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All Sims 225pm 10052016.R
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All Sims 225pm 10052016.R
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##This is where all the side by side simulations will be performed.
#### CU039543EYRS-ZZBZ-SZX2
#install.packages("coin")
library(coin)
########
########
########
###Data Creation for CA Trend. Y binary, X_j trinary.
makeYBinary <- function(n, percent0 = 0.5)
{
sample(c(0,1),n,replace = TRUE, prob = c(percent0,1-percent0))###These are the Y's
}
####Should we generate the levels of X_j based on a uniform sample, or a binomial sample? sample() versus rbinom()
#### It seems that it will be much easier to get a trend-like pattern for the levels of X_j if we use rbinom.
#### Use probabilities such as (0.45, 0.55) for Y = 0,1. This will cause more "successes" to correspond with higher levels of X_j.
makeX_ijTrinary <- function(n,p, trueSize = 10, Y)
{
probability = c(0.3, 0.4, 0.6, 0.7, 0.2, 0.4, 0.3, 0.8, 0.4, 0.2,
0.6, 0.1, 0.1, 0.4, 0.8, 0.7, 0.9, 0.2, 0.7, 0.6)####Table 4.1
table4_1 = matrix(data =probability , 2,10, byrow = TRUE)
X_ij = matrix(rep(-1,n*10), nrow = n, ncol = p)##The X_js are stored here for all n-many replicates.
####Initialized to -1 for ease of locating missed assignments.
for(j in 1:trueSize)
{
table4_1Vals = table4_1[Y+1,j]###If Y = m, the (m+1)th row of the jth column is the probability pi_mj given Y = m.
###This collects the requisite table values and puts them in a vector.
X_ij[,j] = sapply(table4_1Vals, rbinom, n = 1, size = 2)
###We define a whole column here! Each entry takes on the value of 0, 1, or 2.
}
for(j in (trueSize+1):p)
{
X_ij[,j] = sample(c(0,1,2), n, replace= TRUE, prob = rep(0.333333,3))
}
return(X_ij)
}
########################################################################
########################################################################
########################################################################
##### Create the simulation data from Huang et al.
##### For standardness sake, Y = 0,1,2,3. In Huang, it its 1-4, but I am abandoning that in my code.
makeYHuang <- function(n)
{
sample(c(1,2,3,0),n,replace = TRUE, prob = rep(0.25,4))###These are the Y's
}
probability = c(0.2, 0.8, 0.7, 0.2, 0.2, 0.9, 0.1,0.1,0.7,0.7,
0.9,0.3,0.3,0.7,0.8, 0.4, 0.7, 0.6, 0.4, 0.1,
0.7,0.2,0.1,0.6,0.7,0.6,0.8,0.9,0.1,0.8,
0.1, 0.9, 0.6, 0.1, 0.3, 0.1, 0.4, 0.3, 0.6, 0.4)####Table 1
table1 = matrix(data =probability , 4,10, byrow = TRUE)
makeX_ijHuang <- function(n,p, trueSize, Y)
{
X_ij = matrix(rep(-1,n*10), nrow = n, ncol = p)##The X_js are stored here for all n-many replicates.
####Initialized to -1 for ease of locating missed assignments.
for(i in 1:n)
{
for(j in 1:trueSize)
{
k = Y[i]
table1Val = table1[k+1,j]###the (k+1)th row of the jth column is the probability of X_j = 1 given Y = k.
#####Remember that I am taking Y = 0,1,2,3.
X_ij[i,j] = rbinom(1, 1, table1Val)
}
}
for(j in (trueSize+1):p)
{
X_ij[,j] = rbinom(n, 1, 0.5)
}
return(X_ij)
}
Y = makeYBinary(200, percent0 = 0.35)
covarsX = makeX_ijHuang(n = 200, p = 1000, trueSize = 10, Y = Y)
dta <- data.frame(
y = gl(3, 2),
x = sample(gl(3, 2))
)
## Asymptotic Cochran-Mantel-Haenszel Test
ct <- cmh_test(y ~ x, data = dta)
ct######Not the CA trend test we are looking for.
#####cmh_test()
######Testing correlation of Y and X.
