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}
for(i in 1:Groups){
curve(Linf_g[i,1] * (1 - exp(-k_g[i,1] * (x - t0_g[i,1]))), from = 0, to = 15, col = i, lwd = 3, add = TRUE)
}
# https://github.com/grantdadams/Growth-Models/tree/master
library(RTMB)
###### Simulate data
set.seed(1234)
# Number of Groups
Groups=6
# True VBGM hyperparameters c(mean, sd)
true.Linf = c(500,20)
true.k = c(.3,.05)
true.t0 = c(1.5,.4)
sigma <- 15
# Age range
ages = seq(from=1,to=15, by = .05)
# Empty matrix and vectors to fill with parameters and data, respectively
param.mat = matrix(NA,Groups,3,byrow = T)
colnames(param.mat) <- c("Linf", "k", "t0")
ctr = 0
age = c()
length = c()
group = c()
# Simulate group level parameters
for(i in 1:Groups){
# This should be a multi-variate normal ideally
param.mat[i,1] = rnorm(1,true.Linf[1],true.Linf[2]) # Assign group level Linf
param.mat[i,2] = rnorm(1,true.k[1],true.k[2]) # Assign group level k
param.mat[i,3] = rnorm(1,true.t0[1],true.t0[2]) # Assign group level t0
n.samples = sample(200:1000, 1) # Number of samples per group s
# Simulate data
for(j in 1:n.samples) {
ctr = ctr + 1 # Indexing variable
age[ctr] = sample(ages, 1) # Sample randon age from age range
length[ctr] = (param.mat[i,1] * (1 - exp(-param.mat[i,2]*(age[ctr]-param.mat[i,3])))) + rnorm(1,0,sigma)
group[ctr] = i
}
}
# Assign data to data frame
dat = data.frame(age = age, length = length, group = group, N = length(age), G = length(unique(group)))
dat <- dat[which(dat$length > 0),]
# Plot the data
plot(NA, NA, xlim = c(0, 15), ylim = c(0, max(dat$length)), xlab = "Age (yr)", ylab = "Length (mm)")
points(dat$age, dat$length , col = dat$group)
###### Write model
VBGM <- function(parms, dataList) {
# - Data
Age_i <- dataList$Age_i
Length_i <- dataList$Length_i
Group_i <- dataList$Group_i
# - Parameters
Linf <- exp(parms$logLinf) # To keep > 0
k <- exp(parms$logk)
t0 <- parms$t0
SD <- exp(parms$logSD)
# random effects params
log_Linf_d <- parms$coef_Linf
Linf_d <- exp(log_Linf_d)
Linf_d_sigma <- exp(parms$log_Linf_sigma)
log_k_d <- parms$coef_k
k_d <- exp(log_k_d)
k_d_sigma <- exp(parms$log_k_sigma)
t0_d <- parms$coef_t0
t0_d_sigma <- exp(parms$log_t0_sigma)
# - Model
Linf_g = Linf * Linf_d
k_g = k_d * k
t0_g = t0 + t0_d
Pred_Length_i = Linf_g[Group_i] * (1 - exp(-k_g[Group_i]* (Age_i - t0_g[Group_i])))
# - Likelihood
nll = 0
nll = nll - sum(dnorm(x = log_Linf_d, mean = 0, sd = Linf_d_sigma, log = TRUE))
nll = nll - sum(dnorm(x = log_k_d, mean = 0, sd = k_d_sigma, log = TRUE))
nll = nll - sum(dnorm(x = t0_d, mean = 0, sd = t0_d_sigma, log = TRUE))
nll = nll - sum(dnorm(x = Length_i, mean = Pred_Length_i, sd = SD, log = TRUE))
# - Report
REPORT(Linf_g)
REPORT(k_g)
REPORT(t0_g)
ADREPORT(Linf);
ADREPORT(k);
ADREPORT(t0);
ADREPORT(SD);
ADREPORT(Linf_g);
ADREPORT(k_g);
ADREPORT(t0_g);
# ADREPORT(Linf_g[Group_i] * (1 - exp(-k_g[Group_i]* (Age_i - t0_g[Group_i]))));
nll
}
###### Fit model
# Build model objects
# - Parameters
parameters = list(logLinf = 5,
logk = log(0.3),
t0 = 2,
logSD = 0,
coef_Linf = rep(0, Groups),
log_Linf_sigma = 0,
coef_k = rep(0, Groups),
log_k_sigma = 0,
coef_t0 = rep(0, Groups),
log_t0_sigma = 0
) # CAREFUL WITH STARTING VALUES
# - Map (turn off parameters using NA)
map <- list(
