412,
    2.843045,
    2.855679,
    2.868313,
    2.880946,
    2.89358,
    2.906213,
    2.918847,
    2.931481,
    2.944114,
    2.956748,
    2.969382,
    2.982015,
    2.994649,
    3.007283,
    3.019916,
    3.03255,
    3.045184,
    3.057817,
    3.070451,
    3.083085,
    3.095718,
    3.108352,
    3.120985,
    3.133619,
    3.146253,
    3.158886,
    3.17152,
    3.184154,
    3.196787,
    3.209421,
    3.222055,
    3.234688,
    3.247322,
    3.259956,
    3.272589,
    3.285223,
    3.297857,
    3.31049,
    3.323124,
    3.335758,
    3.348391,
    3.361025,
    3.373658,
    3.386292,
    3.398926,
    3.411559,
    3.424193,
    3.436827,
    3.44946,
    3.462094,
    3.474728,
    3.487361,
    3.499995,
    3.512629
  )
lmode.empcurve.y <-
  c(
    0.000308768,
    0.0003589251,
    0.0004154129,
    0.0004787399,
    0.0005527786,
    0.0006363951,
    0.0007296735,
    0.0008333013,
    0.0009516343,
    0.001085034,
    0.001232409,
    0.001394617,
    0.001575901,
    0.001779545,
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lmode.y.range <- c(3.067011e-05,0.4866475)

lmode.empcurve.x <- rep(lmode.empcurve.x, each = 2)
lmode.empcurve.y <- rep(lmode.empcurve.y, each = 2)

lmode.polygon.cat.x <-
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                         lmode.polygon.cat.y <-
                           c(
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                             0.3586302,
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                             0.3682162,
                             0.370131,
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                             0.3735255,
                             0.3748294,
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                             0.3916798,
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                             0.07333528,
                             0.07190335,
                             0.07052664,
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                             0.06041461,
                             0.05870334,
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                             0.0553575,
                             0.05365062,
                             0.05156719,
                             0.04949152,
                             0.04805206,
                             0.04642083,
                             0.04439801,
                             0.04262152,
                             0.04111224,
                             0.03961771,
                             0.03841783,
                             0.03729827,
                             0.03611871,
                             0.03478452,
                             0.03316134,
                             0.03161981,
                             0.03009377,
                             0.0286083,
                             0.0271649,
                             0.02581098,
                             0.02463498,
                             0.02339842,
                             0.02219479,
                             0.02102613,
                             0.0198921,
                             0.01898283,
                             0.01818166,
                             0.01725163,
                             0.01620197,
                             0.0151924,
                             0.01422445,
                             0.01329824,
                             0.01241187,
                             0.01160302,
                             0.01085882,
                             0.01014643,
                             0.009463052,
                             0.008807697,
                             0.00818799,
                             0.007600264,
                             0.007040695,
                             0.006507935,
                             0.006007934,
                             0.005538401,
                             0.005094818,
                             0.004691446,
                             0.004313108,
                             0.003956575,
                             0.003624698,
                             0.003314155,
                             0.003022145,
                             0.002753391,
                             0.002503722,
                             0.002270694,
                             0.002053386,
                             0.001854499,
                             0.001672431,
                             0.001504028,
                             0.001348341,
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                             0.0006808562,
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                             3.176892e-05,
                             3.703745e-05,
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                             4.986161e-05,
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                             0.1142024,
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                             0.1170245,
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                             0.1295862,
                             0.1311876,
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                             0.1358208,
                             0.1372823,
                             0.1388814,
                             0.1405143,
                             0.1417214,
                             0.1421721,
                             0.1426509,
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                             0.1438327,
                             0.1458101,
                             0.1480551,
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                             0.1520703,
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                             0.1565325,
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                             0.1599391,
                             0.1620091,
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                             0.1672202,
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                             0.1743042,
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                             0.1948641,
                             0.1973131,
                             0.1987942,
                             0.2008541,
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                             0.2216185,
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                             0.3517129,
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                             0.3551978,
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                             0.3549872,
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                             0.3547106,
                             0.3542508,
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                             0.3538241,
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                             0.3502201,
                             0.3485593,
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                             0.347598,
                             0.347356,
                             0.3457576,
                             0.3439945,
                             0.3414014,
                             0.339315,
                             0.337935,
                             0.3362941,
                             0.3349918,
                             0.3332266,
                             0.3314716,
                             0.3297903,
                             0.3267712,
                             0.3251721,
                             0.3236437,
                             0.3221754,
                             0.3199573,
                             0.3177944,
                             0.315628,
                             0.313614,
                             0.3118378,
                             0.3097941,
                             0.3075659,
                             0.3052599,
                             0.3018729,
                             0.2978902,
                             0.2939949,
                             0.2907617,
                             0.2878898,
                             0.2851881,
                             0.2821145,
                             0.2786409,
                             0.2751526,
                             0.2710813,
                             0.2669715,
                             0.2627816,
                             0.258538,
                             0.2542457,
                             0.2499079,
                             0.245513,
                             0.241088,
                             0.2366406,
                             0.2325514,
                             0.2294997,
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                             0.2233573,
                             0.2189407,
                             0.214513,
                             0.2112225,
                             0.2075614,
                             0.2035804,
                             0.1996224,
                             0.1956925,
                             0.1917973,
                             0.1879325,
                             0.1840973,
                             0.1801645,
                             0.1761991,
                             0.1722657,
                             0.1683629,
                             0.1644924,
                             0.1606668,
                             0.1568762,
                             0.1528601,
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                             0.1445703,
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                             0.1287421,
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                             0.116404,
                             0.1135202,
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                             0.1078737,
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                             0.102407,
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                             0.08793864,
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                             0.07812673,
                             0.07568304,
                             0.07331724,
                             0.07152679,
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                             0.06724686,
                             0.06484752,
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                             0.06097293,
                             0.05918117,
                             0.05746637,
                             0.05581666,
                             0.05454649,
                             0.05276026,
                             0.05075704,
                             0.04907076,
                             0.04692594,
                             0.04501482,
                             0.04357747,
                             0.04222499,
                             0.04066127,
                             0.03921168,
                             0.0378395,
                             0.03630266,
                             0.03485851,
                             0.03344439,
                             0.03204584,
                             0.03106729,
                             0.02984231,
                             0.02847634,
                             0.02717224,
                             0.02599344,
                             0.02512336,
                             0.0243095,
                             0.02344566,
                             0.02218792,
                             0.02126408,
                             0.02037259,
                             0.01948184,
                             0.01868337,
                             0.01793507,
                             0.01721586,
                             0.01649646,
                             0.01579623,
                             0.01487462,
                             0.0140887,
                             0.01329002,
                             0.0126349,
                             0.01195779,
                             0.0113718,
                             0.01080446,
                             0.01027648,
                             0.009766005,
                             0.009245126,
                             0.008725482,
                             0.00822994,
                             0.007708676,
                             0.007184732,
                             0.006703352,
                             0.006245552,
                             0.00581396,
                             0.005408188,
                             0.005022227,
                             0.004655563,
                             0.004311333,
                             0.003989656,
                             0.003684923,
                             0.003396669,
                             0.003127061,
                             0.002877112,
                             0.002641477,
                             0.002414799,
                             0.002196397,
                             0.00199718,
                             0.001812519,
                             0.001640701,0.001481193,0.001336139,0.001203737,0.001081372,0.0009685784,0.0008658945,0.0007740341,0.0006897633,0.0006126829,0.0005426341,0.0004808899,0.0004249414,0.0003741848,0.0003283398,0.0002881415,0.0002524219,0.0002202904,0.000191697,0.0001664444,0.000144502,0.0001251048,0.0001079076,9.267972e-05,7.973994e-05,6.839778e-05)

lmode.polygon.dim.x <- lmode.polygon.cat.x
lmode.polygon.dim.y <-
  c(
    0.0002462339,
    0.0002851852,
    0.0003278261,
    0.0003768234,
    0.0004319576,
    0.0004932276,
    0.0005610405,
    0.0006390432,
    0.0007261013,
    0.0008220136,
    0.0009272975,
    0.001046755,
    0.001184743,
    0.001343632,
    0.001523025,
    0.001711545,
    0.00191825,
    0.002142725,
    0.002382415,
    0.002643267,
    0.002926426,
    0.00323031,
    0.003557561,
    0.003912919,
    0.004295613,
    0.004702737,
    0.005137176,
    0.005602906,
    0.006100303,
    0.006624893,
    0.007179603,
    0.007767156,
    0.008378598,
    0.009016927,
    0.009690656,
    0.01039464,
    0.01122301,
    0.01204949,
    0.01289887,
    0.01372098,
    0.01457334,
    0.01542801,
    0.01623752,
    0.01736883,
    0.01840517,
    0.01940984,
    0.02043592,
    0.02146378,
    0.02248333,
    0.02369343,
    0.02488427,
    0.02604787,
    0.02717469,
    0.02843136,
    0.02959534,
    0.03070623,
    0.03181342,
    0.03336068,
    0.03467297,
    0.03593318,
    0.03733671,
    0.03881056,
    0.04019815,
    0.04166277,
    0.04316148,
    0.04500265,
    0.0465156,
    0.04775242,
    0.04916267,
    0.05102272,
    0.05299361,
    0.05477376,
    0.05702728,
    0.05912552,
    0.06124278,
    0.06338828,
    0.06543032,
    0.06775031,
    0.0705258,
    0.07326308,
    0.07582205,
    0.07837823,
    0.08076582,
    0.08315354,
    0.08588856,
    0.08912903,
    0.09239808,
    0.09537361,
    0.09832628,
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    0.008127414,
    0.007597447,
    0.007052103,
    0.006518453,
    0.006027054,
    0.005565304,
    0.005131284,
    0.004732655,
    0.004353249,
    0.003992292,
    0.003658125,
    0.003326296,
    0.003018299,0.002733778,0.002469849,0.002225983,0.002005563,0.001803416,0.001616679,0.001447012,0.001292741,0.001152832,0.001028115,0.0009161677,0.0008168681,0.0007263861,0.0006437258,0.0005684735,0.0005026466,0.0004434762,0.0003900786,0.0003418572,0.0002998507,0.0002625762,0.0002290589,0.0001990393,0.0001720848,0.0001480015)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line1.cat.y <-
  rep(
    c(
      3.17259e-05,
      3.659479e-05,
      4.204575e-05,
      4.812534e-05,
      5.487754e-05,
      6.265843e-05,
      7.144285e-05,
      8.117247e-05,
      9.190826e-05,
      0.0001042222,
      0.0001179681,
      0.0001330946,
      0.0001496838,
      0.0001686245,
      0.0001895515,
      0.0002124434,
      0.0002374094,
      0.0002657915,
      0.0002968624,
      0.0003306703,
      0.0003673581,
      0.0004089072,
      0.0004540247,
      0.0005028903,
      0.0005558504,
      0.0006152989,
      0.0006795724,
      0.0007489144,
      0.0008240139,
      0.0009076475,
      0.0009977564,
      0.001094657,
      0.001199572,
      0.001315611,
      0.001440273,
      0.001573968,
      0.001718716,
      0.001877839,
      0.002048351,
      0.00223077,
      0.002428276,
      0.002644143,
      0.002874878,
      0.003121117,
      0.003387645,
      0.003677242,
      0.00398592,
      0.004314427,
      0.004669647,
      0.005053183,
      0.005460634,
      0.005892822,
      0.006359204,
      0.006859287,
      0.007388429,
      0.007947463,
      0.008548725,
      0.009188586,
      0.009862438,
      0.01057102,
      0.01132955,
      0.0121303,
      0.01296905,
      0.01384632,
      0.01476595,
      0.01551857,
      0.01625563,
      0.01702091,
      0.01782089,
      0.01831249,
      0.01875606,
      0.01920608,
      0.01966343,
      0.02012915,
      0.02061022,
      0.02110372,
      0.0216108,
      0.02213314,
      0.02268107,
      0.02324888,
      0.02383794,
      0.02445079,
      0.02510108,
      0.02577985,
      0.0264886,
      0.02723102,
      0.02802378,
      0.02885436,
      0.02972434,
      0.03060022,
      0.03136113,
      0.03216561,
      0.03301461,
      0.03391742,
      0.03488076,
      0.03589238,
      0.03695291,
      0.03806778,
      0.03925147,
      0.04048619,
      0.04177217,
      0.04311037,
      0.04452304,
      0.04598705,
      0.04750211,
      0.04906793,
      0.05070336,
      0.05239084,
      0.05412623,
      0.0559087,
      0.05775097,
      0.05964323,
      0.06157751,
      0.06355259,
      0.0655756,
      0.06764342,
      0.06974578,
      0.07188137,
      0.07405323,
      0.07626346,
      0.07850127,
      0.08076571,
      0.08305754,
      0.08538331,
      0.0877328,
      0.09010591,
      0.09250256,
      0.09493399,
      0.09739089,
      0.09987395,
      0.1023842,
      0.1049346,
      0.1075204,
      0.1101409,
      0.112798,
      0.1155064,
      0.1182667,
      0.1210744,
      0.1239318,
      0.126853,
      0.1298462,
      0.1328999,
      0.136016,
      0.1392048,
      0.1424837,
      0.1458317,
      0.1492496,
      0.1527407,
      0.1563315,
      0.1599914,
      0.1637192,
      0.1675134,
      0.171397,
      0.1753412,
      0.17934,
      0.1833903,
      0.1875011,
      0.1916539,
      0.1958383,
      0.2000495,
      0.2042853,
      0.2085329,
      0.2127831,
      0.2170305,
      0.2212664,
      0.2254772,
      0.2296608,
      0.2338124,
      0.2379228,
      0.2419708,
      0.2459664,
      0.249906,
      0.2537853,
      0.2575704,
      0.261286,
      0.2649301,
      0.2685006,
      0.2719655,
      0.2753475,
      0.2786512,
      0.2818764,
      0.2847557,
      0.2872813,
      0.2897987,
      0.2923095,
      0.2948174,
      0.2973255,
      0.2998351,
      0.3023483,
      0.3048676,
      0.3073923,
      0.3091885,
      0.3100253,
      0.3108383,
      0.3116337,
      0.312419,
      0.3132088,
      0.3140102,
      0.3148289,
      0.3156786,
      0.3165707,
      0.3175031,
      0.3184796,
      0.3195152,
      0.32062,
      0.3217822,
      0.3230033,
      0.3242954,
      0.3256678,
      0.3271009,
      0.3270932,
      0.3261202,
      0.3252554,
      0.3244985,
      0.3238402,
      0.3232796,
      0.322852,
      0.3225265,
      0.3222906,
      0.3221421,
      0.3216189,
      0.3204836,
      0.3194133,
      0.3184068,
      0.3163694,
      0.3142142,
      0.3120749,
      0.3099638,
      0.3078818,
      0.3058295,
      0.3038094,
      0.3018351,
      0.2999093,
      0.2980273,
      0.296191,
      0.2944118,
      0.291086,
      0.2867737,
      0.282436,
      0.2780762,
      0.2736979,
      0.2693038,
      0.2648989,
      0.260491,
      0.256084,
      0.2516821,
      0.2472912,
      0.2429198,
      0.2385698,
      0.2342449,
      0.2299491,
      0.2256915,
      0.2214805,
      0.2173129,
      0.213192,
      0.2091211,
      0.2051136,
      0.2011752,
      0.1973,
      0.193491,
      0.1897516,
      0.1861008,
      0.1825404,
      0.179063,
      0.1756723,
      0.1723715,
      0.1691865,
      0.1661126,
      0.1631418,
      0.1602769,
      0.1575208,
      0.154905,
      0.1524145,
      0.1500405,
      0.1477841,
      0.1456459,
      0.1436588,
      0.1417962,
      0.1400491,
      0.1384155,
      0.1368933,
      0.1355109,
      0.1342337,
      0.1330537,
      0.1319665,
      0.1309675,
      0.1300757,
      0.1292569,
      0.1285048,
      0.1278138,
      0.127179,
      0.1266056,
      0.12607,
      0.1255665,
      0.1250892,
      0.1246331,
      0.1241921,
      0.1237547,
      0.1233155,
      0.1228689,
      0.1224082,
      0.1219203,
      0.1214039,
      0.1208539,
      0.1202654,
      0.1196287,
      0.1189289,
      0.1181728,
      0.117357,
      0.116478,
      0.1155243,
      0.1144858,
      0.113376,
      0.1121945,
      0.1109415,
      0.1096072,
      0.1081926,
      0.1067144,
      0.1051766,
      0.1035836,
      0.1019332,
      0.100237,
      0.09850989,
      0.09675903,
      0.09499181,
      0.09321697,
      0.09144826,
      0.08969402,
      0.08796151,
      0.08625772,
      0.08460017,
      0.08299376,
      0.08143889,
      0.07993952,
      0.07849909,
      0.07713715,
      0.07584477,
      0.07461682,
      0.07345282,
      0.07235186,
      0.07132874,
      0.07036554,
      0.06945586,
      0.06859651,
      0.06778416,
      0.06702686,
      0.06630739,
      0.0656214,
      0.06496595,
      0.06433826,
      0.06374311,
      0.06316962,
      0.06261653,
      0.06208289,
      0.06156849,
      0.0610784,
      0.06060703,
      0.0601548,
      0.05972219,
      0.05931085,
      0.05892663,
      0.05856396,
      0.05822294,
      0.05790348,
      0.05760692,
      0.05733566,
      0.05708262,
      0.05684605,
      0.05662395,
      0.05641489,
      0.05621528,
      0.05601913,
      0.05582318,
      0.05562411,
      0.05541691,
      0.05519492,
      0.0549566,
      0.05469911,
      0.05441981,
      0.05411189,
      0.05377165,
      0.0534027,
      0.05300446,
      0.05257668,
      0.05211432,
      0.05161996,
      0.05109993,
      0.05055621,
      0.04999107,
      0.04940415,
      0.04880205,
      0.04819035,
      0.04757229,
      0.04695116,
      0.04633177,
      0.04571918,
      0.04511609,
      0.04452521,
      0.04394908,
      0.04339555,
      0.04286413,
      0.04235477,
      0.04186855,
      0.04140636,
      0.04062875,
      0.0397048,
      0.03882268,
      0.03798675,
      0.03718287,
      0.03640928,
      0.03566418,
      0.03495496,
      0.03426821,
      0.0336016,
      0.03295332,
      0.03232517,
      0.03171135,
      0.03082742,
      0.0297336,
      0.02867259,
      0.02764286,
      0.02663913,
      0.02566117,
      0.02471168,
      0.02379489,
      0.0229023,
      0.02203349,
      0.02118803,
      0.0203749,
      0.01958375,
      0.018618,
      0.01756263,
      0.01656296,
      0.01562825,
      0.01475543,
      0.01393028,
      0.01315105,
      0.01242089,
      0.01174478,
      0.01110657,
      0.01050461,
      0.009938005,
      0.009416576,
      0.008924102,
      0.008459147,
      0.00802029,
      0.007614269,
      0.007231341,
      0.006868608,
      0.00652493,
      0.006203582,
      0.005900515,
      0.005611902,
      0.00533689,
      0.005076714,
      0.004830742,
      0.004595037,
      0.004369013,
      0.004152817,
      0.003947743,
      0.003750137,
      0.00355964,
      0.003375904,
      0.00320116,
      0.00303227,
      0.002868984,
      0.002711119,
      0.00256021,
      0.002414782,
      0.0022742,
      0.002138381,
      0.002008383,
      0.001863738,
      0.001724512,
      0.00159529,
      0.001473424,
      0.001358636,
      0.001252258,
      0.001153603,
      0.001060774,
      0.0009735561,
      0.0008931481,
      0.0008187292,
      0.0007489418,
      0.0006836135,
      0.000623797,
      0.0005686105,
      0.0005170874,
      0.0004690853,
      0.0004255024,
      0.0003854534,
      0.0003482622,
      0.000313809,
      0.0002828341,
      0.0002545001,
      0.0002283472,
      0.000204275,
      0.0001828711,
      0.0001633863,
      0.0001455205,
      0.0001291911,
      0.0001148459,
      0.0001018505,
      9.001888e-05,
      7.928518e-05,
      6.997676e-05,
      6.158424e-05,
      5.399957e-05,
      4.717222e-05,
      4.133153e-05,
      3.582857e-05,
      3.083714e-05
    ),
    each = 2
  )