Y = makeYBinary(500)
X_ij = makeX_ijTrinary(n = 500, p =3000, Y = Y)
for(j in 1:20)
print(cor(x =X_ij[,j], y = Y ))
##############################################################################################
##############################################################################################
##############################################################################################
###Distance Correlation
DCSIS = function(u, v, n){
u = as.numeric(u)
v = as.numeric(v)
m.u = matrix(u, n, n, byrow = TRUE)
m.v = matrix(v, n, n, byrow = TRUE)
s.u = abs(m.u - t(m.u))
s.v = abs(m.v - t(m.v))
s1 = sum((s.u) * (s.v)) / (n * n)
s2 = sum(s.u) * sum(s.v) / (n * n * n * n)
s3 = sum(rowSums(s.u) * (s.v)) / (n * n * n)
dcov <- sqrt(abs(s1 + s2 -2 * s3))
return(dcov)
}
Y = makeYEx1(4)
Xij = makeX_ijEx1(n = 4, p =20, Y = Y)
for(j in 1:20)
{
print(DCSIS(Xij[,j], Y, n = 4))
}
DCSIS(Xij[,2], Y, n = 4)
Xij[,2]
Y
Y = makeYHuang(200)
Xij = makeX_ijHuang(n = 200, p =1000, Y = Y)
p = dim(Xij)[2]
N = dim(Xij)[1]
rank.DCSIS = rep(0, p)
omega = matrix(0, 1, p)
dcov.y = DCSIS(Y,Y, n = N)
for(j in 1:p){
X.j = matrix(Xij[, j])
dcov.xy = DCSIS(X.j, Y, n = N)
dcov.xx = DCSIS(X.j, X.j, n = N)
dcorr = dcov.xy / sqrt(dcov.xx * dcov.y)
omega[, j] = dcorr * dcorr
}
rank.DCSIS = p +1- rank(omega, ties.method = 'random')
rank.DCSIS
in.TrueModel = (rank.DCSIS <= 10)
max(which(in.TrueModel))#####This finds the smallest model size required to include the true model.
###################################################################################################
###################################################################################################
####### CA-Trend specific code.
calculatep_lk <- function(X_ijMat, numYlevels = 2, capK_j, vscores = c(0,1,2), p, n, Y)
{
maxK = max(capK_j)
p_lk = array(dim = c(numYlevels,maxK, p))
for(j in 1:p)
for(k in 1:capK_j[j])
{
for(m in 0:(numYlevels-1))
{
p_lk[m+1,k,j] = 1/n *sum((Y == m)*(X_ijMat[,j] == vscores[k]))
###The total proportion of X_ij=v_k when Y = m
}
}
return(p_lk)
}
calculate_rSquared <- function(v_kj, p_lk, capK_j, p, Y, numYlevels = 2)
{####v_kj is a (perhaps ragged) K_j x p matrix of categorical scores for each level k of X_j.
####In practice, v_kj is the same for every column. Above I just
###p_lk is a (perhaps ragged) m x K_j x p array
### with the total proportion (out of n) of the X_ij=k associated with response l.
###capK_j is a vector of all of the K_j associated with the X_j
###p is p, the number of full model covariates.
numSummands = matrix(nrow = max(capK_j), ncol = p)###
XvarSummands = matrix(nrow = max(capK_j), ncol = p)###
YvarSummands = vector(length = numYlevels)
##print(numSummands)
yBar = mean(Y)
v_jBar = apply(v_kj, MARGIN = 2, mean)###v_jBar is the average score for the levels of X_j.
numerator = vector(length = p)
denominator = vector(length = p)
#print((1-yBar)*(v_kj[1,1] - v_jBar[1])*p_lk[2,1,1] - yBar*(v_kj[1,1] - v_jBar[1])*p_lk[1,1,1])
for(j in 1:p)
{
for(k in 1:capK_j[j])
{
iterationOverM = vector(length = numYlevels)
for(m in 0:(numYlevels-1))
{
iterationOverM[m+1] = (m-yBar)*(v_kj[k,j] - v_jBar[j])*p_lk[m+1,k,j]
YvarSummands[m+1] = (m-yBar)^2*sum(p_lk[m+1,,j])
}
numSummands[k,j] = sum(iterationOverM)
XvarSummands[k,j] = sum(p_lk[,k,j])*(v_kj[k,j] - v_jBar[j])^2
}
numerator[j] = sum(numSummands[,j])^2
denominator[j] = sum(YvarSummands) * sum(XvarSummands[,j])
}
rSquared = numerator/denominator
return(list(rSquared, numerator))####This is a vector of length p. So we have each r^2_j in a vector.
}
findCutoff <- function(sorted_r)##The rSquareds should be sorted in descending order.
