In BarkleyBG/glmerGOF: Goodness of Fit of Random Effect Distribution in Logistic Mixed Model

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
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This is an introduction and tutorial to the glmerGOF package. This package implements a test of the goodness of fit of the presumed Gaussian random effect distribution in the logistic mixed models fit with lme4::glmer(). The method is introduced in Tchetgen Tchetgen, E. J., & Coull, B. A. (2006) A Diagnostic Test for the Mixing Distribution in a Generalised Linear Mixed Model. Biometrika, 93(4), 1003-1010. \url{https://doi.org/10.1093/biomet/93.4.1003}. This test is implemented in glmerGOF::testGOF(), as described below.

Using glmerGOF

We begin with a simple data example, with data simulated as shown in the geex package

library(glmerGOF)
set.seed(1)
#generate data; 50 clusters
n <- 50
m <- 4
beta <- c(2, 2)
id <- rep(1:n, each=m)
x <- rnorm(m*n)
b <- rep(rnorm(n), each=m)
y <- rbinom(m*n, 1, plogis(cbind(1, x) %*% beta + b))
my_data <- data.frame(y,x,id) 

knitr::kable(head(my_data), digits = 2)

The testGOF() function in this package takes arguments for the original data, as well as two models. One model is fit with lme4::glmer(), and the other is a conditional logistic model fit with survival::clogit().

Fitting the two models

The two models are fit outside of the glmerGOF() package. The testGOF() function attempts to match the coefficients of the two models to produce the test results.

Generalized logistic mixed model

library(lme4)
fit_glmm <- lme4::glmer(
  formula = y ~ x + (1|id),
  family = "binomial",
  data = my_data
)

Conditional logistic model

library(survival)
fit_clogit <- survival::clogit(
  formula = y ~ x + strata(id),
  data = my_data,
  method = "exact"
)

Executing the GOF test

Once the models are fit, there are only a few more steps. One step is to provide a list of two important variable names, as strings. DV is the dependent variable in the model, and grouping is the variable indicating the cluster membership.

variable_names <- list(DV = "y", grouping = "id")

Lastly, choose whether you want

deriv_method <- 
  # "Richardson" ## for slower but more accurate computations
  "simple" ## for faster computation

Now, testGOF can be run by passing in the data, models, and variable names:

TC_test <- testGOF(
  data = my_data,
  fitted_model_clogit = fit_clogit,
  fitted_model_glmm  = fit_glmm,
  var_names = variable_names, 
  gradient_derivative_method = deriv_method
)

The test statistic follows a chi-squared distribution with degrees of freedom equal to the number of parameters:

TC_test$results

BarkleyBG/glmerGOF documentation built on July 18, 2019, 6:43 p.m.