lmode.line1.dim.y <-
  rep(
    c(
      6.528919e-05,
      7.652629e-05,
      8.930802e-05,
      0.0001037788,
      0.000120087,
      0.0001392833,
      0.0001611058,
      0.0001856085,
      0.0002130074,
      0.0002444584,
      0.0002803049,
      0.000320228,
      0.0003645276,
      0.000414252,
      0.0004709953,
      0.0005336965,
      0.0006027531,
      0.0006787436,
      0.0007654703,
      0.0008605887,
      0.0009646046,
      0.001078032,
      0.001205364,
      0.001345073,
      0.001496837,
      0.001661286,
      0.001842562,
      0.002041774,
      0.00225482,
      0.002454746,
      0.002667493,
      0.002891903,
      0.003128191,
      0.003380755,
      0.003647851,
      0.003927775,
      0.004220707,
      0.004530955,
      0.004857278,
      0.005197422,
      0.005551549,
      0.005923838,
      0.006313759,
      0.006718513,
      0.007138294,
      0.007577207,
      0.008035671,
      0.008510319,
      0.009001442,
      0.009513201,
      0.01004728,
      0.01059962,
      0.01117068,
      0.01176483,
      0.01238545,
      0.01302752,
      0.01369171,
      0.0143827,
      0.01510622,
      0.01585573,
      0.01663218,
      0.01744059,
      0.01828976,
      0.01917101,
      0.02008554,
      0.02103852,
      0.02204287,
      0.02308686,
      0.0241719,
      0.02518771,
      0.02569331,
      0.02621239,
      0.02674652,
      0.0273044,
      0.02788515,
      0.02848818,
      0.02911493,
      0.02977444,
      0.03046758,
      0.03119052,
      0.03194441,
      0.03273696,
      0.03357287,
      0.03444423,
      0.03535185,
      0.036301,
      0.03730177,
      0.03834192,
      0.03942199,
      0.04054422,
      0.04172526,
      0.04294851,
      0.04421439,
      0.04552336,
      0.0468949,
      0.04831258,
      0.0497753,
      0.05128345,
      0.05285386,
      0.05447619,
      0.05614565,
      0.05786253,
      0.05964037,
      0.06147534,
      0.06335853,
      0.06528994,
      0.06727907,
      0.06932849,
      0.07142507,
      0.0735683,
      0.07576312,
      0.07801758,
      0.08031499,
      0.08265426,
      0.08503605,
      0.08747186,
      0.08994326,
      0.0924487,
      0.09498662,
      0.09756687,
      0.1001744,
      0.1028068,
      0.1054624,
      0.1081462,
      0.1108502,
      0.1135712,
      0.1163082,
      0.119064,
      0.1218361,
      0.1246218,
      0.1274211,
      0.1302371,
      0.133072,
      0.1359236,
      0.1387929,
      0.1416842,
      0.1446058,
      0.1475533,
      0.1505289,
      0.1535366,
      0.1565933,
      0.1596892,
      0.1628263,
      0.1660072,
      0.1692567,
      0.1725586,
      0.1759136,
      0.179323,
      0.181552,
      0.1834155,
      0.1852693,
      0.1871155,
      0.1889599,
      0.1908056,
      0.1926546,
      0.1945108,
      0.1963778,
      0.1982551,
      0.2001436,
      0.2020473,
      0.203968,
      0.2059024,
      0.2078506,
      0.2098154,
      0.2117973,
      0.2137918,
      0.2157984,
      0.2178183,
      0.2198513,
      0.221893,
      0.2239427,
      0.2260002,
      0.2280643,
      0.230132,
      0.2322022,
      0.2342738,
      0.2363444,
      0.2384125,
      0.2404767,
      0.2425352,
      0.2445832,
      0.2466212,
      0.2486477,
      0.2506596,
      0.2526489,
      0.2546186,
      0.2565672,
      0.2584903,
      0.2603754,
      0.2622297,
      0.2640512,
      0.2658355,
      0.2675644,
      0.2692509,
      0.2708934,
      0.2724877,
      0.2740113,
      0.2754836,
      0.2769036,
      0.2782688,
      0.2795547,
      0.2807862,
      0.2819637,
      0.283087,
      0.2841333,
      0.2851304,
      0.28608,
      0.2869841,
      0.2878274,
      0.2877657,
      0.2873745,
      0.2870804,
      0.2868575,
      0.2867029,
      0.2866163,
      0.2866225,
      0.2867034,
      0.2868516,
      0.287067,
      0.2873693,
      0.2877487,
      0.2881937,
      0.2887039,
      0.2892946,
      0.2899634,
      0.2906954,
      0.2914898,
      0.2923574,
      0.2933028,
      0.2943077,
      0.2953711,
      0.2964992,
      0.2963727,
      0.2952411,
      0.2941856,
      0.2932116,
      0.2923417,
      0.2915451,
      0.2908207,
      0.2895311,
      0.2879683,
      0.286396,
      0.2848134,
      0.2832175,
      0.2816058,
      0.2799806,
      0.278341,
      0.2766857,
      0.2750075,
      0.2733113,
      0.2715961,
      0.269861,
      0.2677696,
      0.2642756,
      0.2607996,
      0.2573455,
      0.2539238,
      0.2505426,
      0.2472008,
      0.2439025,
      0.2406517,
      0.2374737,
      0.2343571,
      0.2313033,
      0.2283154,
      0.225406,
      0.2225881,
      0.2198455,
      0.2171793,
      0.2145906,
      0.2121033,
      0.2097007,
      0.2073751,
      0.2051252,
      0.2029551,
      0.2008783,
      0.1988688,
      0.1969239,
      0.1950406,
      0.1932279,
      0.1914742,
      0.1897671,
      0.1881029,
      0.186478,
      0.1848976,
      0.1833434,
      0.1818115,
      0.1802983,
      0.1788015,
      0.1773149,
      0.1756719,
      0.1728733,
      0.170084,
      0.1673049,
      0.1645365,
      0.1617836,
      0.1590444,
      0.156318,
      0.1536049,
      0.150908,
      0.1482285,
      0.1455635,
      0.1429134,
      0.1402794,
      0.1376673,
      0.135072,
      0.1324942,
      0.1299347,
      0.127402,
      0.124892,
      0.1224047,
      0.1199413,
      0.1175099,
      0.1151125,
      0.1127459,
      0.1104118,
      0.1081159,
      0.1058705,
      0.1036662,
      0.101505,
      0.09938879,
      0.09734094,
      0.09534643,
      0.09340584,
      0.09152099,
      0.0897105,
      0.08797069,
      0.08629357,
      0.08468032,
      0.08314162,
      0.08168873,
      0.08030299,
      0.07898456,
      0.0777343,
      0.07657914,
      0.07548969,
      0.07446491,
      0.07350369,
      0.07262312,
      0.07180789,
      0.07104847,
      0.07034269,
      0.06969664,
      0.06910817,
      0.06856166,
      0.06805423,
      0.06758448,
      0.06715703,
      0.06675499,
      0.06637531,
      0.06601495,
      0.06567415,
      0.06534351,
      0.06501914,
      0.06469839,
      0.06437777,
      0.06405232,
      0.06372005,
      0.06337904,
      0.06302626,
      0.06265526,
      0.06226867,
      0.06186545,
      0.06144461,
      0.06099749,
      0.06052966,
      0.06004165,
      0.05922628,
      0.05779359,
      0.05642756,
      0.05512755,
      0.053899,
      0.0527555,
      0.05167319,
      0.05065057,
      0.04968608,
      0.04879968,
      0.04796595,
      0.04718154,
      0.04644429,
      0.04576383,
      0.04512837,
      0.04452933,
      0.04396423,
      0.04343535,
      0.04293949,
      0.04246622,
      0.0420131,
      0.04090469,
      0.03963676,
      0.03845151,
      0.03733189,
      0.03627187,
      0.03527056,
      0.0343387,
      0.03347402,
      0.03266229,
      0.03190188,
      0.03119464,
      0.03054984,
      0.02994778,
      0.02938636,
      0.02886341,
      0.02838827,
      0.02794576,
      0.0275316,
      0.02714353,
      0.0267839,
      0.02576788,
      0.02458736,
      0.02344097,
      0.02233101,
      0.02127388,
      0.02026099,
      0.01929155,
      0.01836661,
      0.01749238,
      0.0166773,
      0.01590893,
      0.01518727,
      0.01451218,
      0.01389596,
      0.01332993,
      0.01280818,
      0.01232986,
      0.01189621,
      0.01132294,
      0.01075228,
      0.01021127,
      0.009702383,
      0.009229173,
      0.008782339,
      0.008361082,
      0.007964595,
      0.007599626,
      0.007258174,
      0.006937826,
      0.006637732,
      0.006359906,
      0.006104162,
      0.005864896,
      0.005641244,
      0.005432346,
      0.00524199,
      0.005063754,
      0.004896563,
      0.004739593,
      0.004593668,
      0.004457112,
      0.004327373,
      0.004203738,
      0.004085629,
      0.003973414,
      0.003864494,
      0.003758334,
      0.003654421,
      0.003552491,
      0.003451606,
      0.00335122,
      0.003251049,
      0.003150803,
      0.003050055,
      0.002948753,
      0.00284684,
      0.002744278,
      0.002640889,
      0.002536919,
      0.002432553,
      0.002327917,
      0.002223177,
      0.002118704,
      0.002014731,
      0.001895474,
      0.001774428,
      0.001657905,
      0.00154644,
      0.001440852,
      0.001339655,
      0.001242816,
      0.001150428,
      0.001064084,
      0.0009817947,
      0.0009036205,
      0.0008267246,
      0.0007544178,
      0.0006868498,
      0.0006244143,
      0.0005675323,
      0.0005145441,
      0.0004652902,
      0.0004198998,
      0.0003790392,
      0.0003412034,
      0.0003062574,
      0.0002741562,
      0.0002456609,
      0.0002194535,
      0.0001954209,
      0.0001734504,
      0.0001541956,
      0.0001366451,
      0.0001206747,
      0.0001061927,
      9.358783e-05,
      8.225135e-05,
      7.201838e-05,
      6.281751e-05,
      5.486165e-05,
      4.781016e-05,
      4.132463e-05,
      3.575435e-05,
      3.067011e-05
    ),
    each = 2
  )

