Diagnostic analysis in mixed effects models via Plot Half-Normal chart

Question

I am intending to perform the Plot half-normal chart for a mixed effects model that has been adjusted using the package lme4. To visualize the diagnostic analysis of this model, I intend to use Pearson residues, however, I am facing some difficulties.

The data used can be found here.

Dice: https://drive.google.com/file/d/1q4XuSPnZXx7TsrT3JVoucFyxeOSegWFz/view?usp=sharing

In the computational routine described below is the adjusted model.

library(lme4)
library(ggplot2)
library(gridExtra)
library(hnp)

lmm <- lmer(log(Var1)~log(Var2)+log(Var3)+
                  (Var4)+(Var5)+(Var7||Var6),
                Dados2, REML=T)

By default, the package hnp informs that the residues deviance are considered in cases that the adjustment of mixed effects models by the function lmer, however, to use another option available for this class of templates within the package hnp just use the function resid.type. Thus, below is the construction of the graph considering the default (Ga) and also the Pearson residues (Gb).

Grap5=hnp(lmm, xlab = 'Theoretical quantiles', ylab = 'Residuals')

G5 <- with(Grap5, data.frame(x, lower, upper, median, residuals))

Ga=ggplot(data = G5, aes(x)) +
  geom_point(aes(y = residuals)) +
  geom_line(aes(y = lower)) +
  geom_line(aes(y = upper)) +
  geom_line(aes(y = median), linetype = "dashed") + 
  ylab("Residuals") +
  xlab("Theoretical quantiles")+ggtitle("Deviance")+
  theme(legend.title = element_text(size = 17),
        legend.text = element_text(size = 17),
        axis.text.x = element_text(size = 20,color = "black"),
        axis.text.y = element_text(size = 20,color = "black"),
        axis.title = element_text(size = 20),
        axis.text = element_text(size = 25),
        plot.title = element_text(size = 20))

Grap6=hnp(lmm, xlab = 'Theoretical quantiles', ylab = 'Residuals', 
          resid.type="pearson")

G6 <- with(Grap6, data.frame(x, lower, upper, median, residuals))

Gb=ggplot(data = G6, aes(x)) +
  geom_point(aes(y = residuals)) +
  geom_line(aes(y = lower)) +
  geom_line(aes(y = upper)) +
  geom_line(aes(y = median), linetype = "dashed") + 
  ylab("Residuals") +
  xlab("Theoretical quantiles")+ggtitle("Pearson")+
  theme(legend.title = element_text(size = 17),
        legend.text = element_text(size = 17),
        axis.text.x = element_text(size = 20,color = "black"),
        axis.text.y = element_text(size = 20,color = "black"),
        axis.title = element_text(size = 20),
        axis.text = element_text(size = 25),
        plot.title = element_text(size = 20))

grid.arrange(Ga,Gb,ncol=2)

See in the figure below that no difference was observed between the desired options, therefore it seems to me that some problem should be happening.

Answer 1

Here is a solution to have graphics with waste "deviance" and "response", which seems to me to be the most useful.

The code has also been simplified to show how to use facets directly, without having to draw two graphs and then join them with grid.arrange.

1. Defining a new theme.

First of all, I defined a theme custom.

theme_BrenoG <- function(){ 
  theme_bw() %+replace%    #replace elements we want to change
    theme(legend.title = element_text(size = 17),
          legend.text = element_text(size = 17),
          axis.text.x = element_text(size = 20, color = "black"),
          axis.text.y = element_text(size = 20, color = "black"),
          axis.title = element_text(size = 20),
          axis.text = element_text(size = 25),
          plot.title = element_text(size = 20),
          strip.text.x = element_text(size = 20))
}

2. The model shall be.

library(lme4)
library(ggplot2)
library(gridExtra)
library(hnp)

lmm <- lmer(log(Var1) ~ log(Var2) + log(Var3) + Var4 + Var5 + (Var7||Var6),
            data = Dados2,
            REML = TRUE)

Grap5 <- hnp(lmm, xlab = 'Theoretical quantiles', ylab = 'Residuals',
             resid.type = "deviance")
Grap6 <- hnp(lmm, xlab = 'Theoretical quantiles', ylab = 'Residuals',
             resid.type = "response")

G5 <- with(Grap5, data.frame(x, lower, upper, median, residuals))
G6 <- with(Grap6, data.frame(x, lower, upper, median, residuals))

3. The graph.

By creating a column with the type of waste that the models have, one can then facet by this variable.

G5$type <- "Deviance"
G6$type <- "Response"


ggplot(data = rbind(G5, G6), aes(x)) +
  geom_point(aes(y = residuals)) +
  geom_line(aes(y = lower)) +
  geom_line(aes(y = upper)) +
  geom_line(aes(y = median), linetype = "dashed") +
  ylab("Residuals") +
  xlab("Theoretical quantiles") +
  facet_wrap(~ type) +
  theme_BrenoG()

4. Reading of data.

The data is read with read.csv because the separators are ";" and decimals are marked with ",".

google_id <- "1q4XuSPnZXx7TsrT3JVoucFyxeOSegWFz"
google_file <- sprintf("https://docs.google.com/uc?id=%s&export=download", google_id)
Dados2 <- read.csv2(google_file)