{
#####I am going to ignore the tail values (j = 1, and the very very small rSquareds )
#### The tail values are throwing it off. We do not want the empty model or the (near) full model.
#### The issue is that some of the rSquared_j for large j are so small that their ratio is huge.
pShortened = length(sorted_r)###Accounting for removing the really tiny r^2 values.
ratios = vector(length = pShortened)###
ratios[1] = sorted_r[1]/sorted_r[2]
for(j in 2:pShortened)###Ignoring the tail values on each end
{
ratios[j] = sorted_r[j]/sorted_r[j+1]
}
dHat =which.max(ratios) ####This which.max function is equivalnet to argmax (which is not a function in R)
#print(ratios)
return(dHat)
}
runSimulationCATrend_findCutoff <- function(n, p)
{
set.seed(7919)
#Y = makeYHuang(n)
Y = makeYBinary(n)
#print(head(Y,20))
#scoresV = matrix(data = c(0,1), nrow = 2, ncol = p)
#print(scoresV)
scoresV = matrix(data = c(0,1,2), nrow = 3, ncol = p)
# K_jVect = rep(2, p)
K_jVect = rep(3, p)
#print(K_jVect)
#covarsX_ij = makeX_ijHuang(n = n, p = p, trueSize = 10, Y = Y)
covarsX_ij = makeX_ijTrinary(n = n, p = p, trueSize = 10, Y = Y)
#print(head.matrix(covarsX_ij, 3))
p_lkMat = calculatep_lk(X_ijMat = covarsX_ij,numYlevels = 2, capK_j = K_jVect, p = p,n = n, Y = Y)
#print(p_lkMat[,,1:15])
rSquared_j = calculate_rSquared(v_kj = scoresV,p_lk = p_lkMat, capK_j = K_jVect, p= p, Y = Y , numYlevels = 2)[[1]]
rSquared_j = rSquared_j[rSquared_j > 5e-6]
#print(rSquared_j)
sorted_r = sort(rSquared_j, index.return = TRUE, decreasing = TRUE)
#print(head(sorted_r$ix,10))
if(sum(head(sorted_r$ix, 10))>sum(1:10))
{warning("The largest rSquareds were not the first ten!")}
dHat = findCutoff(sorted_r$x[1:(length(sorted_r$x)-(p*(30/n)))])
#print(sorted_r$x[dHat])
#print(sorted_r$x[dHat+1])
return(dHat)
}
runSimulationCATrend_findCutoff(n = 200, p = 1000)
##########################################################
##########################################################
#### MMLE METHOD
#### I USE THE BULIT IN glm() function. It performs mle.
extractBeta_j_2ndMethod <- function(p, X_ij, Y)
{
Beta_jHatVect = vector(length = p)####A vector of all the beta_j hats taken in MAGNITUDE.
for(j in 1:p)
{
Beta_jHatVect[j] = glm(Y ~ X_ij[,j], family = "binomial")$coefficients[[2]]
}
Beta_jHatVect = abs(Beta_jHatVect)###We just want magnitude.
}
##########################################################
##########################################################
#### Huang's METHOD Huang's METHOD Huang's METHOD
#### I ADAPT THE BULIT IN chisq.test() function.
makeAllDelta_j_Prefab <- function(X_ij, Y, n)
{
#####The returned value from the built in method chisq.test is n*Delta.
Deltas = apply(X_ij, MARGIN = 2, function(X_jColumn, y){return(1/n * as.numeric(chisq.test(x = X_jColumn, y = Y)$statistic))}, y = Y)
#apply(covarsX, MARGIN = 2, chisq.test, y = Y)
return(Deltas)
}
#####################################################################################################
#####################################################################################################
######################## THE ACTUAL SIMULATIONS ######################
#####################################################################################################
#####################################################################################################
########Doing CA-trend on Huang's data is proving very difficult for some reason.
########Either CA-doesn't work on Huang data....or something is off in the code. Look at the packages perhaps.
######## Although none of the packages seem to be quickly implementable or even what we want.
######## coin for cmh_test() is not what we want. It is a different method.
######A function to find p_j as she calls it (p_s in DCSIS)
prepForp_j <-function(sortedIndicies, d)
{
firstDfeatures = sortedIndicies[1:d]
containsEach = 1:10 %in% firstDfeatures
return(containsEach)