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line2.cat.y <-
  rep(
    c(
      0.0004024151,
      0.0004659952,
      0.0005373556,
      0.0006192823,
      0.0007138093,
      0.0008194876,
      0.0009371345,
      0.001070282,
      0.001222815,
      0.001391881,
      0.001578558,
      0.001786984,
      0.002023939,
      0.002284331,
      0.002569498,
      0.002883835,
      0.003238308,
      0.003624533,
      0.004044056,
      0.004500954,
      0.005011804,
      0.005563737,
      0.006158405,
      0.006798788,
      0.007508429,
      0.008268807,
      0.009081527,
      0.009948194,
      0.01089851,
      0.0119092,
      0.01298104,
      0.0141154,
      0.01534259,
      0.0166401,
      0.01800571,
      0.01944039,
      0.0209733,
      0.02258424,
      0.02426747,
      0.0260234,
      0.02787843,
      0.02981596,
      0.0318266,
      0.03391016,
      0.03608899,
      0.03835095,
      0.04068335,
      0.04308543,
      0.04557483,
      0.04814403,
      0.05077793,
      0.0534753,
      0.05624897,
      0.05909568,
      0.06199904,
      0.06495752,
      0.06797958,
      0.07106541,
      0.07419854,
      0.07737732,
      0.08060664,
      0.08388908,
      0.08720917,
      0.09056533,
      0.09395979,
      0.09739645,
      0.1008617,
      0.1043541,
      0.1078741,
      0.1114261,
      0.1149988,
      0.1185909,
      0.122202,
      0.1258361,
      0.1294844,
      0.133146,
      0.13682,
      0.1405098,
      0.1442088,
      0.1479164,
      0.1516319,
      0.1553572,
      0.1590884,
      0.1628247,
      0.1665658,
      0.1703124,
      0.1740623,
      0.1778149,
      0.1815698,
      0.185327,
      0.1890854,
      0.1928444,
      0.1966036,
      0.2003623,
      0.2041198,
      0.2078757,
      0.2116296,
      0.2153802,
      0.2191266,
      0.222869,
      0.2266069,
      0.2303382,
      0.2340621,
      0.2377791,
      0.2414888,
      0.2451888,
      0.2488776,
      0.2525568,
      0.256226,
      0.2598826,
      0.2635243,
      0.267154,
      0.270771,
      0.2743732,
      0.2779569,
      0.281526,
      0.2850803,
      0.2886174,
      0.2921319,
      0.2956676,
      0.3021868,
      0.308707,
      0.3152201,
      0.3217146,
      0.3281743,
      0.3345946,
      0.340968,
      0.3472866,
      0.3535314,
      0.3596876,
      0.3657607,
      0.3717444,
      0.3776327,
      0.3833997,
      0.3890387,
      0.3945617,
      0.3999646,
      0.4052433,
      0.4103662,
      0.4153381,
      0.4201734,
      0.4248699,
      0.4294253,
      0.4338031,
      0.4380195,
      0.442088,
      0.4460074,
      0.4497762,
      0.4533523,
      0.4567614,
      0.4600139,
      0.4631078,
      0.4660413,
      0.4687636,
      0.4713098,
      0.4736853,
      0.4758872,
      0.4779123,
      0.4796979,
      0.4812919,
      0.4826954,
      0.483905,
      0.484917,
      0.4856589,
      0.4861956,
      0.4865256,
      0.4866475,
      0.4865546,
      0.4861879,
      0.4856148,
      0.4848381,
      0.4838608,
      0.4826765,
      0.4812502,
      0.4796453,
      0.4778695,
      0.4759311,
      0.4738276,
      0.471551,
      0.4711101,
      0.4725971,
      0.4738902,
      0.4749874,
      0.4758392,
      0.4764524,
      0.4768659,
      0.4770802,
      0.4770742,
      0.4768084,
      0.4763498,
      0.475701,
      0.4748648,
      0.4737713,
      0.4724995,
      0.4710571,
      0.4694486,
      0.4676353,
      0.4656492,
      0.4635192,
      0.4612503,
      0.4588285,
      0.4562498,
      0.4535561,
      0.4507527,
      0.4478421,
      0.4447972,
      0.4416654,
      0.4384513,
      0.4361656,
      0.436046,
      0.4358001,
      0.4354021,
      0.4348393,
      0.4341475,
      0.4333264,
      0.4323555,
      0.4312131,
      0.4299415,
      0.4285411,
      0.4269976,
      0.4252812,
      0.4234399,
      0.4224721,
      0.4216215,
      0.4206578,
      0.4195831,
      0.4183995,
      0.4170641,
      0.4156271,
      0.4140917,
      0.4124603,
      0.410705,
      0.4088536,
      0.4069184,
      0.4049022,
      0.4031349,
      0.4020283,
      0.4012002,
      0.4015938,
      0.4023286,
      0.4029456,
      0.4034329,
      0.4038127,
      0.4040818,
      0.4042083,
      0.4041839,
      0.4040372,
      0.4037668,
      0.4033406,
      0.402756,
      0.4020462,
      0.4012117,
      0.4002241,
      0.3990868,
      0.3978341,
      0.3964685,
      0.3949673,
      0.3933393,
      0.3916155,
      0.3897999,
      0.3878765,
      0.3858562,
      0.3837643,
      0.3821008,
      0.3811327,
      0.3800312,
      0.378826,
      0.3775162,
      0.3760863,
      0.3745135,
      0.3728346,
      0.37105,
      0.3691497,
      0.3671076,
      0.3649655,
      0.3627254,
      0.3603833,
      0.3579132,
      0.3553582,
      0.3527219,
      0.3500052,
      0.347187,
      0.3443066,
      0.3435245,
      0.3434602,
      0.3433176,
      0.3431053,
      0.3428226,
      0.3424406,
      0.3419769,
      0.3414399,
      0.3408292,
      0.3401144,
      0.3393165,
      0.3384434,
      0.3374948,
      0.3364383,
      0.3352983,
      0.3340813,
      0.3327871,
      0.3313816,
      0.329892,
      0.3283238,
      0.3266771,
      0.3249159,
      0.3230712,
      0.3211476,
      0.3191454,
      0.3170291,
      0.3148327,
      0.3125607,
      0.310214,
      0.3077603,
      0.3052359,
      0.3026449,
      0.3002703,
      0.2980143,
      0.295697,
      0.2933191,
      0.2908596,
      0.2883395,
      0.2857644,
      0.2831356,
      0.2804395,
      0.2776882,
      0.2752737,
      0.2738134,
      0.2723303,
      0.2708318,
      0.2693186,
      0.2677905,
      0.2662433,
      0.2646831,
      0.2631098,
      0.2615236,
      0.2599186,
      0.2583002,
      0.2566685,
      0.2550235,
      0.2533598,
      0.2516816,
      0.24999,
      0.2482851,
      0.2465629,
      0.2448265,
      0.2434008,
      0.2431528,
      0.2428235,
      0.2424189,
      0.2419365,
      0.241346,
      0.2406555,
      0.2398756,
      0.2390043,
      0.2380114,
      0.2369006,
      0.235689,
      0.2343752,
      0.2329316,
      0.2327687,
      0.2328728,
      0.2329331,
      0.2329382,
      0.2328703,
      0.2327421,
      0.23255,
      0.2322824,
      0.2319119,
      0.2314603,
      0.2309243,
      0.2302941,
      0.2295298,
      0.228665,
      0.227792,
      0.2273463,
      0.2270514,
      0.227642,
      0.2281764,
      0.2286499,
      0.2290385,
      0.2293308,
      0.2295402,
      0.2296631,
      0.2296692,
      0.2295527,
      0.2293333,
      0.2290084,
      0.2285435,
      0.2279402,
      0.2272219,
      0.2263874,
      0.2254,
      0.2242693,
      0.2230201,
      0.2219295,
      0.2218155,
      0.2215552,
      0.2211677,
      0.2206652,
      0.2200453,
      0.2192602,
      0.2183362,
      0.2172884,
      0.2161161,
      0.2147719,
      0.2132877,
      0.2116803,
      0.2099503,
      0.2080546,
      0.2060279,
      0.2038872,
      0.2016347,
      0.1992336,
      0.1967188,
      0.1941062,
      0.1913989,
      0.1885685,
      0.1856469,
      0.182648,
      0.1795754,
      0.1764094,
      0.1731771,
      0.1698895,
      0.1665503,
      0.1631483,
      0.1597041,
      0.1562259,
      0.1527173,
      0.1491741,
      0.1456106,
      0.1420323,
      0.138442,
      0.1348421,
      0.1312404,
      0.1276401,
      0.1240436,
      0.1204583,
      0.1168867,
      0.1133299,
      0.1097901,
      0.1062791,
      0.1027946,
      0.09933642,
      0.09590633,
      0.09252023,
      0.08917178,
      0.0858597,
      0.08258558,
      0.07936912,
      0.07620029,
      0.07307697,
      0.07000059,
      0.0669944,
      0.06404488,
      0.06114912,
      0.0583084,
      0.05554909,
      0.05285423,
      0.05022021,
      0.04764805,
      0.04516652,
      0.04275538,
      0.04041038,
      0.03813222,
      0.03595096,
      0.03384357,
      0.03180524,
      0.02983624,
      0.02796672,
      0.02617156,
      0.02444561,
      0.02278863,
      0.02122956,
      0.01974227,
      0.01832143,
      0.01696636,
      0.01570363,
      0.01450725,
      0.01337201,
      0.01229685,
      0.01130508,
      0.01037206,
      0.009492924,
      0.008666349,
      0.007911917,
      0.007207295,
      0.00654817,
      0.005933098,
      0.005377807,
      0.004862984,
      0.004384968,
      0.003942334,
      0.003547173,
      0.00318352,
      0.002848415,
      0.002540553,
      0.002268831,
      0.002020634,
      0.00179367,
      0.001586824,
      0.001406368,
      0.001242759,
      0.001094305,
      0.0009637337,
      0.0008502333,
      0.0007473599,
      0.0006544882,
      0.0005722607,
      0.0005009712,
      0.000436842,
      0.0003794076,
      0.0003301612
    ),
    each = 2
  )

lmode.line2.dim.y <-
  rep(
    c(
      0.0003388559,
      0.0003897661,
      0.0004467307,
      0.0005134762,
      0.0005878494,
      0.0006703754,
      0.0007660825,
      0.0008769624,
      0.001004005,
      0.001147251,
      0.001305779,
      0.001480549,
      0.001675766,
      0.001895577,
      0.002136291,
      0.002398972,
      0.002685817,
      0.003007547,
      0.003356097,
      0.003732487,
      0.004137727,
      0.004584398,
      0.005065539,
      0.005579565,
      0.006127214,
      0.00671769,
      0.007350706,
      0.008019651,
      0.008724761,
      0.00947048,
      0.01026415,
      0.01109368,
      0.01195864,
      0.01285856,
      0.0138068,
      0.01478725,
      0.0157986,
      0.01683967,
      0.01791697,
      0.01902239,
      0.02015068,
      0.02130014,
      0.02247191,
      0.02366296,
      0.02486668,
      0.02608114,
      0.02730479,
      0.02853569,
      0.02976892,
      0.03100286,
      0.03223587,
      0.03346426,
      0.03468684,
      0.03590286,
      0.03756347,
      0.03965226,
      0.04180125,
      0.0440102,
      0.04629129,
      0.04864448,
      0.05105611,
      0.05377553,
      0.05674502,
      0.05981306,
      0.06298018,
      0.06625714,
      0.06967264,
      0.07318822,
      0.07680363,
      0.08052589,
      0.08438684,
      0.08834426,
      0.09239686,
      0.09654748,
      0.1008281,
      0.1051951,
      0.1096459,
      0.1141793,
      0.1188233,
      0.123536,
      0.1283138,
      0.1331528,
      0.13807,
      0.1430319,
      0.1480328,
      0.1530679,
      0.1581382,
      0.1632228,
      0.1683149,
      0.1734088,
      0.1784903,
      0.1835501,
      0.188583,
      0.1935828,
      0.1985222,
      0.2034019,
      0.2082203,
      0.2129718,
      0.2176197,
      0.2221712,
      0.2266312,
      0.2309949,
      0.2352208,
      0.2393195,
      0.2433034,
      0.2471694,
      0.2508754,
      0.2544323,
      0.2578604,
      0.2611584,
      0.2642877,
      0.267257,
      0.2700936,
      0.2727978,
      0.2753374,
      0.2777172,
      0.2799698,
      0.2840125,
      0.2885329,
      0.2929491,
      0.2972848,
      0.301539,
      0.305711,
      0.3097677,
      0.3137408,
      0.3176343,
      0.3214499,
      0.3251702,
      0.3288085,
      0.3323801,
      0.3358882,
      0.3393286,
      0.3427,
      0.3460234,
      0.3493023,
      0.3525401,
      0.3557276,
      0.3588849,
      0.3620147,
      0.3651192,
      0.3681946,
      0.3712474,
      0.3742809,
      0.3772953,
      0.380287,
      0.3832522,
      0.3861938,
      0.3891094,
      0.391995,
      0.3948324,
      0.3976282,
      0.4003779,
      0.4030765,
      0.4056951,
      0.4082378,
      0.4107038,
      0.4130868,
      0.4153585,
      0.4175042,
      0.4195378,
      0.4214529,
      0.4232317,
      0.4248261,
      0.4262748,
      0.4275726,
      0.4287144,
      0.4296299,
      0.4303667,
      0.43093,
      0.4313172,
      0.4314801,
      0.4314288,
      0.431196,
      0.4307819,
      0.430166,
      0.4293171,
      0.4282951,
      0.4271033,
      0.4257451,
      0.4241612,
      0.4224258,
      0.4205466,
      0.4185293,
      0.4163462,
      0.4140297,
      0.4116055,
      0.4090808,
      0.4064503,
      0.4037202,
      0.400923,
      0.4000229,
      0.4009087,
      0.4017647,
      0.4025684,
      0.4033114,
      0.4041307,
      0.4047848,
      0.4052591,
      0.4055557,
      0.4069637,
      0.4091551,
      0.4111393,
      0.4129388,
      0.4145613,
      0.416,
      0.4172009,
      0.4181587,
      0.4189108,
      0.4194546,
      0.4197619,
      0.4197905,
      0.4196102,
      0.4192236,
      0.4186313,
      0.4177591,
      0.4167021,
      0.4154675,
      0.4140626,
      0.4124473,
      0.4106779,
      0.4087805,
      0.4067654,
      0.4046238,
      0.4023812,
      0.4000704,
      0.4002491,
      0.4006426,
      0.4008988,
      0.4010118,
      0.4009527,
      0.4006971,
      0.4002801,
      0.3996995,
      0.3989532,
      0.3979796,
      0.3968319,
      0.3962804,
      0.3972491,
      0.3981011,
      0.3988282,
      0.3993909,
      0.3998365,
      0.4001658,
      0.4003795,
      0.4004287,
      0.4003668,
      0.4001969,
      0.3999209,
      0.3995044,
      0.3989828,
      0.3983676,
      0.3976617,
      0.3968438,
      0.3959336,
      0.3949479,
      0.3938901,
      0.3927494,
      0.3915337,
      0.3902618,
      0.388937,
      0.3875559,
      0.3861188,
      0.3846436,
      0.3831331,
      0.3815878,
      0.3800049,
      0.3783988,
      0.3767716,
      0.3751254,
      0.3734568,
      0.3717759,
      0.3700839,
      0.3683823,
      0.3684939,
      0.3687258,
      0.3688546,
      0.3688657,
      0.3687414,
      0.3685186,
      0.3681989,
      0.3677724,
      0.3672226,
      0.3665864,
      0.3658664,
      0.3650569,
      0.3641434,
      0.3631595,
      0.362108,
      0.3609865,
      0.3597826,
      0.3585247,
      0.3572153,
      0.3559658,
      0.3553696,
      0.3546971,
      0.3539448,
      0.3530817,
      0.3521086,
      0.3510401,
      0.3498736,
      0.3485743,
      0.3471492,
      0.3456173,
      0.3439778,
      0.3421965,
      0.3402867,
      0.3382707,
      0.3361499,
      0.3345905,
      0.3329641,
      0.3312417,
      0.3294155,
      0.3275112,
      0.32553,
      0.3247319,
      0.3250051,
      0.3251574,
      0.3251995,
      0.3251421,
      0.3249825,
      0.3246777,
      0.3242457,
      0.3237003,
      0.3230399,
      0.322219,
      0.3212626,
      0.3201867,
      0.3189909,
      0.317631,
      0.3161376,
      0.3145275,
      0.3128022,
      0.310922,
      0.3089208,
      0.3068151,
      0.3046079,
      0.3022674,
      0.2998274,
      0.2973031,
      0.2946982,
      0.2919914,
      0.2892127,
      0.2863746,
      0.2834815,
      0.2805225,
      0.2775211,
      0.2744866,
      0.271423,
      0.268329,
      0.2652196,
      0.2626777,
      0.2611519,
      0.2596218,
      0.2580846,
      0.2565382,
      0.2549825,
      0.253416,
      0.2518332,
      0.2502299,
      0.2486073,
      0.2469632,
      0.245289,
      0.2435784,
      0.2418356,
      0.2400583,
      0.2382356,
      0.2363596,
      0.2344391,
      0.2324724,
      0.2304481,
      0.2283576,
      0.226215,
      0.2240194,
      0.2217615,
      0.2194331,
      0.2170522,
      0.2146195,
      0.2121288,
      0.2095741,
      0.2069746,
      0.2043323,
      0.2016446,
      0.1989086,
      0.1961416,
      0.1933461,
      0.1905226,
      0.1876716,
      0.1848053,
      0.1819262,
      0.1790364,
      0.176139,
      0.1732398,
      0.1703405,
      0.1674434,
      0.1645527,
      0.1616685,
      0.1587913,
      0.1559224,
      0.1530657,
      0.1502762,
      0.1484616,
      0.1466359,
      0.1447978,
      0.1429457,
      0.1410693,
      0.1391711,
      0.1372508,
      0.1353067,
      0.1333244,
      0.1313111,
      0.1292676,
      0.1271927,
      0.1250704,
      0.1229123,
      0.1207203,
      0.1184942,
      0.1162193,
      0.1139101,
      0.1115692,
      0.1091976,
      0.1067846,
      0.1043449,
      0.1018817,
      0.09939661,
      0.09688531,
      0.09435971,
      0.0918229,
      0.08927717,
      0.0867251,
      0.08417355,
      0.08162513,
      0.07908224,
      0.07655425,
      0.07404154,
      0.07154597,
      0.06906971,
      0.06662786,
      0.064214,
      0.0618292,
      0.05947519,
      0.05717127,
      0.05490492,
      0.05267654,
      0.0507662,
      0.04986959,
      0.04894601,
      0.04799533,
      0.04701584,
      0.04599861,
      0.04495515,
      0.04388604,
      0.0427919,
      0.04166374,
      0.04051376,
      0.03934357,
      0.03815449,
      0.03694283,
      0.03571661,
      0.0344791,
      0.0332321,
      0.03197663,
      0.03071789,
      0.029459,
      0.02820203,
      0.02695101,
      0.02571073,
      0.02448205,
      0.02326693,
      0.02207032,
      0.02089924,
      0.01975034,
      0.01862522,
      0.01752763,
      0.016469,
      0.01544054,
      0.01444328,
      0.01347834,
      0.01256252,
      0.01168145,
      0.01083552,
      0.01002508,
      0.009264483,
      0.008542198,
      0.007855495,
      0.007204147,
      0.006598689,
      0.006032035,
      0.005498505,
      0.004997444,
      0.004535476,
      0.004109975,
      0.003713164,
      0.003344143,
      0.003006211,
      0.002700338,
      0.002417759,
      0.002157503,
      0.001920454,
      0.001709916,
      0.001517195,
      0.001341383,
      0.001181886,
      0.001043096,
      0.0009171882,
      0.000803398,
      0.0007009674,
      0.0006127939,
      0.0005339796,
      0.0004634012,
      0.0004004742,
      0.0003465926,
      0.0002993128
    ),
    each = 2
  )