coef_Linf = as.factor(rep(NA, Groups)),
coef_k = as.factor(rep(NA, Groups)),
coef_t0 = as.factor(rep(NA, Groups)),
log_Linf_sigma = as.factor(NA),
log_k_sigma = as.factor(NA),
log_t0_sigma = as.factor(NA)
)
# - Data
data = list(Length_i = dat$length, Age_i = dat$age, Group_i = dat$group)
random = c('coef_Linf', 'coef_k', 'coef_t0')
# - Model object
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
obj <- MakeADFun(cmb(VBGM, data), parameters, random = random)
# Estimate
obj$hessian <- TRUE
opt <- nlminb(obj$par, obj$fn, obj$gr)
opt
# Get uncertainty via Delta method
rep <- sdreport(obj)
summ <- summary(rep)
# Plot
plot(NA, NA, xlim = c(0, 15), ylim = c(0, max(dat$length)), xlab = "Age (yr)", ylab = "Length (mm)")
points(dat$age, dat$length , col = dat$group)
# - Rearrange parameters
library(dplyr)
library(stringr)
summ <- as.data.frame(summ)
summ$Parm <- rownames(summ)
Linf_g <- summ %>%
filter(str_detect(Parm, regex("Linf_g", ignore_case = TRUE)))
k_g <- summ %>%
filter(str_detect(Parm, regex("k_g", ignore_case = TRUE)))
t0_g <- summ %>%
filter(str_detect(Parm, regex("t0_g", ignore_case = TRUE)))
for(i in 1:Groups){
curve(Linf_g[i,1] * (1 - exp(-k_g[i,1] * (x - t0_g[i,1]))), from = 0, to = 15, col = i, lwd = 3, add = TRUE)
}
# https://github.com/grantdadams/Growth-Models/tree/master
library(RTMB)
###### Simulate data ----
set.seed(1234)
# Number of Groups
Groups=6
# True VBGM hyperparameters c(mean, sd)
true.Linf = c(500,20)
true.k = c(.3,.05)
true.t0 = c(1.5,.4)
sigma <- 15
# Age range
ages = seq(from=1,to=15, by = .05)
# Empty matrix and vectors to fill with parameters and data, respectively
param.mat = matrix(NA,Groups,3,byrow = T)
colnames(param.mat) <- c("Linf", "k", "t0")
ctr = 0
age = c()
length = c()
group = c()
# Simulate group level parameters
for(i in 1:Groups){
# This should be a multi-variate normal ideally
param.mat[i,1] = rnorm(1,true.Linf[1],true.Linf[2]) # Assign group level Linf
param.mat[i,2] = rnorm(1,true.k[1],true.k[2]) # Assign group level k
param.mat[i,3] = rnorm(1,true.t0[1],true.t0[2]) # Assign group level t0
n.samples = sample(200:1000, 1) # Number of samples per group s
# Simulate data
for(j in 1:n.samples) {
ctr = ctr + 1 # Indexing variable
age[ctr] = sample(ages, 1) # Sample randon age from age range
length[ctr] = (param.mat[i,1] * (1 - exp(-param.mat[i,2]*(age[ctr]-param.mat[i,3])))) + rnorm(1,0,sigma)
group[ctr] = i
}
}
# Assign data to data frame
dat = data.frame(age = age, length = length, group = group, N = length(age), G = length(unique(group)))
dat <- dat[which(dat$length > 0),]
# Plot the data
plot(NA, NA, xlim = c(0, 15), ylim = c(0, max(dat$length)), xlab = "Age (yr)", ylab = "Length (mm)")
points(dat$age, dat$length , col = dat$group)
###### Write model ----
VBGM <- function(parms, dataList) {
# - Data
Age_i <- dataList$Age_i
Length_i <- dataList$Length_i
Group_i <- dataList$Group_i
# - Parameters
Linf <- exp(parms$logLinf) # To keep > 0
k <- exp(parms$logk)
t0 <- parms$t0
SD <- exp(parms$logSD)
# random effects params
log_Linf_d <- parms$coef_Linf
Linf_d <- exp(log_Linf_d)
Linf_d_sigma <- exp(parms$log_Linf_sigma)
log_k_d <- parms$coef_k
k_d <- exp(log_k_d)
k_d_sigma <- exp(parms$log_k_sigma)
t0_d <- parms$coef_t0