}
#### We report the minimum model size required to contain all true predictors.
######-------------------------------------------------------------------------------------------------------------------------------
#########CA Trend CA Trend CA Trend CA Trend CA Trend CA Trend
######-------------------------------------------------------------------------------------------------------------------------------
runSimCATrend_minModSize <- function(n, p, preseed = 7919)
{
set.seed(preseed)
#Y = makeYHuang(n)
Y = makeYBinary(n, percent0 = 0.5)
#print(head(Y,20))
#scoresV = matrix(data = c(0,1), nrow = 2, ncol = p)
#print(scoresV)
scoresV = matrix(data = c(0,1,2), nrow = 3, ncol = p)
# K_jVect = rep(2, p)
K_jVect = rep(3, p)
#print(K_jVect)
#covarsX_ij = makeX_ijHuang(n = n, p = p, trueSize = 10, Y = Y)
covarsX_ij = makeX_ijTrinary(n = n, p = p, trueSize = 10, Y = Y)
#print(head.matrix(covarsX_ij, 3))
#print(covarsX_ij[1:10, 1:20])
p_lkMat = calculatep_lk(X_ijMat = covarsX_ij,numYlevels = 2, capK_j = K_jVect, p = p,n = n, Y = Y)
#print(p_lkMat[,,1:15])
rSquared_j = calculate_rSquared(v_kj = scoresV,p_lk = p_lkMat, capK_j = K_jVect, p= p, Y = Y , numYlevels = 2)[[1]]
rSquared_j = rSquared_j[rSquared_j > 5e-6]
#print(rSquared_j)
sorted_r = sort(rSquared_j, index.return = TRUE, decreasing = TRUE)
first10 = prepForp_j(sorted_r$ix, 10)
first11 = prepForp_j(sorted_r$ix, 11)
first15 = prepForp_j(sorted_r$ix, 15)
in.TrueModel = (sorted_r$ix <= 10)
minModelSize = max(which(in.TrueModel))#####This finds the smallest model size required to include the true model.
return(list(minModelSize,first10, first11, first15))
}
runSimCATrend_minModSize(n = 100, p = 3000)
reps = 500
minModelSizes = vector(length = reps)
p_j_forD10 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD11 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD15 = matrix(data = -1, nrow = reps, ncol = 10)
timestamp()##------ Wed Aug 17 11:37:34 2016 ------##
for(w in 1:reps)
{
if(w %% 100 == 0)
{print("Benchmark" )}
newSeed = 7919 +20*w + w^2 - w^3
simList = runSimCATrend_minModSize(n = 200, p = 5000, preseed = newSeed)
minModelSizes[w] = simList[[1]]
p_j_forD10[w,] = simList[[2]]
p_j_forD11[w,] = simList[[3]]
p_j_forD15[w,] = simList[[4]]
}
timestamp()##------ Wed Aug 17 11:40:53 2016 ------##
mean(minModelSizes)## 10.302#####The listed menas are all for percent0 = 0.5
head(minModelSizes)
CAminModelSizes = c(11,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,12,10,10,10,10,11,10,10,10,10,
10,19,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,11,10,10,10,10,10,10,10,54,10,10,10,10,10,10,10,11,11,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,12,11,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,32,10,10,10,12,10,11,10,10,10,10,10,10,10,
11,11,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,14,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,11,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,12,10,11,10,10,10,10,10,10,10,10,10,10,11,10,11,10,10,10,10,11,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,11,10,10,10,10,10,10,
10,10,10,10,10,10,10,11,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,12,10,10,
10,12,10,10,10,10,10,11,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,17,10,16,
10,10,10,10,10,11,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,12,10,10,10,10,
10,10,10,10,10,14,10,10,11,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,11,10,10,10,
10,10,10,10,10,10,10,10,11,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,15,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10)
quantile(minModelSizes, probs =c(0.25,0.75, 0.9,0.95, 0.99))
get_p_a <-function(minModSzs,d)
{
fullTrueModelNum = sum((minModSzs <= d))
return(fullTrueModelNum/length(minModSzs))
}
get_p_j <-function(first10, first11, first15)
{
p_j_10 = apply(first10, MARGIN = 2, sum)/reps
p_j_11 = apply(first11, MARGIN = 2, sum)/reps
p_j_15 = apply(first15, MARGIN = 2, sum)/reps
return(list(p_j_10, p_j_11, p_j_15))
}
get_p_a(minModSzs = CAminModelSizes, d = 10)
get_p_a(minModSzs = CAminModelSizes, d = 11)
get_p_a(minModSzs = CAminModelSizes, d = 12)
get_p_a(minModSzs = CAminModelSizes, d = 15)
get_p_j(p_j_forD10, p_j_forD11, p_j_forD15)
######-------------------------------------------------------------------------------------------------------------------------------
######### MMLE MMLE MMLE MMLE MMLE
######-------------------------------------------------------------------------------------------------------------------------------
runSimMMLE_minModSize <- function(n, p, preseed = 7919)
{
set.seed(preseed)
Y = makeYBinary(n, percent0 = 0.5)
covarsX_ij = makeX_ijTrinary(n = n, p = p, trueSize = 10, Y = Y)
theBetas = extractBeta_j_2ndMethod(p,covarsX_ij, Y)###Faster than my method
sorted_beta = sort(theBetas, index.return = TRUE, decreasing = TRUE)
first10 = prepForp_j(sorted_beta$ix, 10)
first11 = prepForp_j(sorted_beta$ix, 11)
first15 = prepForp_j(sorted_beta$ix, 15)
in.TrueModel = (sorted_beta$ix <= 10)
minModSz = max(which(in.TrueModel))#####This finds the smallest model size required to include the true model.