lmode.vline1.cat.x <- c(-0.01215921,-0.01215921)
lmode.vline1.cat.y <- c(0.0001,0.3563374)

lmode.vline2.cat.x <- c(0.2152464,0.2152464)
lmode.vline2.cat.y <- c(0.0001,0.3636451)

lmo.emp <- data.frame(lmode.empcurve.x, lmode.empcurve.y)
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.x"] <- "xvalues"
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.y"] <- "yvalues"



# Plots ---------------------------------------------------------

#MAMBAC

mambac.plot.cat <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.cat.x,
                                        y = mambac.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = mambac.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = mambac.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Categorical comparison data",
          subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  scale_y_continuous(breaks=seq(round(mambac.y.range[1], digits = 1),
                                round(mambac.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

mambac.plot.dim <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.dim.x,
                                        y = mambac.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = mambac.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = mambac.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Dimensional comparison data", subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#MAXEIG

maxeig.plot.cat <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.cat.x,
                                        y = maxeig.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = maxeig.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = maxeig.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  scale_y_continuous(breaks=seq(round(maxeig.y.range[1], digits = 1),
                                round(maxeig.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

maxeig.plot.dim <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.dim.x,
                                        y = maxeig.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = maxeig.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = maxeig.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  ) 
#L-Mode

lmode.plot.cat <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.cat.x, y = lmode.polygon.cat.y), fill = "#0b5db5") +
  geom_line(aes(y = lmode.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = lmode.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  scale_y_continuous(breaks=seq(round(lmode.y.range[1], digits = 1),
                                round(lmode.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

lmode.plot.dim <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.dim.x, y = lmode.polygon.dim.y), fill = "#5aa007") +
  geom_line(aes(y = lmode.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = lmode.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#Grid
grid.title <- textGrob(expression(bold("HGSHS:A subscales ("~bolditalic("a priori")~"base rate: .15 )")), gp = gpar(fontsize = 14, fontfamily = "Arial"))
grid.arrange(mambac.plot.cat, mambac.plot.dim, maxeig.plot.cat, maxeig.plot.dim, lmode.plot.cat, lmode.plot.dim,
             nrow = 3,
             top=grid.title)


# Suggestibility subscales; p = .10 --------------------------------------
# MAMBAC ------------------------------------------------------------------

mambac.empcurve.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)
mambac.empcurve.y <- c(0.2292449,0.2192762,0.2144773,0.2126005,0.2100936,0.2057979,0.2084946,0.2080038,0.2092769,0.2094957,0.2060984,0.2076548,0.2103101,0.2114907,0.2050027,0.2020279,0.1988059,0.2005859,0.1990418,0.1988522,0.1961747,0.1951831,0.1943646,0.1996629,0.202197,0.2024106,0.2059006,0.210348,0.2100039,0.21047,0.2154429,0.218485,0.2251188,0.2317541,0.2394182,0.2425859,0.2468407,0.2504697,0.2534494,0.2561029,0.2643259,0.2729222,0.2846569,0.2980858,0.3189283,0.3332559,0.3436559,0.363785,0.3937016,0.3936345)
mambac.y.range <- c(0.05862575,0.5598377)

#Duplicate empirical values to allow the simulated polygon to be more smooth
mambac.empcurve.x <- rep(mambac.empcurve.x, each = 2)
mambac.empcurve.y <- rep(mambac.empcurve.y, each = 2)

mambac.polygon.cat.x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1)
mambac.polygon.cat.y <- c(0.1912752,0.1843605,0.1844734,0.1856069,0.1855963,0.1856532,0.188821,0.1909647,0.1953201,0.1969958,0.1994994,0.2016106,0.2040194,0.20483,0.2078837,0.2094273,0.2091708,0.2105071,0.2106959,0.2133691,0.2153858,0.2191114,0.2225859,0.227253,0.2320878,0.2377943,0.2430907,0.2497845,0.2570953,0.2638631,0.2686996,0.2767748,0.2869203,0.2944447,0.3030103,0.3086155,0.3129358,0.3170393,0.324325,0.3269271,0.3368286,0.3485453,0.3656152,0.3865795,0.4064866,0.4253938,0.433695,0.4431199,0.4542899,0.4532704,0.3773694,0.3788716,0.3680657,0.3566958,0.3452275,0.3325237,0.3113576,0.2950267,0.2848154,0.2749688,0.2680171,0.2631384,0.2601925,0.25738,0.2543197,0.2475781,0.2407097,0.2322037,0.2236077,0.2195296,0.2110914,0.2054295,0.2010534,0.1973347,0.1905906,0.1876063,0.1854963,0.1816312,0.1766339,0.1735802,0.171306,0.1693934,0.1679339,0.1654173,0.1633479,0.1620664,0.1599844,0.1598955,0.1591748,0.1548742,0.154425,0.1533781,0.1519811,0.1497558,0.1460563,0.1442376,0.1443101,0.1419483,0.1352143,0.1392796)

mambac.polygon.dim.x <- mambac.polygon.cat.x
mambac.polygon.dim.y <- c(0.2237113,0.2180285,0.2156479,0.2165968,0.2130975,0.2140561,0.2139027,0.2142418,0.2158891,0.2168927,0.2169869,0.2152771,0.2160177,0.2168897,0.219542,0.2182975,0.2184924,0.2184053,0.2180667,0.220507,0.2200546,0.2212129,0.223604,0.2278786,0.2300192,0.2336971,0.2378896,0.2414429,0.2471194,0.2515766,0.258583,0.2658234,0.2728032,0.2811247,0.2877635,0.2913322,0.2910254,0.2911901,0.2926744,0.2947231,0.2997042,0.3084249,0.3178044,0.3334948,0.3448546,0.3580124,0.3646376,0.3700662,0.3735591,0.3748798,0.2886088,0.2969367,0.2972848,0.2955571,0.2917485,0.2853149,0.2737856,0.2644676,0.2549809,0.2467086,0.2423857,0.2392831,0.2378599,0.2369568,0.2366877,0.232538,0.2291956,0.2215209,0.2153897,0.2088892,0.2046454,0.2006936,0.1972047,0.1966888,0.1958402,0.1930974,0.1898679,0.1890406,0.1884516,0.1866466,0.1850311,0.1850389,0.1842522,0.1847424,0.1864952,0.1879382,0.1864977,0.1848358,0.186542,0.1858007,0.1841385,0.1861302,0.1813085,0.1788601,0.1759026,0.1737487,0.1738964,0.1723541,0.1717088,0.1720183)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line1.cat.y <- rep(c(0.07616859,0.07645349,0.08334866,0.08866842,0.09686062,0.1008852,0.104604,0.1051714,0.1085503,0.1085526,0.1090972,0.1064135,0.1087069,0.1086177,0.1133932,0.1150842,0.1165919,0.115342,0.119798,0.1201141,0.1232453,0.1234927,0.1257903,0.1262446,0.1314219,0.1358514,0.1409523,0.1424967,0.1450119,0.1518091,0.1558122,0.1610081,0.1662263,0.1673217,0.1701666,0.1713875,0.1757847,0.1716093,0.1741048,0.1767189,0.1818255,0.1876306,0.193145,0.2051335,0.2197019,0.2388199,0.2489338,0.2542984,0.2725966,0.250956), each = 2)

mambac.line1.dim.y <- rep(c(0.05862575,0.06717818,0.08451669,0.08902512,0.09348849,0.09373713,0.09748763,0.1048435,0.1079211,0.1128739,0.118399,0.1216387,0.1217007,0.1187064,0.1193774,0.1215554,0.1213778,0.1178603,0.120842,0.1180036,0.1175693,0.1205951,0.1229532,0.1235957,0.125093,0.1285299,0.1335991,0.1391975,0.1430444,0.1454028,0.1532417,0.158278,0.1639316,0.1707262,0.1710803,0.1704368,0.1710452,0.1701055,0.1683117,0.1699272,0.1699839,0.1740253,0.1847825,0.1822134,0.1808617,0.1779211,0.1856654,0.1877635,0.1804866,0.178421), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
mambac.line2.cat.y <- rep(c(0.2424978,0.224809,0.2338724,0.2290734,0.2278779,0.2338632,0.2356181,0.2406169,0.2454385,0.2491968,0.2515713,0.2588432,0.2617196,0.2680506,0.2697272,0.2711586,0.2725175,0.2767083,0.2803845,0.2794767,0.2779154,0.2828663,0.2868293,0.2903776,0.2967146,0.3020515,0.3095577,0.3152752,0.3259788,0.3374181,0.3480239,0.3586775,0.3727294,0.3811517,0.3894954,0.3940486,0.397761,0.401293,0.408572,0.4192696,0.431908,0.4474272,0.4734168,0.4975767,0.5225485,0.5245911,0.5268983,0.5489573,0.5598377,0.5540984), each = 2)

mambac.line2.dim.y <- rep(c(0.2763473,0.2761072,0.2845878,0.2858162,0.2836237,0.2817967,0.2789929,0.2787602,0.2744511,0.2822766,0.2836924,0.2884168,0.2929553,0.2976511,0.2942966,0.2949934,0.2972064,0.297814,0.2976106,0.2973379,0.30009,0.3003951,0.3043887,0.3053118,0.3023161,0.3046959,0.3111528,0.3138703,0.3205344,0.3294376,0.3368081,0.3448629,0.3511797,0.3580818,0.3709324,0.3717959,0.3679691,0.3688362,0.3740818,0.3804452,0.3833967,0.3901707,0.4028073,0.4298899,0.4322252,0.4412816,0.4399846,0.4427782,0.4569094,0.4629185), each = 2)

mamb.emp <- data.frame(mambac.empcurve.x, mambac.empcurve.y)
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.x"] <- "xvalues"
names(mamb.emp)[names(mamb.emp) == "mambac.empcurve.y"] <- "yvalues"


# MAXEIG ------------------------------------------------------------------

maxeig.empcurve.x <- c(-0.9966096,-0.9469235,-0.9046903,-0.8754229,-0.8358321,-0.8002005,-0.7730312,-0.7557992,-0.7162084,-0.6766177,-0.6370269,-0.5974362,-0.5548959,-0.5049817,-0.4653909,-0.4297592,-0.3901685,-0.353062,-0.3383143,-0.3235666,-0.3088189,-0.2940712,-0.282273,-0.2719496,-0.2572019,-0.243929,-0.2291813,-0.2144336,-0.1996858,-0.1849381,-0.1231402,-0.04231268,0.04736342,0.1326152,0.2134427,0.2861874,0.3670149,0.4478424,0.5286699,0.6094974,0.6432746,0.6580223,0.6972679,0.7887596,0.8802513,0.9625938,1.091199,1.223927,1.356655,1.489384)
maxeig.empcurve.y <- c(0.1415029,0.1459383,0.1392974,0.1345531,0.1374021,0.1387434,0.1330988,0.1281651,0.1287427,0.1287714,0.1243269,0.1220841,0.1288351,0.1291892,0.1254458,0.1321098,0.1315375,0.1289015,0.1309998,0.1354513,0.1372789,0.1370821,0.1401328,0.1378786,0.1432502,0.1381576,0.1433227,0.1393582,0.1378605,0.1402092,0.1429857,0.1451735,0.1524007,0.1598572,0.1597182,0.1606444,0.163251,0.1723198,0.1811244,0.1745771,0.1707309,0.1718957,0.16528,0.1703093,0.1732796,0.1753757,0.1913427,0.1941044,0.1976606,0.1952715)
maxeig.y.range <- c(0.07286874,0.4274781)