t0_d_sigma <- exp(parms$log_t0_sigma)
# - Model
Linf_g = Linf * Linf_d
k_g = k_d * k
t0_g = t0 + t0_d
Pred_Length_i = Linf_g[Group_i] * (1 - exp(-k_g[Group_i]* (Age_i - t0_g[Group_i])))
# - Likelihood
nll = 0
nll = nll - sum(dnorm(x = log_Linf_d, mean = 0, sd = Linf_d_sigma, log = TRUE))
nll = nll - sum(dnorm(x = log_k_d, mean = 0, sd = k_d_sigma, log = TRUE))
nll = nll - sum(dnorm(x = t0_d, mean = 0, sd = t0_d_sigma, log = TRUE))
nll = nll - sum(dnorm(x = Length_i, mean = Pred_Length_i, sd = SD, log = TRUE))
# - Report
REPORT(Linf_g)
REPORT(k_g)
REPORT(t0_g)
ADREPORT(Linf);
ADREPORT(k);
ADREPORT(t0);
ADREPORT(SD);
ADREPORT(Linf_g);
ADREPORT(k_g);
ADREPORT(t0_g);
# ADREPORT(Linf_g[Group_i] * (1 - exp(-k_g[Group_i]* (Age_i - t0_g[Group_i]))));
nll
}
###### Fit model ----
# Build model objects
# - Parameters
parameters = list(logLinf = 5,
logk = log(0.3),
t0 = 2,
logSD = 0,
coef_Linf = rep(0, Groups),
log_Linf_sigma = 0,
coef_k = rep(0, Groups),
log_k_sigma = 0,
coef_t0 = rep(0, Groups),
log_t0_sigma = 0
) # CAREFUL WITH STARTING VALUES
# - Map (turn off parameters using NA)
map <- list(
coef_Linf = as.factor(rep(NA, Groups)),
coef_k = as.factor(rep(NA, Groups)),
coef_t0 = as.factor(rep(NA, Groups)),
log_Linf_sigma = as.factor(NA),
log_k_sigma = as.factor(NA),
log_t0_sigma = as.factor(NA)
)
# - Data
data = list(Length_i = dat$length, Age_i = dat$age, Group_i = dat$group)
random = c('coef_Linf', 'coef_k', 'coef_t0')
# - Model object
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
obj <- MakeADFun(cmb(VBGM, data), parameters, random = random)
# Estimate
obj$hessian <- TRUE
opt <- nlminb(obj$par, obj$fn, obj$gr)
opt
# Get uncertainty via Delta method
rep <- sdreport(obj)
summ <- summary(rep)
###### Plot ----
plot(NA, NA, xlim = c(0, 15), ylim = c(0, max(dat$length)), xlab = "Age (yr)", ylab = "Length (mm)")
points(dat$age, dat$length , col = dat$group)
# - Rearrange parameters
library(dplyr)
library(stringr)
summ <- as.data.frame(summ)
summ$Parm <- rownames(summ)
Linf_g <- summ %>%
filter(str_detect(Parm, regex("Linf_g", ignore_case = TRUE)))
k_g <- summ %>%
filter(str_detect(Parm, regex("k_g", ignore_case = TRUE)))
t0_g <- summ %>%
filter(str_detect(Parm, regex("t0_g", ignore_case = TRUE)))
# - Plot curves
for(i in 1:Groups){
curve(Linf_g[i,1] * (1 - exp(-k_g[i,1] * (x - t0_g[i,1]))), from = 0, to = 15, col = i, lwd = 3, add = TRUE)
}
###### Likelihood profile ----
logLinf_vec <- log(seq(from = 350, to = 500, by = 1))
i
###### Likelihood profile ----
# Profile over global Linf
# - Map (turn off logLinf using NA)
map <- list(logLinf = as.factor(NA))
# - Vector of logLinf
logLinf_vec <- log(seq(from = 350, to = 500, by = 1))
# - Update logLinf fixed value
parameters$logLinf <- logLinf_vec[i]
# - Model object
obj <- MakeADFun(cmb(VBGM, data), parameters, random = random, map = map, silent = TRUE)
opt <- nlminb(obj$par, obj$fn, obj$gr)
opt$objective
# Profile over global Linf
# - Map (turn off logLinf using NA)
map <- list(logLinf = as.factor(NA))
# - Vector of logLinf
logLinf_vec <- log(seq(from = 350, to = 500, by = 1))
nll_vec <- c()
for(i in 1:length(logLinf_vec)){
# - Update logLinf fixed value
parameters$logLinf <- logLinf_vec[i]