return(list(minModSz, first10, first11, first15))
}
runSimMMLE_minModSize(n = 200, p = 3000)
reps = 500
minModelSizes = vector(length = reps)
p_j_forD10 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD11 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD15 = matrix(data = -1, nrow = reps, ncol = 10)
timestamp()#####Rather slow. Can this be vectorized?
for(w in 1:reps)
{
newSeed = 7919 +20*w + w^2 - w^3
simList = runSimMMLE_minModSize(n = 200, p = 3000, preseed = newSeed)
if(w %% 100 == 0)
{print("Benchmark" )}
minModelSizes[w] = simList[[1]]
p_j_forD10[w,] = simList[[2]]
p_j_forD11[w,] = simList[[3]]
p_j_forD15[w,] = simList[[4]]
}
timestamp()
mean(minModelSizes)####10.042#####The listed menas are all for percent0 = 0.5
head(minModelSizes)
MMLEminModelSizes = c(10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,20,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,15,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10)
mean(MMLEminModelSizes)
quantile(MMLEminModelSizes, probs =c(0.25,0.5,0.9,0.95, 0.99))
get_p_a(minModSzs = MMLEminModelSizes, d = 10)
get_p_a(minModSzs = MMLEminModelSizes, d = 11)
get_p_a(minModSzs = MMLEminModelSizes, d = 12)
get_p_a(minModSzs = MMLEminModelSizes, d = 15)
get_p_j(p_j_forD10, p_j_forD11, p_j_forD15)
######-------------------------------------------------------------------------------------------------------------------------------
#########DCSIS DCSIS DCSIS DCSIS DCSIS DCSIS DCSIS
######-------------------------------------------------------------------------------------------------------------------------------
runSimDCSIS_minModSize <- function(n, p, preseed = 7919)
{
set.seed(preseed)
Y = makeYBinary(n)
covarsX_ij = makeX_ijTrinary(n = n, p = p, trueSize = 10, Y = Y)
#p = dim(covarsX_ij)[2]
#N = dim(covarsX_ij)[1]
rank.DCSIS = rep(0, p)
omega = matrix(0, 1, p)
dcov.y = DCSIS(Y,Y, n = n)
for(j in 1:p)
{
X.j = matrix(covarsX_ij[, j])
dcov.xy = DCSIS(X.j, Y, n = n)
dcov.xx = DCSIS(X.j, X.j, n = n)
dcorr = dcov.xy / sqrt(dcov.xx * dcov.y)
omega[, j] = dcorr * dcorr
}
#sorted.DCSIS = p +1- rank(omega, ties.method = 'random')
sorted.DCSIS = sort(omega, index.return = TRUE, decreasing = TRUE)
first10 = prepForp_j(sorted.DCSIS$ix, 10)
first11 = prepForp_j(sorted.DCSIS$ix, 11)
first15 = prepForp_j(sorted.DCSIS$ix, 15)
in.TrueModel = (sorted.DCSIS$ix <= 10)
minModSz = max(which(in.TrueModel))
return(list(minModSz, first10, first11, first15))
}
reps = 500
minModelSizes = vector(length = reps)
p_j_forD10 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD11 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD15 = matrix(data = -1, nrow = reps, ncol = 10)
timestamp()##------ Wed Aug 17 11:46:22 2016 ------####------ Mon Aug 29 12:50:34 2016 ------##
for(w in 1:reps)
{
if(w %% 100 == 0)
{print("Benchmark" )}
newSeed = 7919 +20*w + w^2 - w^3
simList = runSimDCSIS_minModSize(n = 200, p = 5000, preseed = newSeed)
minModelSizes[w] = simList[[1]]
p_j_forD10[w,] = simList[[2]]
p_j_forD11[w,] = simList[[3]]
p_j_forD15[w,] = simList[[4]]
}
timestamp()##------ Wed Aug 17 13:12:45 2016 ------####------ Mon Aug 29 14:11:51 2016 ------##
mean(minModelSizes)#10.324#####The listed menas are all for percent0 = 0.5
head(minModelSizes)
###
DCSISminModelSizes = c(12,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,12,10,10,10,10,10,10,10,10,10,10,17,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,59,10,10,10,10,10,10,10,11,11,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,13,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,36,10,11,10,10,10,11,10,10,10,10,10,10,10,11,12,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,15,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,14,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,12,10,11,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,13,10,11,10,10,10,10,10,10,10,10,10,10,
11,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,11,10,10,10,10,10,10,10,10,10,11,10,10,10,10,
10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,12,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,20,10,19,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,19,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10)