#Duplicate empirical values to allow the simulated polygon to be more smooth
maxeig.empcurve.x <- rep(maxeig.empcurve.x, each = 2)
maxeig.empcurve.y <- rep(maxeig.empcurve.y, each = 2)

maxeig.polygon.cat.x <- c(-0.9966096,-0.9469235,-0.9046903,-0.8754229,-0.8358321,-0.8002005,-0.7730312,-0.7557992,-0.7162084,-0.6766177,-0.6370269,-0.5974362,-0.5548959,-0.5049817,-0.4653909,-0.4297592,-0.3901685,-0.353062,-0.3383143,-0.3235666,-0.3088189,-0.2940712,-0.282273,-0.2719496,-0.2572019,-0.243929,-0.2291813,-0.2144336,-0.1996858,-0.1849381,-0.1231402,-0.04231268,0.04736342,0.1326152,0.2134427,0.2861874,0.3670149,0.4478424,0.5286699,0.6094974,0.6432746,0.6580223,0.6972679,0.7887596,0.8802513,0.9625938,1.091199,1.223927,1.356655,1.489384,1.489384,1.356655,1.223927,1.091199,0.9625938,0.8802513,0.7887596,0.6972679,0.6580223,0.6432746,0.6094974,0.5286699,0.4478424,0.3670149,0.2861874,0.2134427,0.1326152,0.04736342,-0.04231268,-0.1231402,-0.1849381,-0.1996858,-0.2144336,-0.2291813,-0.243929,-0.2572019,-0.2719496,-0.282273,-0.2940712,-0.3088189,-0.3235666,-0.3383143,-0.353062,-0.3901685,-0.4297592,-0.4653909,-0.5049817,-0.5548959,-0.5974362,-0.6370269,-0.6766177,-0.7162084,-0.7557992,-0.7730312,-0.8002005,-0.8358321,-0.8754229,-0.9046903,-0.9469235,-0.9966096)
maxeig.polygon.cat.y <- c(0.1202215,0.1220715,0.1220136,0.121563,0.1219023,0.1234141,0.1235753,0.1245651,0.1253392,0.1257578,0.1283181,0.1275594,0.1263152,0.1281689,0.1296652,0.128939,0.1332773,0.1357782,0.1381191,0.1374216,0.136034,0.1371076,0.1366797,0.1371306,0.1348651,0.1381597,0.1382849,0.1399122,0.1407184,0.1447459,0.1499088,0.1574056,0.1655497,0.1723669,0.1846111,0.1921289,0.2035165,0.2123107,0.2202637,0.2313012,0.2354404,0.2374942,0.2404512,0.249543,0.2581868,0.2676985,0.2790231,0.2859796,0.2968087,0.3009483,0.2455063,0.2387461,0.2271466,0.2173817,0.2112696,0.2019421,0.1991534,0.1954584,0.1919837,0.191611,0.1879572,0.1807135,0.1779629,0.1713513,0.1625001,0.1535837,0.1486395,0.136693,0.129909,0.124402,0.1195091,0.1169533,0.1142889,0.1153416,0.1138993,0.113649,0.109891,0.1091394,0.1114141,0.1133303,0.1122496,0.1137751,0.112661,0.1120472,0.1106116,0.1122729,0.1101336,0.1085328,0.1063341,0.1054463,0.1035314,0.1049734,0.1025584,0.1019337,0.1025473,0.1025586,0.1025038,0.1026317,0.1024355,0.1028857)

maxeig.polygon.dim.x <- maxeig.polygon.cat.x
maxeig.polygon.dim.y <- c(0.1455629,0.1462861,0.1459563,0.1456019,0.1487208,0.1492617,0.1483652,0.1484303,0.1502583,0.1495564,0.1512471,0.153016,0.1544588,0.1539062,0.1523613,0.1513439,0.1538048,0.1542808,0.1526442,0.1541199,0.1556821,0.1565186,0.1562116,0.1589413,0.1561282,0.1581834,0.1578581,0.1603573,0.1570582,0.1591396,0.161646,0.1642198,0.1670553,0.1676163,0.1700949,0.1703913,0.1719311,0.1727244,0.1755202,0.1757802,0.1759192,0.1750695,0.1772011,0.1795162,0.183241,0.183486,0.1859112,0.1844231,0.181808,0.1784546,0.1362672,0.140225,0.1454011,0.1439301,0.1442298,0.1432086,0.1401406,0.1388986,0.1393679,0.1382007,0.138828,0.1414635,0.1427956,0.1428092,0.1430798,0.1412795,0.1417304,0.1415097,0.1387706,0.1361736,0.1371014,0.1366119,0.1354426,0.1361521,0.1363888,0.1358569,0.1337312,0.1349639,0.1338762,0.1334848,0.132416,0.1331941,0.1316565,0.130208,0.1295557,0.1308982,0.1285261,0.1289682,0.1255202,0.1243559,0.1217543,0.1227452,0.1242933,0.1214646,0.1217614,0.1228326,0.1213801,0.1214393,0.120333,0.1180152)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line1.cat.y <- rep(c(0.07815586,0.08204698,0.07601688,0.07561639,0.07590105,0.07286874,0.07464598,0.07415471,0.07861941,0.08061215,0.08542068,0.08646273,0.08265264,0.08137907,0.08576597,0.08270539,0.08520368,0.08964661,0.09333967,0.09157949,0.09102755,0.0949763,0.09611256,0.09028737,0.09064322,0.09270383,0.09311715,0.09209681,0.09274111,0.0968348,0.09997821,0.1071731,0.1128413,0.116629,0.1233123,0.1292347,0.1314716,0.1260026,0.1345915,0.1508121,0.1442347,0.1404294,0.135804,0.1479,0.1496287,0.1505121,0.1591411,0.1622398,0.1729551,0.175495), each = 2)

maxeig.line1.dim.y <- rep(c(0.09092749,0.09453679,0.09837469,0.1001329,0.09808936,0.09563426,0.09313657,0.09536056,0.09963814,0.09791048,0.1016968,0.0969926,0.09420945,0.09865394,0.09857057,0.098477,0.1011509,0.100859,0.09634005,0.09733011,0.09354062,0.09730269,0.1023085,0.1038037,0.105258,0.1065944,0.1101221,0.1109956,0.1020802,0.10044,0.09882359,0.103373,0.0980194,0.1012765,0.1064735,0.1095735,0.110887,0.1079682,0.1007561,0.09418008,0.09287816,0.09908957,0.1003516,0.09696593,0.1053002,0.1028652,0.1032009,0.1024764,0.09948704,0.09404864), each = 2)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
maxeig.line2.cat.y <- rep(c(0.1423363,0.1414009,0.1458549,0.1470296,0.1436427,0.1468498,0.1507238,0.1585642,0.1541203,0.1588423,0.1548833,0.1546418,0.1552125,0.154305,0.1550354,0.1576135,0.1646649,0.1624771,0.1643921,0.1703161,0.1743818,0.1722141,0.1676624,0.1684426,0.1705674,0.1690118,0.1695011,0.1675639,0.1731225,0.1727921,0.1843247,0.1939909,0.2114079,0.2243231,0.2351163,0.254531,0.2795403,0.2874032,0.3007022,0.3101714,0.3128997,0.3085549,0.3211865,0.3458469,0.3601753,0.3677441,0.3777672,0.3969691,0.4170468,0.4274781), each = 2)

maxeig.line2.dim.y <- rep(c(0.1804977,0.177778,0.175889,0.178145,0.1819103,0.1884415,0.192268,0.1851564,0.1874001,0.1886255,0.1919185,0.1819307,0.1879152,0.1860297,0.1917686,0.1929486,0.1962845,0.1989961,0.1976087,0.1965151,0.194275,0.1929342,0.1881394,0.1938599,0.1976375,0.1972338,0.1987696,0.2010341,0.2071785,0.2110399,0.2133606,0.2164874,0.2195043,0.219638,0.2167276,0.212564,0.2133408,0.208707,0.2108165,0.2111121,0.2173838,0.2205083,0.2276915,0.2316814,0.235004,0.2421944,0.2425441,0.2472696,0.2485121,0.2492476), each = 2)

maxe.emp <- data.frame(maxeig.empcurve.x, maxeig.empcurve.y)
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.x"] <- "xvalues"
names(maxe.emp)[names(maxe.emp) == "maxeig.empcurve.y"] <- "yvalues"

# L-Mode ------------------------------------------------------------------
lmode.empcurve.x <-
  c(
    -2.943166,
    -2.930532,
    -2.917898,
    -2.905265,
    -2.892631,
    -2.879997,
    -2.867364,
    -2.85473,
    -2.842096,
    -2.829463,
    -2.816829,
    -2.804195,
    -2.791562,
    -2.778928,
    -2.766294,
    -2.753661,
    -2.741027,
    -2.728394,
    -2.71576,
    -2.703126,
    -2.690493,
    -2.677859,
    -2.665225,
    -2.652592,
    -2.639958,
    -2.627324,
    -2.614691,
    -2.602057,
    -2.589423,
    -2.57679,
    -2.564156,
    -2.551522,
    -2.538889,
    -2.526255,
    -2.513622,
    -2.500988,
    -2.488354,
    -2.475721,
    -2.463087,
    -2.450453,
    -2.43782,
    -2.425186,
    -2.412552,
    -2.399919,
    -2.387285,
    -2.374651,
    -2.362018,
    -2.349384,
    -2.33675,
    -2.324117,
    -2.311483,
    -2.29885,
    -2.286216,
    -2.273582,
    -2.260949,
    -2.248315,
    -2.235681,
    -2.223048,
    -2.210414,
    -2.19778,
    -2.185147,
    -2.172513,
    -2.159879,
    -2.147246,
    -2.134612,
    -2.121978,
    -2.109345,
    -2.096711,
    -2.084077,
    -2.071444,
    -2.05881,
    -2.046177,
    -2.033543,
    -2.020909,
    -2.008276,
    -1.995642,
    -1.983008,
    -1.970375,
    -1.957741,
    -1.945107,
    -1.932474,
    -1.91984,
    -1.907206,
    -1.894573,
    -1.881939,
    -1.869305,
    -1.856672,
    -1.844038,
    -1.831405,
    -1.818771,
    -1.806137,
    -1.793504,
    -1.78087,
    -1.768236,
    -1.755603,
    -1.742969,
    -1.730335,
    -1.717702,
    -1.705068,
    -1.692434,
    -1.679801,
    -1.667167,
    -1.654533,
    -1.6419,
    -1.629266,
    -1.616633,
    -1.603999,
    -1.591365,
    -1.578732,
    -1.566098,
    -1.553464,
    -1.540831,
    -1.528197,
    -1.515563,
    -1.50293,
    -1.490296,
    -1.477662,
    -1.465029,
    -1.452395,
    -1.439761,
    -1.427128,
    -1.414494,
    -1.40186,
    -1.389227,
    -1.376593,
    -1.36396,
    -1.351326,
    -1.338692,
    -1.326059,
    -1.313425,
    -1.300791,
    -1.288158,
    -1.275524,
    -1.26289,
    -1.250257,
    -1.237623,
    -1.224989,
    -1.212356,
    -1.199722,
    -1.187088,
    -1.174455,
    -1.161821,
    -1.149188,
    -1.136554,
    -1.12392,
    -1.111287,
    -1.098653,
    -1.086019,
    -1.073386,
    -1.060752,
    -1.048118,
    -1.035485,
    -1.022851,
    -1.010217,
    -0.9975838,
    -0.9849501,
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  )
lmode.empcurve.y <-
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  )
lmode.y.range <- c(3.05591e-05,0.4376128)

lmode.empcurve.x <- rep(lmode.empcurve.x, each = 2)
lmode.empcurve.y <- rep(lmode.empcurve.y, each = 2)

lmode.polygon.cat.x <-
  c(
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                         lmode.polygon.cat.y <-
                           c(
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                             0.000217128,
                             0.0002521735,
                             0.0002918261,
                             0.0003362939,
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                             0.001083715,
                             0.001221923,
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                             0.002430058,
                             0.002688637,
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                             0.0043142,
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                             0.005136841,
                             0.005583874,
                             0.006054156,
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                             0.008808415,
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                             0.01007701,
                             0.01074335,
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                             0.01288468,
                             0.01363791,
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                             0.01846111,
                             0.01938606,
                             0.02027211,
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                             0.02206751,
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                             0.0276719,
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                             0.03141102,
                             0.03259496,
                             0.03358385,
                             0.03460852,
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                             0.03690495,
                             0.03815015,
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                             0.04303034,
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                             0.07604778,
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                             0.08424715,
                             0.0867446,
                             0.08946556,
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                             0.1074836,
                             0.1107763,
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                             0.1273053,
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                             0.1822566,
                             0.1868992,
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                             0.2010673,
                             0.205852,
                             0.2106524,
                             0.2154636,
                             0.220277,
                             0.2245739,
                             0.2278688,
                             0.2328181,
                             0.2374189,
                             0.2410969,
                             0.2445113,
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                             0.251693,
                             0.2550788,
                             0.2583736,
                             0.2615883,
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                             0.2690444,
                             0.2723581,
                             0.275337,
                             0.2780329,
                             0.2807502,
                             0.2836105,
                             0.286341,
                             0.288967,
                             0.2923064,
                             0.2956125,
                             0.2983417,
                             0.3013428,
                             0.305406,
                             0.3093752,
                             0.3124341,
                             0.3161382,
                             0.3193435,
                             0.3226457,
                             0.3258614,
                             0.328489,
                             0.3315068,
                             0.3344406,
                             0.3356464,
                             0.3362297,
                             0.3386882,
                             0.3410436,
                             0.3433211,
                             0.3452341,
                             0.347115,
                             0.348966,
                             0.3507907,
                             0.3525935,
                             0.3540875,
                             0.3544786,
                             0.3556873,
                             0.3567066,
                             0.3582621,
                             0.3597912,
                             0.3617498,
                             0.3636205,
                             0.3650635,
                             0.3668747,
                             0.3687471,
                             0.3697857,
                             0.3710157,
                             0.3724621,
                             0.3737224,
                             0.3746203,
                             0.3746252,
                             0.3751411,
                             0.3763528,
                             0.3771267,
                             0.3786985,
                             0.3795326,
                             0.3809885,
                             0.3821625,
                             0.3828017,
                             0.3816246,
                             0.3825221,
                             0.3813655,
                             0.3808382,
                             0.3799312,
                             0.3805659,
                             0.3815592,
                             0.3825187,
                             0.383568,
                             0.3839597,
                             0.3842156,
                             0.3841052,
                             0.3828715,
                             0.3829677,
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                             0.3820631,
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                             0.3803176,
                             0.3804765,
                             0.3803326,
                             0.3809865,
                             0.3822336,
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                             0.3805503,
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                             0.3799287,
                             0.3795032,
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                             0.3764671,
                             0.3754822,
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                             0.3613622,
                             0.3604285,
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                             0.355152,
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                             0.3531297,
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                             0.351533,
                             0.3510175,
                             0.3506581,
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                             0.3443302,
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                             0.3384586,
                             0.3370967,
                             0.3355285,
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                             0.3325332,
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                             0.3290293,
                             0.3270663,
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                             0.3201279,
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                             0.3055854,
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                             0.2976021,
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                             0.1796995,
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                             0.1866445,
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                             0.1902312,
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                             0.1939523,
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                             0.2077078,
                             0.2111771,
                             0.2146737,
                             0.2181933,
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                             0.3459644,
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                             0.3458857,
                             0.3453351,
                             0.3450429,
                             0.3452061,
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                             0.3460058,
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                             0.3439905,
                             0.3432696,
                             0.3427201,
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                             0.3419682,
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                             0.3415224,
                             0.339559,
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                             0.3366729,
                             0.3363756,
                             0.3355681,
                             0.3350148,
                             0.3338495,
                             0.3330155,
                             0.3328458,
                             0.3313467,
                             0.3300944,
                             0.329054,
                             0.3272119,
                             0.3251254,
                             0.3231089,
                             0.3207925,
                             0.3186143,
                             0.3176812,
                             0.3163768,
                             0.3148636,
                             0.3132052,
                             0.3103844,
                             0.3084238,
                             0.3050516,
                             0.3008466,
                             0.2970028,
                             0.2942076,
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                             0.290775,
                             0.287347,
                             0.2846422,
                             0.2817464,
                             0.2781815,
                             0.2756696,
                             0.2734447,
                             0.2702399,
                             0.2673585,
                             0.264412,
                             0.2621114,
                             0.2597129,
                             0.2570374,
                             0.2542676,
                             0.2515334,
                             0.2486761,
                             0.2451115,
                             0.241689,
                             0.2382831,
                             0.2352614,
                             0.2322082,
                             0.2291251,
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                             0.2217991,
                             0.2170591,
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                             0.2075874,
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                             0.1992425,
                             0.1961174,
                             0.1932137,
                             0.1902755,
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                             0.08136374,
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                             0.07077633,
                             0.06846067,
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                             0.05682163,
                             0.05528012,
                             0.05380344,
                             0.05200785,
                             0.05022803,
                             0.04852194,
                             0.04700603,
                             0.04508796,
                             0.04350603,
                             0.04178082,
                             0.04027398,
                             0.03887448,
                             0.03744891,
                             0.03604072,
                             0.03473126,
                             0.03330799,
                             0.0320406,
                             0.03090109,
                             0.02949108,
                             0.02834899,
                             0.0271332,
                             0.02601625,
                             0.02508044,
                             0.0242112,
                             0.02323056,
                             0.02247173,
                             0.02168692,
                             0.02088372,
                             0.02012938,
                             0.01920802,
                             0.01834639,
                             0.01749794,
                             0.01675297,
                             0.01610853,
                             0.01532936,
                             0.01454902,
                             0.01382993,
                             0.0131874,
                             0.01247874,
                             0.01181237,
                             0.01113693,
                             0.01051576,
                             0.009867674,
                             0.009243789,
                             0.008631739,
                             0.008127193,
                             0.007589326,
                             0.007097969,
                             0.006627446,
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                             0.005771404,
                             0.005377894,
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                             0.004561317,
                             0.004201359,
                             0.003865613,
                             0.003548617,
                             0.00324965,
                             0.002971312,
                             0.002713058,
                             0.002471375,
                             0.002245107,0.002034819,0.001842709,0.001664716,0.001499434,0.001346371,0.001208267,0.001082119,0.0009659988,0.0008594377,0.0007633241,0.0006775356,0.0005992804,0.0005281405,0.0004639911,0.0004080008,0.0003575093,0.0003120446,0.0002712694,0.0002360176,0.000204869,0.0001770866,0.0001524153,0.0001310761,0.0001128269,9.668803e-05)