# - Fit model object and save NLL
obj <- MakeADFun(cmb(VBGM, data), parameters, random = random, map = map, silent = TRUE)
opt <- nlminb(obj$par, obj$fn, obj$gr)
nll_vec[i] <- opt$objective
}
plot(x = exp(logLinf_vec), y = nll_vec - min(nll_vec), ylab = "NLL - min(NLL)", xlab = "Linf")
min(nll_vec)
Linf_g
# - Vector of logLinf
logLinf_vec <- log(seq(from = 450, to = 550, by = 1))
nll_vec <- c()
for(i in 1:length(logLinf_vec)){
# - Update logLinf fixed value
parameters$logLinf <- logLinf_vec[i]
# - Fit model object and save NLL
obj <- MakeADFun(cmb(VBGM, data), parameters, random = random, map = map, silent = TRUE)
opt <- nlminb(obj$par, obj$fn, obj$gr)
nll_vec[i] <- opt$objective
}
plot(x = exp(logLinf_vec), y = nll_vec - min(nll_vec), ylab = "NLL - min(NLL)", xlab = "Linf")
plot(x = exp(logLinf_vec), y = nll_vec - min(nll_vec), ylab = "NLL - min(NLL)", xlab = "Linf", typw = "l")
plot(x = exp(logLinf_vec), y = nll_vec - min(nll_vec), ylab = "NLL - min(NLL)", xlab = "Linf", type = "l")
abline(h = 2, col = 3)
nll_vec - min(nll_vec)
nll_vec - min(nll_vec) - 2
# https://grantdadams.wordpress.com/von-bertalanffy-in-template-model-builder/
library(RTMB)
library(readxl)
datos <- read_excel("datos.xlsx")
setwd("~/Library/CloudStorage/[email protected]/.shortcut-targets-by-id/1qJ3rMYRcXVSrilod5Sn-3ynjR7PlWc-F/University of Concepcion")
# https://grantdadams.wordpress.com/von-bertalanffy-in-template-model-builder/
library(RTMB)
library(readxl)
datos <- read_excel("datos.xlsx")
# Plot length-at-age
plot(datos$Edad, datos$`LH (cm)` , xlab = "Age (yr)", ylab = "Length (mm)", pch = 16)
###### Write model
VBGM <- function(parms, dataList) {
# - Data
Age_i <- dataList$Age_i
Length_i <- dataList$Length_i
# - Parameters
Linf <- exp(parms$logLinf) # To keep > 0
k <- exp(parms$logk)
t0 <- parms$t0
h <- parms$h
th <- exp(parms$logTH)
SD <- exp(parms$logSD)
# - Likelihood
a_t <- 1 - h/(1+Age_i - th)^2
predicted_length_i = Linf * (1 - exp(-k * a_t * (Age_i - t0)))
nll = -sum(dnorm(Length_i, predicted_length_i, SD, TRUE))
# - Report
RTMB::REPORT(predicted_length_i)
ADREPORT(Linf);
ADREPORT(k);
ADREPORT(t0);
ADREPORT(SD);
nll
}
###### Fit model
# Build model objects
parameters = list(logLinf = 1, logk = (0.3), t0 = -5, h = 0, logTH = log(15), logSD = 0) # CAREFUL WITH STARTING VALUES
data = list(Length_i = datos$`LH (cm)`, Age_i = datos$Edad)
map <- list(h = factor(NA),
logTH = factor(NA))
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
# - Build model
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
obj <- MakeADFun(cmb(VBGM, data), parameters)
# Estimate
obj$hessian <- TRUE
opt <- nlminb(obj$par, obj$fn, obj$gr)
###### Fit model
# Build model objects
parameters = list(logLinf = log(400), logk = (0.3), t0 = -5, h = 0, logTH = log(15), logSD = 0) # CAREFUL WITH STARTING VALUES
data = list(Length_i = datos$`LH (cm)`, Age_i = datos$Edad)
map <- list(h = factor(NA),
logTH = factor(NA))
# - Build model
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
obj <- MakeADFun(cmb(VBGM, data), parameters)
# Estimate
obj$hessian <- TRUE
opt <- nlminb(obj$par, obj$fn, obj$gr)
dataList <- data
parms = parameters
# - Data
Age_i <- dataList$Age_i
Length_i <- dataList$Length_i
# - Parameters
Linf <- exp(parms$logLinf) # To keep > 0
k <- exp(parms$logk)
t0 <- parms$t0
