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Example3.R
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# Tutorial: Template Model Builder (TMB) R package ----------------------------
# Example 3: Multivariate GLMM for continuous bounded outcomes ----------------
# Body fat percentage data set ------------------------------------------------
# Authors: Henrique Laureano, Ricardo Petterle and Wagner Bonat LEG/UFPR ------
# Date: 08/09/2021 ------------------------------------------------------------
rm(list=ls())
# Loading extra packages
library(knitr)
library(TMB)
library(betareg)
library(ggplot2)
library(tidyverse)
library(cowplot)
library(ggcorrplot)
# Loading data set ------------------------------------------------------------
data3 <- read.table("Data_Set.csv", header = TRUE, sep = ",", na.strings = "")
data3$ARMS <- data3$ARMS/100
data3$LEGS <- data3$LEGS/100
data3$TRUNK <- data3$TRUNK/100
data3$ANDROID <- data3$ANDROID/100
data3$GYNOID <- data3$GYNOID/100
data3$SEX <- as.factor(data3$SEX)
data3$IPAQ <- as.factor(data3$IPAQ)
# Preparing data set
# SEX
data3$SEX <- factor(data3$SEX)
levels(data3$SEX) <- c("Female", "Male")
# IPAQ
data3$IPAQ <- factor(data3$IPAQ)
levels(data3$IPAQ) <- c("Sedentary", "Insufficiently active", "Active")
tail(data3, n = 10)
# Descriptive analysis
summary(data3)
# Preparing
par(mfrow = c(4,5), mar=c(2.8, 2.6, 1.2, 0.5), mgp = c(1.6, 0.6, 0))
# cex (theme_cowplot)
fig_cex = 12
# Age
p1 <- data3 %>%
ggplot(aes(x = AGE, y = ARMS)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab("Age (years)") +
ylab("Arms") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p2 <- data3 %>%
ggplot(aes(x = AGE, y = LEGS)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab("Age (years)") +
ylab("Legs") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p3 <- data3 %>%
ggplot(aes(x = AGE, y = TRUNK)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab("Age (years)") +
ylab("Trunk") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p4 <- data3 %>%
ggplot(aes(x = AGE, y = ANDROID)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab("Age (years)") +
ylab("Android") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p5 <- data3 %>%
ggplot(aes(x = AGE, y = GYNOID)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab("Age (years)") +
ylab("Gynoid") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
# BMI
p6 <- data3 %>%
ggplot(aes(x = BMI, y = ARMS)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab(expression(paste("BMI (kg/m"^2,")"))) +
ylab("Arms") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p7 <- data3 %>%
ggplot(aes(x = BMI, y = LEGS)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab(expression(paste("BMI (kg/m"^2,")"))) +
ylab("Legs") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p8 <- data3 %>%
ggplot(aes(x = BMI, y = TRUNK)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab(expression(paste("BMI (kg/m"^2,")"))) +
ylab("Trunk") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p9 <- data3 %>%
ggplot(aes(x = BMI, y = ANDROID)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab(expression(paste("BMI (kg/m"^2,")"))) +
ylab("Android") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
p10 <- data3 %>%
ggplot(aes(x = BMI, y = GYNOID)) +
geom_point(size = 1.1, alpha = 0.8, color = "gray80") +
xlab(expression(paste("BMI (kg/m"^2,")"))) +
ylab("Gynoid") +
geom_smooth(method = lm, color = "gray70",
formula = y ~ splines::bs(x, 3),
se = T) +
theme_cowplot(fig_cex)
# Gender
p11 <- data3 %>%
ggplot(aes(x = SEX, y = ARMS)) +
geom_boxplot(fill = "gray80") +
xlab("Gender") +
ylab("Arms") +
theme_cowplot(fig_cex)
p12 <- data3 %>%
ggplot(aes(x = SEX, y = LEGS)) +
geom_boxplot(fill = "gray80") +
xlab("Gender") +
ylab("Legs") +
theme_cowplot(fig_cex)
p13 <- data3 %>%
ggplot(aes(x = SEX, y = TRUNK)) +
geom_boxplot(fill = "gray80") +