lmode.polygon.dim.x <- lmode.polygon.cat.x
lmode.polygon.dim.y <-
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    0.001458413,
    0.001582585,
    0.001716961,
    0.001859686,
    0.002010386,
    0.002169638,
    0.002340038,
    0.00252036,
    0.002714144,
    0.002919735,
    0.003136963,
    0.003369644,
    0.003604897,
    0.003849447,
    0.004106634,
    0.004351213,
    0.004606834,
    0.004899674,
    0.005221433,
    0.005483128,
    0.005711262,
    0.006024265,
    0.006407655,
    0.00666579,
    0.006995043,
    0.007368163,
    0.007780788,
    0.008219539,
    0.00866035,
    0.009060427,
    0.009396331,
    0.0098526,
    0.01025663,
    0.01074219,
    0.01123721,
    0.0117965,
    0.01241836,
    0.0129624,
    0.01340279,
    0.01385801,
    0.0145181,
    0.01530921,
    0.01613255,
    0.01653455,
    0.01714569,
    0.01794278,
    0.01876212,
    0.01939394,
    0.0202536,
    0.02092944,
    0.02180065,
    0.02268265,
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    0.02634454,
    0.02691086,
    0.02747381,
    0.02809232,
    0.0288958,
    0.02994471,
    0.03108244,
    0.03173231,
    0.03255792,
    0.03378163,
    0.03484377,
    0.03573372,
    0.03679375,
    0.0375041,
    0.03907241,
    0.04025455,
    0.04079045,
    0.04231273,
    0.04306544,
    0.04389303,
    0.04411849,
    0.04455368,
    0.04531617,
    0.04594091,
    0.04750362,
    0.04870724,
    0.04996616,
    0.05139244,
    0.05244123,
    0.05343915,
    0.054755,
    0.05617424,
    0.05731894,
    0.05864724,
    0.06003275,
    0.06132109,
    0.06240183,
    0.063652,
    0.0649443,
    0.0665155,
    0.06813405,
    0.06943054,
    0.07056015,
    0.0715125,
    0.07287157,
    0.07460819,
    0.07566924,
    0.07724369,
    0.07917948,
    0.08072243,
    0.08244418,
    0.08410769,
    0.08567742,
    0.0872534,
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    0.0904722,
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    0.09675078,
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    0.1095283,
    0.1114811,
    0.1132318,
    0.115342,
    0.1174733,
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    0.1216156,
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    0.1407888,
    0.1427993,
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    0.146942,
    0.1491488,
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    0.152528,
    0.1539795,
    0.1557352,
    0.1574909,
    0.1597005,
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    0.1697531,
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    0.1832662,
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    0.2020372,
    0.2039537,
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    0.2091016,
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    0.2130433,
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    0.3183734,
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    0.3255332,
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    0.3285867,
    0.327903,
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    0.3294215,
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    0.328639,
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    0.3276621,
    0.3271954,
    0.3284939,
    0.3296101,
    0.3305776,
    0.3308701,
    0.3315096,
    0.3319861,
    0.3325569,
    0.3323739,
    0.3322109,
    0.3318868,
    0.331655,
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    0.3294326,
    0.328459,
    0.3278223,
    0.3277235,
    0.3271847,
    0.3275577,
    0.3274536,
    0.3265857,
    0.3256878,
    0.3247804,
    0.3238661,
    0.3224176,
    0.3222926,
    0.3231107,
    0.3227106,
    0.3218016,
    0.3206659,
    0.3187342,
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    0.3167941,
    0.3159169,
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    0.3027392,
    0.3003262,
    0.2978432,
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    0.1153086,
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    0.1099287,
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    0.067068,
    0.06443586,
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    0.06105073,
    0.05954526,
    0.05793641,
    0.05605872,
    0.05415758,
    0.05220562,
    0.05028811,
    0.04844837,
    0.04664238,
    0.04503973,
    0.04377866,
    0.04264103,
    0.04105037,
    0.04001233,
    0.03881827,
    0.03755458,
    0.03651223,
    0.03591608,
    0.03461621,
    0.03326531,
    0.03150462,
    0.02996008,
    0.02899641,
    0.02814582,
    0.0269132,
    0.02573296,
    0.0247305,
    0.02343831,
    0.02235718,
    0.02149878,
    0.02067659,
    0.01970114,
    0.01862398,
    0.01769796,
    0.01675795,
    0.01586295,
    0.01487612,
    0.01410603,
    0.01330293,
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    0.01172409,
    0.01098912,
    0.01031921,
    0.009681798,
    0.009078835,
    0.008448201,
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    0.007304893,
    0.006778362,
    0.006276935,
    0.005800366,
    0.005357472,
    0.004938897,
    0.004542727,
    0.004158372,
    0.003799779,
    0.003463781,
    0.003149325,
    0.002858544,0.002592261,0.002344966,0.002115251,0.001903347,0.001712217,0.001536445,0.00137449,0.001228209,0.001098474,0.0009840846,0.0008766882,0.0007757451,0.0006846038,0.000602523,0.0005304312,0.0004652483,0.0004067841,0.0003546296,0.0003092909,0.0002671643,0.0002311029,0.0001993106,0.000171673,0.0001478121,0.0001270755)

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line1.cat.y <-
  rep(
    c(
      3.13485e-05,
      3.639139e-05,
      4.234624e-05,
      4.913493e-05,
      5.677246e-05,
      6.532745e-05,
      7.517683e-05,
      8.641596e-05,
      9.894725e-05,
      0.0001128645,
      0.0001285272,
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      0.0001661297,
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      0.0002118452,
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      0.0004209393,
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      0.0005194499,
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      0.0007751896,
      0.0008525672,
      0.0009370402,
      0.001027432,
      0.001123977,
      0.001227385,
      0.001340271,
      0.001460484,
      0.001588305,
      0.00172402,
      0.001871596,
      0.002028523,
      0.002194831,
      0.002370875,
      0.00256035,
      0.00276247,
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      0.00320195,
      0.003442871,
      0.003700802,
      0.003973112,
      0.004260366,
      0.00456462,
      0.004891593,
      0.005236375,
      0.005599654,
      0.005982126,
      0.006393873,
      0.006827894,
      0.007284628,
      0.00776489,
      0.00827802,
      0.008820892,
      0.009391334,
      0.009990275,
      0.01062546,
      0.01129957,
      0.01200674,
      0.01274805,
      0.01352862,
      0.01435928,
      0.01522926,
      0.01613978,
      0.01709215,
      0.01810821,
      0.01917077,
      0.02028125,
      0.02144106,
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      0.0358506,
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      0.1032884,
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      0.1093338,
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      0.1224043,
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      0.1804164,
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      0.1927376,
      0.1954115,
      0.1981397,
      0.2009202,
      0.2037524,
      0.2066497,
      0.2095875,
      0.212563,
      0.2155734,
      0.218627,
      0.2217054,
      0.2248054,
      0.2279242,
      0.2310629,
      0.2342119,
      0.2373679,
      0.2405286,
      0.243691,
      0.2468508,
      0.250006,
      0.253155,
      0.2562927,
      0.2594167,
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      0.2656227,
      0.2686973,
      0.2717475,
      0.2747758,
      0.2777808,
      0.2807558,
      0.2836938,
      0.2866003,
      0.2894736,
      0.2923069,
      0.2950867,
      0.2978234,
      0.3005146,
      0.3020465,
      0.3026757,
      0.3033536,
      0.3040864,
      0.3048642,
      0.3056883,
      0.3061873,
      0.3058243,
      0.3055009,
      0.3052187,
      0.3050024,
      0.3048329,
      0.3047112,
      0.3046382,
      0.3046393,
      0.3046926,
      0.3047975,
      0.3049542,
      0.305186,
      0.3054713,
      0.3058076,
      0.3061945,
      0.3066522,
      0.307161,
      0.3077169,
      0.3082353,
      0.3076862,
      0.307221,
      0.3068402,
      0.3065517,
      0.3063799,
      0.3062917,
      0.3062864,
      0.3053317,
      0.3044882,
      0.3037229,
      0.3030357,
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      0.04539497,
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      0.04553666,
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      0.04523908,
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      0.04381494,
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      0.04123323,
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      0.04047583,
      0.04031802,
      0.04016889,
      0.04002343,
      0.03967766,
      0.03912569,
      0.03856121,
      0.03776527,
      0.03699676,
      0.03624971,
      0.03552192,
      0.03432074,
      0.03299525,
      0.03172965,
      0.03052226,
      0.0293714,
      0.02829789,
      0.0272754,
      0.02630069,
      0.02524615,
      0.02403455,
      0.02287498,
      0.02175345,
      0.02066989,
      0.01962423,
      0.01863289,
      0.01767884,
      0.01676144,
      0.01588031,
      0.0150473,
      0.01425223,
      0.01349099,
      0.01276293,
      0.01207555,
      0.01142495,
      0.0108042,
      0.01021251,
      0.009653615,
      0.009128714,
      0.008629025,
      0.008153701,
      0.007703617,
      0.007283567,
      0.006883956,
      0.006503969,
      0.006142797,
      0.005806698,
      0.005486844,
      0.005182304,
      0.004892384,
      0.004620731,
      0.004362811,
      0.004116655,
      0.003881723,
      0.003659966,
      0.003449763,
      0.003248663,
      0.003056285,
      0.002873529,
      0.002700685,
      0.002535115,
      0.002376572,
      0.002225282,
      0.002082815,
      0.001946437,
      0.00181599,
      0.001691321,
      0.001574592,
      0.001463275,
      0.001357152,
      0.001256112,
      0.001161669,
      0.001072478,
      0.0009878944,
      0.0009078193,
      0.0008332011,
      0.0007636114,
      0.0006980596,
      0.0006364416,
      0.000579224,
      0.0005266703,
      0.0004775477,
      0.0004317448,
      0.0003893489,
      0.0003510982,
      0.0003156419,
      0.0002828676,
      0.0002526631,
      0.0002258469,
      0.0002012595,
      0.0001787357,
      0.0001581711,
      0.0001400069,
      0.0001236524,
      0.0001088064,
      9.537986e-05,
      8.356544e-05,
      7.314112e-05,
      6.376396e-05,
      5.536351e-05,
      4.798875e-05,
      4.162529e-05,
      3.59521e-05,
      3.091739e-05
    ),
    each = 2
  )