h <- parms$h
th <- exp(parms$logTH)
SD <- exp(parms$logSD)
# - Likelihood
a_t <- 1 - h/(1+Age_i - th)^2
a_t
th
Age_i
# - Likelihood
a_t <- 1 - h/(1+(Age_i - th)^2)
a_t
###### Write model
VBGM <- function(parms, dataList) {
# - Data
Age_i <- dataList$Age_i
Length_i <- dataList$Length_i
# - Parameters
Linf <- exp(parms$logLinf) # To keep > 0
k <- exp(parms$logk)
t0 <- parms$t0
h <- parms$h
th <- exp(parms$logTH)
SD <- exp(parms$logSD)
# - Likelihood
a_t <- 1 - h/(1+(Age_i - th)^2)
predicted_length_i = Linf * (1 - exp(-k * a_t * (Age_i - t0)))
nll = -sum(dnorm(Length_i, predicted_length_i, SD, TRUE))
# - Report
RTMB::REPORT(predicted_length_i)
ADREPORT(Linf);
ADREPORT(k);
ADREPORT(t0);
ADREPORT(SD);
nll
}
###### Fit model
# Build model objects
parameters = list(logLinf = log(400), logk = (0.3), t0 = -5, h = 0, logTH = log(15), logSD = 0) # CAREFUL WITH STARTING VALUES
data = list(Length_i = datos$`LH (cm)`, Age_i = datos$Edad)
map <- list(h = factor(NA),
logTH = factor(NA))
# - Build model
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
obj <- MakeADFun(cmb(VBGM, data), parameters)
# Estimate
obj$hessian <- TRUE
opt <- nlminb(obj$par, obj$fn, obj$gr)
opt
###### Write model
VBGM <- function(parms, dataList) {
# - Data
Age_i <- dataList$Age_i
Length_i <- dataList$Length_i
# - Parameters
Linf <- exp(parms$logLinf) # To keep > 0
k <- exp(parms$logk)
t0 <- parms$t0
h <- parms$h
th <- exp(parms$logTH)
SD <- exp(parms$logSD)
# - Likelihood
a_t <- 1 - h/(1+(Age_i - th)^2)
predicted_length_i = Linf * (1 - exp(-k * a_t * (Age_i - t0)))
nll = -sum(dnorm(Length_i, predicted_length_i, SD, TRUE))
# - Report
RTMB::REPORT(predicted_length_i)
ADREPORT(Linf);
ADREPORT(k);
ADREPORT(t0);
ADREPORT(th);
ADREPORT(SD);
nll
}
###### Fit model
# Build model objects
parameters = list(logLinf = log(400), logk = (0.3), t0 = -5, h = 0, logTH = log(15), logSD = 0) # CAREFUL WITH STARTING VALUES
data = list(Length_i = datos$`LH (cm)`, Age_i = datos$Edad)
map <- list(h = factor(NA),
logTH = factor(NA))
# - Build model
cmb <- function(f, d) function(p) f(p, d) ## Helper to make data and explicit input
obj <- MakeADFun(cmb(VBGM, data), parameters)
# Estimate
obj$hessian <- TRUE
opt <- nlminb(obj$par, obj$fn, obj$gr)
opt
# Get uncertainty via Delta method
rep <- sdreport(obj)
summ <- summary(rep)
summ
summ <- as.data.frame(summary(rep))
summ
summ$Parameter = rownames(summ)
mle <- t(summ[,1])
mle
colnames(mle) <- summ$Parameter
mle
mle <- as.data.frame(t(summ[,1]))
colnames(mle) <- summ$Parameter
curve(mle$Linf[1] * (1 - exp(-mle$k[1] * (1 - mle$h[1]/(1+(x - mle$th[1])^2)) (x - mle$t0[1]))), from = 0, to = 30, col = 2, lwd = 4, add = TRUE)
# Plot
plot(datos$Edad, datos$`LH (cm)` , xlab = "Age (yr)", ylab = "Length (mm)", pch = 16)
mle <- as.data.frame(t(summ[,1]))
colnames(mle) <- summ$Parameter
curve(mle$Linf[1] * (1 - exp(-mle$k[1] * (1 - mle$h[1]/(1+(x - mle$th[1])^2)) (x - mle$t0[1]))), from = 0, to = 30, col = 2, lwd = 4, add = TRUE)
x = 5
mle$Linf[1]
mle$Linf[1] * (1 - exp(-mle$k[1] * (1 - mle$h[1]/(1+(x - mle$th[1])^2)) (x - mle$t0[1])))
mle$h[1]
x - mle$th[1]
curve(mle$Linf[1] * (1 - exp(-mle$k[1] * (1 - mle$h[1]/(1+(x - mle$th[1])^2)) * (x - mle$t0[1]))), from = 0, to = 30, col = 2, lwd = 4, add = TRUE)