xlab("Gender") +
ylab("Trunk") +
theme_cowplot(fig_cex)
p14 <- data3 %>%
ggplot(aes(x = SEX, y = ANDROID)) +
geom_boxplot(fill = "gray80") +
xlab("Gender") +
ylab("Android") +
theme_cowplot(fig_cex)
p15 <- data3 %>%
ggplot(aes(x = SEX, y = GYNOID)) +
geom_boxplot(fill = "gray80") +
xlab("Gender") +
ylab("Gynoid") +
theme_cowplot(fig_cex)
# IPAQ
data3$IPAQ <- factor(data3$IPAQ)
levels(data3$IPAQ) <- c("S", "IA", "A")
p16 <- data3 %>%
ggplot(aes(x = IPAQ, y = ARMS)) +
geom_boxplot(fill = "gray80") +
xlab("IPAQ") +
ylab("Arms") +
theme_cowplot(fig_cex)
p17 <- data3 %>%
ggplot(aes(x = IPAQ, y = LEGS)) +
geom_boxplot(fill = "gray80") +
xlab("IPAQ") +
ylab("Legs") +
theme_cowplot(fig_cex)
p18 <- data3 %>%
ggplot(aes(x = IPAQ, y = TRUNK)) +
geom_boxplot(fill = "gray80") +
xlab("IPAQ") +
ylab("Trunk") +
theme_cowplot(fig_cex)
p19 <- data3 %>%
ggplot(aes(x = IPAQ, y = ANDROID)) +
geom_boxplot(fill = "gray80") +
xlab("IPAQ") +
ylab("Android") +
theme_cowplot(fig_cex)
p20 <- data3 %>%
ggplot(aes(x = IPAQ, y = GYNOID)) +
geom_boxplot(fill = "gray80") +
xlab("IPAQ") +
ylab("Gynoid") +
theme_cowplot(fig_cex)
# Figure
plot_grid(p1, p2, p3, p4, p5,
p6, p7, p8, p9, p10,
p11, p12, p13, p14, p15,
p16, p17, p18, p19, p20,
label_size = 13,
labels = c("(A)", "(B)", "(C)", "(D)", "(E)",
"(F)", "(G)", "(H)", "(I)", "(J)",
"(K)", "(L)", "(M)", "(N)", "(O)",
"(P)", "(Q)", "(R)", "(S)", "(T)"),
hjust = -0.05, vjust = 1,
ncol = 5, nrow = 4)
# Univariate beta regression model
# Response 1
fit1 <- betareg::betareg(ARMS ~ AGE + BMI + SEX + IPAQ,
data = data3)
# Response 2
fit2 <- betareg::betareg(LEGS ~ AGE + BMI + SEX + IPAQ,
data = data3)
# Response 3
fit3 <- betareg::betareg(TRUNK ~ AGE + BMI + SEX + IPAQ,
data = data3)
# Response 4
fit4 <- betareg::betareg(ANDROID ~ AGE + BMI + SEX + IPAQ,
data = data3)
# Response 5
fit5 <- betareg::betareg(GYNOID ~ AGE + BMI + SEX + IPAQ,
data = data3)
# Initial values from BoundedReg
beta1 = as.numeric(coef(fit1)[-7])
beta2 = as.numeric(coef(fit2)[-7])
beta3 = as.numeric(coef(fit3)[-7])
beta4 = as.numeric(coef(fit4)[-7])
beta5 = as.numeric(coef(fit5)[-7])
# Precision
phi1 <- log(as.numeric(coef(fit1)[7]))
phi2 <- log(as.numeric(coef(fit2)[7]))
phi3 <- log(as.numeric(coef(fit3)[7]))
phi4 <- log(as.numeric(coef(fit4)[7]))
phi5 <- log(as.numeric(coef(fit5)[7]))
# Multivariate Beta model full ------------------------------------------------
compile("MGLMM_Beta.cpp")
dyn.load(dynlib("MGLMM_Beta"))
# Data
X <- model.matrix(~ AGE + BMI + SEX + IPAQ, data3)
data <- list(Y1 = data3$ARMS, Y2 = data3$LEGS, Y3 = data3$TRUNK,
Y4 = data3$ANDROID, Y5 = data3$GYNOID, X = X)
## Initial values
parameters <- list(beta1 = beta1, beta2 = beta2, beta3 = beta3,
beta4 = beta4, beta5 = beta5, phi = c(phi1, phi2, phi3, phi4, phi5),
U = matrix(0, ncol = 5, nrow = 298),
rho = rep(0,10), sigma = rep(0.11, 5))
## Log-likelihood function
MGLMM_Beta <- MakeADFun(data, parameters, DLL = "MGLMM_Beta",
random = "U",
hessian = TRUE, silent = F)
# Fitting via nlminb() --------------------------------------------------------
fit_mglmm <- nlminb(start = MGLMM_Beta$par, objective = MGLMM_Beta$fn,
gradient = MGLMM_Beta$gr, control = list(eval.max = 1000,
iter.max = 1000,
abs.tol = 1e-04,
rel.tol = 1e-04))
fit_mglmm
# Report
report <- sdreport(MGLMM_Beta)
# Summary for the fixed effects
summary(report, "fixed", p.value = T)
# Correlation matrix
Beta_report <- MGLMM_Beta$report()
COR_Beta <- Beta_report$Cor
colnames(COR_Beta) <- rownames(COR_Beta) <- c("Arms", "Legs", "Trunk",
"Android", "Gynoid")
COR_Beta
# Plot correlation matrix
ggcorrplot::ggcorrplot(COR_Beta, hc.order = F, type = "lower",
lab = TRUE, show.legend = F, lab_size = 6, tl.cex = 16,
ggtheme = ggplot2::theme_light(),
colors = c("gray60", "gray60", "gray60"))
# END -------------------------------------------------------------------------