lmode.line1.dim.y <-
  rep(
    c(
      3.423779e-05,
      4.00173e-05,
      4.657219e-05,
      5.426812e-05,
      6.317944e-05,
      7.326038e-05,
      8.461499e-05,
      9.765753e-05,
      0.0001127892,
      0.0001297855,
      0.0001488016,
      0.000170219,
      0.0001950955,
      0.0002228488,
      0.0002537032,
      0.0002876899,
      0.0003256493,
      0.000367929,
      0.0004143932,
      0.0004652972,
      0.0005224524,
      0.0005859716,
      0.000655304,
      0.0007307701,
      0.0008143015,
      0.0009068827,
      0.001007276,
      0.001115869,
      0.001234517,
      0.001365607,
      0.001506868,
      0.001658745,
      0.001822747,
      0.002003313,
      0.002196719,
      0.002403456,
      0.002624344,
      0.002866606,
      0.003124604,
      0.003398858,
      0.003689888,
      0.004006109,
      0.004341861,
      0.004696877,
      0.005071677,
      0.005474473,
      0.005901276,
      0.006350295,
      0.006822027,
      0.007324021,
      0.0078102,
      0.008216043,
      0.008637364,
      0.009076107,
      0.009529607,
      0.009998463,
      0.0104839,
      0.01099331,
      0.0115212,
      0.01206839,
      0.01263571,
      0.01323137,
      0.01385272,
      0.01449842,
      0.01516949,
      0.01587198,
      0.01661052,
      0.01737954,
      0.01818027,
      0.01901499,
      0.0198992,
      0.02082117,
      0.02178238,
      0.02278432,
      0.02384281,
      0.02495263,
      0.02611047,
      0.02731805,
      0.02858625,
      0.029924,
      0.03131952,
      0.03277463,
      0.03429253,
      0.03590124,
      0.03757747,
      0.03932282,
      0.04113885,
      0.04267374,
      0.04383123,
      0.04489159,
      0.04605011,
      0.0473195,
      0.04867556,
      0.05011827,
      0.0516514,
      0.05330393,
      0.05504001,
      0.0568582,
      0.05875697,
      0.06076239,
      0.06284613,
      0.06500045,
      0.06722272,
      0.06952574,
      0.07189766,
      0.07432389,
      0.07680127,
      0.07933291,
      0.08191793,
      0.08279772,
      0.08312922,
      0.08348355,
      0.08386322,
      0.08427243,
      0.08472531,
      0.08523044,
      0.0857833,
      0.08638735,
      0.08705526,
      0.08780286,
      0.08861556,
      0.08949576,
      0.09045103,
      0.09150869,
      0.09264296,
      0.09385527,
      0.09514698,
      0.09655682,
      0.09805076,
      0.09962875,
      0.1012916,
      0.1030719,
      0.1049472,
      0.10691,
      0.1089609,
      0.1111261,
      0.1133963,
      0.1157566,
      0.1182073,
      0.1207677,
      0.1234428,
      0.1262096,
      0.1290682,
      0.1320299,
      0.1351138,
      0.1382883,
      0.1415528,
      0.1449104,
      0.1483914,
      0.1519566,
      0.1556042,
      0.1593321,
      0.1631676,
      0.1670758,
      0.1710501,
      0.1750869,
      0.1791982,
      0.183362,
      0.1875664,
      0.191806,
      0.1960794,
      0.2003717,
      0.2046711,
      0.2083578,
      0.2111906,
      0.2141052,
      0.2170764,
      0.2200995,
      0.223173,
      0.2263147,
      0.2294996,
      0.2327232,
      0.2359827,
      0.2392497,
      0.241544,
      0.2437881,
      0.2459696,
      0.2481005,
      0.2501798,
      0.2522049,
      0.2541546,
      0.256052,
      0.257898,
      0.259694,
      0.2614261,
      0.2631121,
      0.2647592,
      0.2663706,
      0.2679439,
      0.2694892,
      0.271017,
      0.2725316,
      0.2740375,
      0.2755442,
      0.2770586,
      0.2785849,
      0.2801281,
      0.2817052,
      0.2831537,
      0.2835594,
      0.2840937,
      0.2847298,
      0.2854657,
      0.2863033,
      0.2872692,
      0.2883583,
      0.2895507,
      0.2908455,
      0.2922508,
      0.2937857,
      0.2954137,
      0.2971317,
      0.2969733,
      0.2967263,
      0.2965299,
      0.2964025,
      0.2963459,
      0.2963514,
      0.2964215,
      0.2965746,
      0.296818,
      0.2971365,
      0.2975319,
      0.2980199,
      0.2986145,
      0.2992922,
      0.3000536,
      0.3009091,
      0.3018783,
      0.3029299,
      0.3034198,
      0.3034774,
      0.302452,
      0.3015181,
      0.3006611,
      0.2998856,
      0.2992137,
      0.2986672,
      0.297742,
      0.2967802,
      0.2958528,
      0.2949553,
      0.2940876,
      0.2932511,
      0.2924611,
      0.2917121,
      0.2910015,
      0.2903304,
      0.2897142,
      0.289148,
      0.2886259,
      0.2881486,
      0.2877295,
      0.2873655,
      0.2870474,
      0.286775,
      0.2856697,
      0.2843567,
      0.2830952,
      0.281886,
      0.2807362,
      0.2796565,
      0.2786293,
      0.2776541,
      0.2755371,
      0.2732391,
      0.2709703,
      0.2687317,
      0.266524,
      0.2643603,
      0.2622317,
      0.260136,
      0.2580731,
      0.2560516,
      0.2540675,
      0.2521142,
      0.2501909,
      0.2483013,
      0.2464459,
      0.2445576,
      0.2412458,
      0.2379772,
      0.2347804,
      0.2316416,
      0.2285645,
      0.2255528,
      0.2226374,
      0.2190209,
      0.2152158,
      0.2114175,
      0.2076418,
      0.2038903,
      0.2001676,
      0.1964781,
      0.1928458,
      0.1892633,
      0.1857322,
      0.1822559,
      0.1788591,
      0.1755354,
      0.1722796,
      0.1690937,
      0.1659987,
      0.1629954,
      0.1600696,
      0.1572221,
      0.1544673,
      0.1518161,
      0.1492453,
      0.1467548,
      0.1443509,
      0.1420553,
      0.139837,
      0.1376949,
      0.1356281,
      0.1336668,
      0.1317751,
      0.1299513,
      0.1281934,
      0.1265224,
      0.1249152,
      0.1233648,
      0.1218693,
      0.1204411,
      0.1190684,
      0.1177412,
      0.1164576,
      0.1152237,
      0.1140366,
      0.1128847,
      0.1117664,
      0.1106842,
      0.1096407,
      0.1086244,
      0.1076341,
      0.1066701,
      0.1057384,
      0.1048281,
      0.1034871,
      0.1017735,
      0.1001314,
      0.09854018,
      0.09699991,
      0.09551065,
      0.09408613,
      0.09272057,
      0.09140632,
      0.09014347,
      0.08893739,
      0.08779915,
      0.08671251,
      0.08567742,
      0.08469382,
      0.08377968,
      0.08291938,
      0.08155794,
      0.07979958,
      0.07809844,
      0.07646432,
      0.07490327,
      0.07339923,
      0.07195189,
      0.07056397,
      0.06925283,
      0.06799574,
      0.06679178,
      0.06534069,
      0.06329299,
      0.06132522,
      0.05943253,
      0.05761739,
      0.05590039,
      0.05428656,
      0.05275892,
      0.05131865,
      0.04997593,
      0.04875337,
      0.04762049,
      0.04657693,
      0.04562221,
      0.044792,
      0.04404746,
      0.04338539,
      0.04280369,
      0.04232253,
      0.04192184,
      0.04158832,
      0.04131849,
      0.04111894,
      0.04098333,
      0.04089294,
      0.03988323,
      0.038863,
      0.03790042,
      0.03698258,
      0.03610264,
      0.03525844,
      0.03445189,
      0.03368297,
      0.03294053,
      0.03222261,
      0.03152731,
      0.03085914,
      0.03020833,
      0.02957273,
      0.02895089,
      0.02834351,
      0.02774803,
      0.02716103,
      0.02609689,
      0.02495453,
      0.02384528,
      0.02277092,
      0.02174562,
      0.02075581,
      0.01980189,
      0.01888421,
      0.01801725,
      0.01718982,
      0.01633386,
      0.0152903,
      0.01430662,
      0.01338265,
      0.01253177,
      0.01174944,
      0.01102379,
      0.01035373,
      0.009741733,
      0.009199448,
      0.008706352,
      0.008260699,
      0.007860701,
      0.007517276,
      0.00721679,
      0.006953188,
      0.006724383,
      0.006532828,
      0.006377017,
      0.006246549,
      0.006139304,
      0.006053165,
      0.005991859,
      0.005944719,
      0.005909755,
      0.005885072,
      0.005869983,
      0.005860438,
      0.005853615,
      0.005848023,
      0.005841992,
      0.005832514,
      0.005818711,
      0.005596832,
      0.005307975,
      0.005029448,
      0.004767468,
      0.004525425,
      0.004296104,
      0.004078645,
      0.00387221,
      0.003678714,
      0.00349334,
      0.003290783,
      0.003097595,
      0.002913593,
      0.002741462,
      0.002576902,
      0.002419619,
      0.002269323,
      0.002128575,
      0.001993981,
      0.001865275,
      0.001742269,
      0.001626964,
      0.001517053,
      0.001412123,
      0.001312048,
      0.001218417,
      0.001129662,
      0.001045245,
      0.0009650677,
      0.0008903742,
      0.0008201244,
      0.0007536703,
      0.0006909216,
      0.0006328083,
      0.0005786883,
      0.0005278342,
      0.0004801537,
      0.0004362943,
      0.0003959179,
      0.0003582626,
      0.0003232343,
      0.0002912422,
      0.0002621703,
      0.0002352747,
      0.0002104645,
      0.0001879646,
      0.0001678066,
      0.0001493119,
      0.0001323986,
      0.0001171636,
      0.0001037212,
      9.149132e-05,
      8.04053e-05,
      7.048187e-05,
      6.186717e-05,
      5.40953e-05,
      4.711239e-05,
      4.089729e-05,
      3.559373e-05,
      3.05591e-05
    ),
    each = 2
  )

#Duplicate SD borders values as well, to allow the simulated polygon to be more smooth
#X is the same as in data
lmode.line2.cat.y <-
  rep(
    c(
      0.0003133908,
      0.0003636568,
      0.0004201973,
      0.000483508,
      0.0005553237,
      0.0006384063,
      0.0007310033,
      0.000833782,
      0.0009484658,
      0.001080278,
      0.001225826,
      0.001385945,
      0.0015619,
      0.001762618,
      0.001982186,
      0.002221568,
      0.002481731,
      0.002774289,
      0.003092194,
      0.00343565,
      0.003805664,
      0.00421451,
      0.004656316,
      0.005129302,
      0.005634378,
      0.006183448,
      0.006772943,
      0.007398329,
      0.008060267,
      0.008769156,
      0.009524663,
      0.010319,
      0.01115242,
      0.01203285,
      0.01296363,
      0.01393368,
      0.01494281,
      0.01599585,
      0.01709954,
      0.01824019,
      0.01941711,
      0.02063208,
      0.02189427,
      0.0231886,
      0.024514,
      0.02586981,
      0.02726623,
      0.02868837,
      0.03013508,
      0.03160517,
      0.03310565,
      0.03462633,
      0.03616523,
      0.03772139,
      0.03929907,
      0.04089275,
      0.04250023,
      0.04412104,
      0.04575856,
      0.04741084,
      0.04907595,
      0.05075415,
      0.05244936,
      0.05416293,
      0.05589279,
      0.05764004,
      0.05940977,
      0.06120752,
      0.06302967,
      0.06487808,
      0.06675863,
      0.06868322,
      0.07064431,
      0.07264942,
      0.07623558,
      0.07989293,
      0.08364154,
      0.08745918,
      0.09133644,
      0.09527065,
      0.09927187,
      0.1033297,
      0.1074313,
      0.1115737,
      0.1157596,
      0.1199854,
      0.1242381,
      0.1285144,
      0.1328128,
      0.1371312,
      0.1414592,
      0.145794,
      0.1501327,
      0.1544693,
      0.1587994,
      0.1631205,
      0.16743,
      0.1717179,
      0.1759842,
      0.1802281,
      0.1844477,
      0.1886325,
      0.1927821,
      0.1968999,
      0.2023602,
      0.2082205,
      0.2140524,
      0.2198394,
      0.2255629,
      0.2312269,
      0.2368252,
      0.2423407,
      0.2477438,
      0.2530539,
      0.2582661,
      0.2633678,
      0.2683127,
      0.2731389,
      0.2778429,
      0.2824211,
      0.2868079,
      0.2910601,
      0.2951763,
      0.2991551,
      0.3029384,
      0.3067445,
      0.3120559,
      0.3172328,
      0.3222214,
      0.3270433,
      0.331712,
      0.3362247,
      0.3405462,
      0.3446675,
      0.348626,
      0.3524216,
      0.3560411,
      0.3594413,
      0.3626824,
      0.3657661,
      0.3686946,
      0.3714113,
      0.3739762,
      0.3763982,
      0.3786806,
      0.3807906,
      0.3827517,
      0.3845891,
      0.3863062,
      0.3878896,
      0.3893336,
      0.3906743,
      0.3919153,
      0.3930569,
      0.3940735,
      0.395007,
      0.3958609,
      0.3966389,
      0.3973217,
      0.3979353,
      0.3984891,
      0.3989863,
      0.4015924,
      0.4046158,
      0.407523,
      0.410295,
      0.4129535,
      0.4154942,
      0.4179126,
      0.4201476,
      0.4222463,
      0.4242049,
      0.4260196,
      0.4276458,
      0.4290937,
      0.430384,
      0.4315143,
      0.4324645,
      0.4331979,
      0.433765,
      0.4341655,
      0.4343992,
      0.4344059,
      0.4342411,
      0.4347974,
      0.4353946,
      0.4358554,
      0.4361777,
      0.4363265,
      0.4362992,
      0.4361258,
      0.4358057,
      0.4353216,
      0.4346419,
      0.4338166,
      0.4328471,
      0.4317346,
      0.4304456,
      0.4306764,
      0.4308671,
      0.43102,
      0.4311332,
      0.4312024,
      0.4312224,
      0.4320015,
      0.4331275,
      0.4341577,
      0.4350489,
      0.4358168,
      0.4364644,
      0.4369866,
      0.4373607,
      0.4375587,
      0.4376128,
      0.4375196,
      0.4372761,
      0.4368256,
      0.4362069,
      0.4354284,
      0.434489,
      0.4333642,
      0.4320348,
      0.4305433,
      0.4288906,
      0.4270776,
      0.425051,
      0.4228624,
      0.4205224,
      0.418034,
      0.4153782,
      0.4125506,
      0.4110227,
      0.4125037,
      0.4138643,
      0.4150982,
      0.4161582,
      0.4170495,
      0.4177897,
      0.4183743,
      0.4187681,
      0.4189499,
      0.4189597,
      0.4187952,
      0.4184394,
      0.417838,
      0.4170558,
      0.4160925,
      0.4149481,
      0.4135466,
      0.4119642,
      0.4102067,
      0.4082764,
      0.4061228,
      0.4037876,
      0.4012959,
      0.3986521,
      0.3958307,
      0.392844,
      0.3897308,
      0.3864978,
      0.3831392,
      0.381961,
      0.3817429,
      0.3813313,
      0.3807204,
      0.379877,
      0.3787693,
      0.3774493,
      0.3759172,
      0.3741739,
      0.3721619,
      0.3699307,
      0.3682631,
      0.3670396,
      0.3657769,
      0.3644787,
      0.363142,
      0.3617755,
      0.3603892,
      0.3589859,
      0.3575663,
      0.3561363,
      0.3547007,
      0.3532613,
      0.3518201,
      0.3503802,
      0.3489424,
      0.3475076,
      0.3460774,
      0.3446522,
      0.3432311,
      0.3418137,
      0.3404004,
      0.3389899,
      0.3375804,
      0.3361712,
      0.3359597,
      0.335988,
      0.3359344,
      0.3358139,
      0.3356241,
      0.3353543,
      0.3349786,
      0.3345222,
      0.3339831,
      0.3333557,
      0.3326039,
      0.3317634,
      0.3308337,
      0.3298144,
      0.3286647,
      0.3274261,
      0.3261011,
      0.3246908,
      0.3231651,
      0.3215569,
      0.3198743,
      0.3181203,
      0.316277,
      0.3143674,
      0.3124033,
      0.3103887,
      0.3083168,
      0.3062021,
      0.3040566,
      0.3018845,
      0.2996866,
      0.2974725,
      0.2952503,
      0.2930238,
      0.2907976,
      0.2885792,
      0.286371,
      0.2841755,
      0.2819975,
      0.2798451,
      0.2777142,
      0.2756058,
      0.2735229,
      0.2714749,
      0.2694522,
      0.2674549,
      0.2664424,
      0.2654201,
      0.2643032,
      0.2630883,
      0.2617524,
      0.260277,
      0.2586913,
      0.2569939,
      0.2551684,
      0.2531906,
      0.2511004,
      0.248899,
      0.2465785,
      0.2441117,
      0.2415446,
      0.2388808,
      0.2364275,
      0.2346326,
      0.2328203,
      0.2309908,
      0.2291421,
      0.2272667,
      0.2253594,
      0.223424,
      0.2214589,
      0.2194567,
      0.217409,
      0.2153246,
      0.2132022,
      0.2110364,
      0.2088148,
      0.2065514,
      0.204246,
      0.2018959,
      0.1994857,
      0.1970338,
      0.1945408,
      0.1920075,
      0.1894176,
      0.1867915,
      0.1841309,
      0.1814373,
      0.1787018,
      0.1759388,
      0.1731522,
      0.1703442,
      0.1675125,
      0.1646661,
      0.1618093,
      0.1589446,
      0.1560741,
      0.1532034,
      0.1503352,
      0.1474715,
      0.1446169,
      0.141775,
      0.1389458,
      0.1361304,
      0.1333335,
      0.130559,
      0.1278031,
      0.1268242,
      0.1262257,
      0.1255956,
      0.1249374,
      0.1242502,
      0.1235226,
      0.122757,
      0.1219581,
      0.1211252,
      0.1202459,
      0.1193236,
      0.1183644,
      0.1173676,
      0.1163204,
      0.1152275,
      0.1140956,
      0.1129245,
      0.1117013,
      0.110432,
      0.1091237,
      0.1077765,
      0.1063783,
      0.1049359,
      0.1034565,
      0.1019405,
      0.1003772,
      0.09877374,
      0.09713698,
      0.0954677,
      0.09375694,
      0.09201181,
      0.09023856,
      0.08843818,
      0.08660385,
      0.08474225,
      0.0828588,
      0.08095459,
      0.07902528,
      0.07707681,
      0.07511357,
      0.07313683,
      0.07114488,
      0.0691428,
      0.06713383,
      0.06511936,
      0.06310068,
      0.06108175,
      0.05906457,
      0.05705064,
      0.05504452,
      0.05304878,
      0.05106407,
      0.04909196,
      0.04714037,
      0.04521019,
      0.04330056,
      0.04141305,
      0.03955878,
      0.03773665,
      0.03594418,
      0.0341828,
      0.03246641,
      0.0307916,
      0.02915432,
      0.02755573,
      0.02601166,
      0.02451641,
      0.02306449,
      0.02165663,
      0.02030966,
      0.01901572,
      0.01776823,
      0.01656745,
      0.0154301,
      0.01434668,
      0.01330994,
      0.01236509,
      0.01147319,
      0.01061888,
      0.009802384,
      0.009040307,
      0.008317703,
      0.007632282,
      0.00698369,
      0.006385953,
      0.005825522,
      0.005298993,
      0.004805617,
      0.004356369,
      0.003939977,
      0.003552425,
      0.003192764,
      0.002869,
      0.002572422,
      0.002298912,
      0.002047489,
      0.00182361,
      0.001620981,
      0.001435792,
      0.001267147,
      0.001118525,
      0.0009856544,
      0.0008652924,
      0.0007566925,
      0.000661925,
      0.000578263,
      0.0005031346,
      0.0004359647,
      0.0003778977
    ),
    each = 2
  )