mean(DCSISminModelSizes)
quantile(DCSISminModelSizes, probs =c(0.25,0.5, 0.9,0.95, 0.99))
get_p_a(minModSzs = minModelSizes, d = 10)
get_p_a(minModSzs = minModelSizes, d = 11)
get_p_a(minModSzs = minModelSizes, d = 12)
get_p_a(minModSzs = minModelSizes, d = 15)
get_p_j(p_j_forD10, p_j_forD11, p_j_forD15)
######-------------------------------------------------------------------------------------------------------------------------------
#########HUANG HUANG HUANG HUANG HUANG
######-------------------------------------------------------------------------------------------------------------------------------
runSimHuang_minModSize <- function(n, p, preseed = 7919)
{
set.seed(preseed)
Y = makeYBinary(n, percent0 = 0.5)
covarsX_ij = makeX_ijTrinary(n = n, p = p, trueSize = 10, Y = Y)
theDeltas = makeAllDelta_j_Prefab(X_ij = covarsX_ij, Y = Y, n = n)
sorted_Delta = sort(theDeltas, index.return = TRUE, decreasing = TRUE)
first10 = prepForp_j(sorted_Delta$ix, 10)
first11 = prepForp_j(sorted_Delta$ix, 11)
first15 = prepForp_j(sorted_Delta$ix, 15)
in.TrueModel = (sorted_Delta$ix <= 10)
minModSz = max(which(in.TrueModel))#####This finds the smallest model size required to include the true model.
return(list(minModSz, first10, first11, first15))
}
runSimHuang_minModSize(n = 200, p = 3000)
reps = 500
minModelSizes = vector(length = reps)
p_j_forD10 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD11 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD15 = matrix(data = -1, nrow = reps, ncol = 10)
timestamp()##------ Thu Aug 18 15:27:57 2016 ------##
for(w in 1:reps)
{
if(w %% 100 == 0)
{print("Benchmark" )}
newSeed = 7919 +20*w + w^2 - w^3
simList = runSimHuang_minModSize(n = 200, p = 5000, preseed = newSeed)
minModelSizes[w] = simList[[1]]
p_j_forD10[w,] = simList[[2]]
p_j_forD11[w,] = simList[[3]]
p_j_forD15[w,] = simList[[4]]
}
timestamp()##------ Thu Aug 18 15:49:23 2016 ------##
mean(minModelSizes)#10.674 #####The listed menas are all for percent0 = 0.5
head(minModelSizes)#13 10 10 10 10 10
HuangminModelSizes = c(13,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,14,10,10,10,10,10,10,10,10,10,10,20,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,13,10,10,10,10,10,10,10,103,10,10,10,10,10,10,10,11,12,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,
10,10,10,10,11,11,10,10,13,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,14,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,49,10,12,10,11,10,16,10,10,10,10,10,10,10,11,13,10,10,10,10,10,10,10,10,10,10,10,11,10,10,12,10,10,10,10,10,10,10,10,10,10,10,24,10,10,10,10,
11,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,19,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,11,10,10,10,10,10,10,10,
11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,13,10,13,11,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,22,10,13,10,10,10,10,10,10,10,10,
10,10,11,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,12,10,10,10,11,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,
10,10,11,11,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,12,10,10,10,11,10,11,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,35,10,37,10,11,11,10,
10,10,10,10,11,10,10,10,15,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,11,10,
10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,28,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,11,10,10,10,10,10,10,10)
mean(HuangminModelSizes)
quantile(minModelSizes, probs =c(0.25,0.75, 0.9, 0.95, 0.99))
get_p_a(minModSzs = minModelSizes, d = 10)
get_p_a(minModSzs = minModelSizes, d = 11)
get_p_a(minModSzs = minModelSizes, d = 12)
get_p_a(minModSzs = minModelSizes, d = 15)
get_p_j(p_j_forD10, p_j_forD11, p_j_forD15)
############## @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ##############
############## Making LINEARLY Correlated Data. ##############
############## @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ##############
########Some preliminary tests.
Ytest = makeYBinary(200)
X_ij = sapply(Ytest, function(y){rnorm(1, mean =y, sd = 1)})
plot(X_ij)
X_ij[X_ij>1.6912] = 2
X_ij[X_ij>0.3088 & X_ij<1.6912] = 1
X_ij[X_ij < 0.3088] = 0
table(X_ij, Ytest)
Ytest = makeYBinary(200)
X_ij = sapply(Ytest, function(y){rnorm(1, mean =y, sd = 1)})
plot(X_ij)
X_ij[X_ij>= 1] = 2
X_ij[X_ij>0.25 & X_ij<1] = 1
X_ij[X_ij <= 0.25] = 0
table(X_ij, Ytest)
findCutoff <- function(kappa, largerMean = 2)
{
return(0.5*(pnorm(kappa, mean = largerMean) + pnorm(kappa)))
}
##################################################################
##### Generating the trend data.
##################################################################
##upperMeanScalers= c(2,2,2,2,2,1,1,1,1,1)
upperMeanScalers= c(1,1,1,1,1,1,1,1,1,1)
#vectorCutoffs = c(0, 2, 0.3088, 1.6912, 1, 1.832, 1, 2.283, 0.5866, 1.4134,
# 0.25,1,0,1,0.1,1,-0.2,1.2,0.213, 0.787)
vectorCutoffs = c(0, 0.75, 0, 1, 0.2, 0.8, 0, 0.9, -0.213, 1.213,
0.25,1,0,1,0.1,1,-0.2,1.2,0.213, 0.787)
#vectorCutoffs = c(0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 0.25,1,0,1,0.1,1,-0.2,1.2,0.213, 0.787)
cutoffs = matrix(vectorCutoffs, nrow = 10,ncol = 2, byrow = TRUE)
cutoffs
###Generate Y as before.
###Then generate X_ij using the following function.
makeX_ijLinear <- function(n,p, trueSize = 10, Y, cutoffs, upperMeanScalers, vscores)
{
X_ij = matrix(-1, nrow = n, ncol = p)##The X_js are stored here for all n-many replicates.
####Initialized to -1 for ease of locating missed assignments.'
#print(X_ij)
for(j in 1:trueSize)
{
column_j = sapply(Y, function(y){rnorm(1, mean =upperMeanScalers[j]*y, sd = 1)})
#Define a whole column.
kappa_L = cutoffs[j,1]
kappa_U = cutoffs[j,2]
column_j[(column_j>kappa_U)] = 222 ###This is done to prevent reassignment when the kappa_U is > 2.
column_j[(column_j>=kappa_L & column_j<=kappa_U)] = vscores[2]
column_j[(column_j < kappa_L)] = vscores[1]
column_j[column_j ==222] = vscores[3] #Switch to the correct value after assignment of other levels.
X_ij[,j] = column_j
}
for(j in (trueSize+1):p)
{
X_ij[,j] = sample(vscores, n, replace= TRUE, prob = rep(0.333333,3))
}
return(X_ij)
}
Y = makeYBinary(200)
covarsX = makeX_ijLinear(n = 200, p = 30, Y = Y, cutoffs = cutoffs, upperMeanScalers = upperMeanScalers, vscores = c(0,2,4))
covarsX
####Look at Spearman's Rho test. Maybe use as another screening method.
table(covarsX[,2], Y)
cor(x = covarsX[,6], y = Y)
cor(x = covarsX[,12], y = Y)
for(j in 1:30)
{
print(cor(x = covarsX[,j], y = Y))
}
##########################################################################
############# SIMULATIONS ON Linearly correlated Data.