lmode.line2.dim.y <-
  rep(
    c(
      0.0005780644,
      0.0006689485,
      0.0007709063,
      0.000884775,
      0.001018171,
      0.001167909,
      0.00133447,
      0.001518999,
      0.001731755,
      0.001969136,
      0.002230942,
      0.002518644,
      0.002845338,
      0.003207464,
      0.003603449,
      0.004035054,
      0.004518075,
      0.005049729,
      0.00562614,
      0.006249257,
      0.006937009,
      0.007688351,
      0.008496025,
      0.009361989,
      0.01030529,
      0.01132766,
      0.01241742,
      0.01357627,
      0.01482302,
      0.01616307,
      0.01757954,
      0.01907364,
      0.02066233,
      0.02235522,
      0.02412999,
      0.02598711,
      0.02794033,
      0.03000321,
      0.03214864,
      0.03437616,
      0.03669536,
      0.03912273,
      0.04162787,
      0.04420938,
      0.04687242,
      0.04963461,
      0.05246458,
      0.05536016,
      0.05832251,
      0.06136815,
      0.06446754,
      0.06761797,
      0.07081775,
      0.07408003,
      0.07737979,
      0.0807142,
      0.08408043,
      0.08748565,
      0.09091234,
      0.09435762,
      0.0978189,
      0.1012967,
      0.1047818,
      0.1082717,
      0.1117642,
      0.1152559,
      0.1187434,
      0.1222252,
      0.1257001,
      0.1291625,
      0.1326125,
      0.1360504,
      0.1394754,
      0.1428816,
      0.1462707,
      0.1496444,
      0.1530023,
      0.1563391,
      0.1596565,
      0.1629573,
      0.1662413,
      0.1695041,
      0.1727462,
      0.1759714,
      0.1791794,
      0.1823663,
      0.1855314,
      0.1886788,
      0.1918084,
      0.1949163,
      0.1980003,
      0.2010651,
      0.2041106,
      0.2071328,
      0.2101277,
      0.2131013,
      0.2160531,
      0.2189796,
      0.2218746,
      0.2247456,
      0.2275922,
      0.2304113,
      0.2331946,
      0.2359514,
      0.2386813,
      0.2413822,
      0.2440433,
      0.2466759,
      0.2492798,
      0.2518538,
      0.254385,
      0.2568863,
      0.2593577,
      0.2638251,
      0.2695643,
      0.2751966,
      0.2807345,
      0.2861741,
      0.2914932,
      0.296673,
      0.3017412,
      0.3066963,
      0.3115263,
      0.3161968,
      0.3207507,
      0.3251881,
      0.3295087,
      0.3336632,
      0.3377056,
      0.3416375,
      0.3454607,
      0.3491375,
      0.3527048,
      0.3561723,
      0.3595421,
      0.3627885,
      0.3659293,
      0.3689807,
      0.3719442,
      0.3748025,
      0.3775563,
      0.3802264,
      0.382813,
      0.3853047,
      0.3876855,
      0.3899811,
      0.3921904,
      0.394307,
      0.3962968,
      0.3981928,
      0.3999929,
      0.4016949,
      0.40325,
      0.4046956,
      0.4060316,
      0.4072555,
      0.408322,
      0.409255,
      0.4100647,
      0.4107489,
      0.4112697,
      0.4116346,
      0.4118663,
      0.4119639,
      0.4119005,
      0.4116649,
      0.4112938,
      0.4107879,
      0.4101333,
      0.4093011,
      0.4083405,
      0.4072537,
      0.4060399,
      0.4046571,
      0.4031624,
      0.4015598,
      0.3998533,
      0.3980117,
      0.3966187,
      0.397088,
      0.3973571,
      0.3974793,
      0.3974702,
      0.3973348,
      0.3970492,
      0.3966354,
      0.3961198,
      0.3955078,
      0.3947918,
      0.3939724,
      0.3940078,
      0.3953396,
      0.3965934,
      0.3977307,
      0.3987705,
      0.3997151,
      0.4005609,
      0.4012738,
      0.4018592,
      0.4023321,
      0.4026901,
      0.4029093,
      0.4029756,
      0.40292,
      0.4027418,
      0.4024307,
      0.4019516,
      0.4017401,
      0.4019941,
      0.4020757,
      0.4019294,
      0.4016285,
      0.4011777,
      0.4008679,
      0.4014939,
      0.4019498,
      0.4021692,
      0.4021955,
      0.4020386,
      0.4016977,
      0.4011461,
      0.4003655,
      0.3994067,
      0.3982733,
      0.3969693,
      0.3954453,
      0.3937614,
      0.3919327,
      0.3899667,
      0.3878531,
      0.3855984,
      0.3832429,
      0.3820475,
      0.3821519,
      0.3821462,
      0.3819826,
      0.3816902,
      0.3812757,
      0.3807374,
      0.3800421,
      0.3791964,
      0.3782247,
      0.3771277,
      0.3767383,
      0.3780281,
      0.3792641,
      0.3804419,
      0.3815574,
      0.3825739,
      0.3835128,
      0.3843725,
      0.38515,
      0.3858128,
      0.3863737,
      0.3868418,
      0.3872155,
      0.3874714,
      0.3876075,
      0.3876452,
      0.3875842,
      0.3874124,
      0.3871104,
      0.3867112,
      0.3862154,
      0.3856216,
      0.3848938,
      0.384074,
      0.3831634,
      0.3821632,
      0.3810429,
      0.3798309,
      0.3785352,
      0.3771572,
      0.375677,
      0.3741051,
      0.3724571,
      0.3707344,
      0.3689264,
      0.3685012,
      0.3680283,
      0.3674866,
      0.3668723,
      0.3661741,
      0.3653639,
      0.3644638,
      0.3634701,
      0.3623792,
      0.3611502,
      0.3598055,
      0.35835,
      0.3567813,
      0.3556611,
      0.354954,
      0.3542293,
      0.3534789,
      0.3527089,
      0.3519193,
      0.351109,
      0.3503588,
      0.3497176,
      0.3489967,
      0.3482161,
      0.3473837,
      0.3465009,
      0.3455511,
      0.3445528,
      0.3435121,
      0.3424305,
      0.3412946,
      0.3401205,
      0.3389128,
      0.3376727,
      0.3363895,
      0.3350767,
      0.3337373,
      0.3323724,
      0.3309728,
      0.3295494,
      0.3281041,
      0.3266374,
      0.3251405,
      0.3236225,
      0.3220843,
      0.3205261,
      0.318938,
      0.3173288,
      0.3156989,
      0.314048,
      0.3123649,
      0.3106594,
      0.3089316,
      0.3071811,
      0.3053961,
      0.3035878,
      0.3017566,
      0.299902,
      0.2980138,
      0.2961039,
      0.2941728,
      0.2922208,
      0.2902408,
      0.2882438,
      0.286231,
      0.2847508,
      0.2838883,
      0.2829415,
      0.2819207,
      0.2808247,
      0.2796257,
      0.278336,
      0.2769676,
      0.2755199,
      0.2739649,
      0.2723174,
      0.2705898,
      0.2687821,
      0.2668667,
      0.2648595,
      0.2627731,
      0.2606077,
      0.2583364,
      0.255976,
      0.2535389,
      0.2510256,
      0.2484104,
      0.245711,
      0.2429394,
      0.2400964,
      0.2371592,
      0.2341458,
      0.2310677,
      0.2279265,
      0.2254455,
      0.2233684,
      0.2212697,
      0.2191443,
      0.2169845,
      0.2147982,
      0.212585,
      0.21034,
      0.2080577,
      0.2057483,
      0.2034121,
      0.2010454,
      0.1986464,
      0.1962249,
      0.1937822,
      0.1913165,
      0.1888292,
      0.1863281,
      0.1838149,
      0.18129,
      0.1787569,
      0.1762201,
      0.1736813,
      0.1711427,
      0.1686082,
      0.1660787,
      0.1635556,
      0.161042,
      0.1585407,
      0.1560499,
      0.1535701,
      0.1511047,
      0.1486543,
      0.1462156,
      0.1437886,
      0.1413754,
      0.138975,
      0.1365839,
      0.1342013,
      0.1318282,
      0.1294622,
      0.1271009,
      0.1247431,
      0.1223883,
      0.1200343,
      0.1176798,
      0.115324,
      0.1129652,
      0.1106021,
      0.108235,
      0.1058634,
      0.1034855,
      0.1011016,
      0.0987127,
      0.09631907,
      0.09391978,
      0.09151648,
      0.08911067,
      0.08670305,
      0.08429479,
      0.08188824,
      0.07948462,
      0.07708506,
      0.0746937,
      0.07231254,
      0.069942,
      0.06758349,
      0.06524468,
      0.06292605,
      0.06062693,
      0.05834882,
      0.05610308,
      0.05388763,
      0.05170066,
      0.04954359,
      0.04743125,
      0.0453749,
      0.04406753,
      0.04272191,
      0.04137729,
      0.04032594,
      0.03922559,
      0.03807436,
      0.03687205,
      0.03563689,
      0.03437266,
      0.0330826,
      0.031767,
      0.03044021,
      0.029106,
      0.02776815,
      0.02643384,
      0.025109,
      0.02379665,
      0.02249994,
      0.02122917,
      0.01998749,
      0.01877384,
      0.0175904,
      0.01644607,
      0.01534703,
      0.01428582,
      0.01326353,
      0.01228493,
      0.0113624,
      0.01048165,
      0.009642806,
      0.008845914,
      0.008109103,
      0.007413391,
      0.006757874,
      0.006141897,
      0.005577416,
      0.005053322,
      0.004564554,
      0.004110044,
      0.003696276,
      0.003319195,
      0.002970972,
      0.002650403,
      0.002359871,
      0.002100456,
      0.001863149,
      0.001646802,
      0.001451204,
      0.001280419,
      0.001127143,
      0.0009973885,
      0.0008793465,
      0.0007745835,
      0.0006816362,
      0.0005975678,
      0.0005218244,
      0.0004547304,
      0.0003965598,
      0.0003454418,
      0.0003006303,
      0.0002625295,
      0.0002283532,
      0.0001978168
    ),
    each = 2
  )

lmode.vline1.cat.x <- c(-0.01215921,-0.01215921)
lmode.vline1.cat.y <- c(0.0001,0.3563374)

lmode.vline2.cat.x <- c(0.2152464,0.2152464)
lmode.vline2.cat.y <- c(0.0001,0.3636451)

lmo.emp <- data.frame(lmode.empcurve.x, lmode.empcurve.y)
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.x"] <- "xvalues"
names(lmo.emp)[names(lmo.emp) == "lmode.empcurve.y"] <- "yvalues"




# Plots ---------------------------------------------------------

#MAMBAC

mambac.plot.cat <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.cat.x,
                                        y = mambac.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = mambac.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = mambac.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Categorical comparison data",
          subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  scale_y_continuous(breaks=seq(round(mambac.y.range[1], digits = 1),
                                round(mambac.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

mambac.plot.dim <- ggplot(mamb.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = mambac.polygon.dim.x,
                                        y = mambac.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = mambac.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = mambac.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(mambac.y.range) +
  ggtitle(label = "Dimensional comparison data", subtitle = "MAMBAC") +
  xlab("Cut") + ylab("Mean difference") +
  theme(
    plot.title = element_text(size=16, hjust = 0.5, family = "Arial"),
    plot.subtitle = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#MAXEIG

maxeig.plot.cat <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.cat.x,
                                        y = maxeig.polygon.cat.y),
               fill = "#0b5db5") +
  geom_line(aes(y = maxeig.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = maxeig.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  scale_y_continuous(breaks=seq(round(maxeig.y.range[1], digits = 1),
                                round(maxeig.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

maxeig.plot.dim <- ggplot(maxe.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = maxeig.polygon.dim.x,
                                        y = maxeig.polygon.dim.y),
               fill = "#5aa007") +
  geom_line(aes(y = maxeig.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = maxeig.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  ylim(maxeig.y.range) +
  ggtitle(label = "MAXEIG") +
  xlab("Score") + ylab("Eigenvalue") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  ) 
#L-Mode

lmode.plot.cat <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.cat.x, y = lmode.polygon.cat.y), fill = "#0b5db5") +
  geom_line(aes(y = lmode.line1.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(aes(y = lmode.line2.cat.y), size = 1.2, color = "#0b5db5") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  scale_y_continuous(breaks=seq(round(lmode.y.range[1], digits = 1),
                                round(lmode.y.range[2], digits = 1),
                                by = 0.1)) +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9)
  )

lmode.plot.dim <- ggplot(lmo.emp, aes(x = xvalues, y = yvalues)) +
  geom_polygon(inherit.aes = FALSE, aes(x = lmode.polygon.dim.x, y = lmode.polygon.dim.y), fill = "#5aa007") +
  geom_line(aes(y = lmode.line1.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(aes(y = lmode.line2.dim.y), size = 1.2, color = "#5aa007") +
  geom_line(size = 1.5) +
  geom_segment(aes(x = lmode.vline1.cat.x[1],
                   y = lmode.vline1.cat.y[1],
                   xend = lmode.vline1.cat.x[2],
                   yend = lmode.vline1.cat.y[2]), size = 1) +
  geom_segment(aes(x = lmode.vline2.cat.x[1],
                   y = lmode.vline2.cat.y[1],
                   xend = lmode.vline2.cat.x[2],
                   yend = lmode.vline2.cat.y[2]), size = 1) +
  ylim(lmode.y.range) +
  ggtitle(label = "L-Mode") +
  xlab("Factor score") + ylab("Density") +
  theme(
    plot.title = element_text(size=12, hjust = 0.5, family = "Arial"),
    axis.title = element_text(size = 12, family = "Arial"),
    axis.text = element_text(colour = "black", size = 12, family = "Arial"),
    axis.ticks = element_line(colour = "black"),
    axis.title.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    panel.background = element_blank(),
    axis.line = element_line(colour = "black", size = 0.9),
    axis.line.y = element_blank()
  )

#Grid
grid.title <- textGrob(expression(bold("HGSHS:A subscales ("~bolditalic("a priori")~"base rate: .10 )")), gp = gpar(fontsize = 14, fontfamily = "Arial"))
grid.arrange(mambac.plot.cat, mambac.plot.dim, maxeig.plot.cat, maxeig.plot.dim, lmode.plot.cat, lmode.plot.dim,
             nrow = 3,
             top=grid.title)