#### We report the minimum model size required to contain all true predictors.
######-------------------------------------------------------------------------------------------------------------------------------
#########CA Trend CA Trend CA Trend CA Trend CA Trend CA Trend
######-------------------------------------------------------------------------------------------------------------------------------
runSimCATrend_Linear <- function(n, p, preseed = 7919, scores)
{
set.seed(preseed)
#Y = makeYHuang(n)
Y = makeYBinary(n, percent0 = 0.5)
#print(head(Y,20))
#scoresV = matrix(data = c(0,1), nrow = 2, ncol = p)
#print(scoresV)
scoresV = matrix(data = scores, nrow = 3, ncol = p)
# K_jVect = rep(2, p)
K_jVect = rep(3, p)
#print(K_jVect)
ums= c(1,1,1,1,1,1,1,1,1,1)
vectorCutoffs = c(0, 0.75, 0, 1, 0.2, 0.8, 0, 0.9, -0.213, 1.213,
0.25,1,0,1,0.1,1,-0.2,1.2,0.213, 0.787)
cutoffs = matrix(vectorCutoffs, nrow = 10,ncol = 2, byrow = TRUE)
#covarsX_ij = makeX_ijHuang(n = n, p = p, trueSize = 10, Y = Y)
covarsX_ij = makeX_ijLinear(n = n, p = p, Y = Y, cutoffs = cutoffs,
upperMeanScalers = ums, vscores = scores)
#print(head.matrix(covarsX_ij, 3))
#print(covarsX_ij[1:10, 1:20])
p_lkMat = calculatep_lk(X_ijMat = covarsX_ij,numYlevels = 2, capK_j = K_jVect,
p = p,n = n, Y = Y, vscores = scores)
#print(p_lkMat[,,1:15])
rSquared_j = calculate_rSquared(v_kj = scoresV,p_lk = p_lkMat,
capK_j = K_jVect, p= p, Y = Y , numYlevels = 2)
#rSquared_j = rSquared_j[rSquared_j > 5e-6]
#print(rSquared_j)
sorted_r = sort(rSquared_j, index.return = TRUE, decreasing = TRUE)
first10 = prepForp_j(sorted_r$ix, 10)
first11 = prepForp_j(sorted_r$ix, 11)
first15 = prepForp_j(sorted_r$ix, 15)
in.TrueModel = (sorted_r$ix <= 10)
minModelSize = max(which(in.TrueModel))
#####This finds the smallest model size required to include the true model.
return(list(minModelSize,first10, first11, first15))
}
runSimCATrend_Linear(n = 200, p = 5000, preseed = round(runif(1)*100000), scores= c(0,2,5))
reps = 500
minModelSizes = vector(length = reps)
p_j_forD10 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD11 = matrix(data = -1, nrow = reps, ncol = 10)
p_j_forD15 = matrix(data = -1, nrow = reps, ncol = 10)
timestamp()##------ Tue Aug 30 11:28:02 2016 ------##
for(w in 1:reps)
{
if(w %% 100 == 0)
{print("Benchmark" )}
newSeed = 7919 +20*w + w^2 - w^3
simList = runSimCATrend_Linear(n = 125, p = 3000, preseed = newSeed, scores = c(0,2,6))
minModelSizes[w] = simList[[1]]
p_j_forD10[w,] = simList[[2]]
p_j_forD11[w,] = simList[[3]]
p_j_forD15[w,] = simList[[4]]
}
timestamp()##------ Tue Aug 30 11:33:11 2016 ------##
mean(minModelSizes)####10.15
head(minModelSizes)
CAminModelLinear = c(10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,15,10,10,10,10,10,10,10,10,16,10,10,10,10,10,10,13,10,10,10,12,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,11,10,10,10,10,11,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,
10,10,10,10,10,10,13,10,11,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,16,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,10,10,10,19,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,10,10,10,10,14,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,12,10,12,10,17,10,10,10,10,10,10,10,10,10,11,10,10,10,10,10,10,10,10,10,10,
10,10,13,10,13,10)
mean(CAminModelLinear)
quantile(minModelSizes, probs =c(0.25,0.75, 0.9,0.95, 0.99))
get_p_a <-function(minModSzs,d)
{
fullTrueModelNum = sum((minModSzs <= d))
return(fullTrueModelNum/length(minModSzs))
}
get_p_j <-function(first10, first11, first15)
{
p_j_10 = apply(first10, MARGIN = 2, sum)/reps
p_j_11 = apply(first11, MARGIN = 2, sum)/reps
p_j_15 = apply(first15, MARGIN = 2, sum)/reps
return(list(p_j_10, p_j_11, p_j_15))
}
get_p_a(minModSzs = minModelSizes, d = 10)
get_p_a(minModSzs = minModelSizes, d = 11)
get_p_a(minModSzs = minModelSizes, d = 12)
get_p_a(minModSzs = minModelSizes, d = 15)
get_p_j(p_j_forD10, p_j_forD11, p_j_forD15)
##############################################################################
##############################################################################
##### MMLE MMLE MMLE MMLE MMLE MMLE MMLE
##############################################################################
##############################################################################
runSimMMLE_Linear <- function(n, p, preseed = 7919, scores = c(0,1,2))
{
set.seed(preseed)
Y = makeYBinary(n, percent0 = 0.5)
ums= c(1,1,1,1,1,1,1,1,1,1)