Question

How to simulate independent binary response for GEE in R?

Answer 1

set.seed(123)
# sample size
sample_size <- 100
# cluster size
cluster_size <- 4
# intercept
beta_intercepts <- 0
# regression parameter associated with the covariate
beta_coefficients <- 0.2
# correlation matrix for the NORTA method
latent_correlation_matrix <- toeplitz(c(1, 0.9, 0.9, 0.9))
# time-stationary covariate
x <- rep(rnorm(sample_size), each = cluster_size)
# simulation of clustered binary responses
simulated_binary_dataset <- rbin(clsize = cluster_size, intercepts = beta_intercepts, 
    betas = beta_coefficients, xformula = ~x, cor.matrix = latent_correlation_matrix, 
    link = "probit")
library(gee)
# fitting a GEE model
binary_gee_model <- gee(y ~ x, family = binomial("probit"), id = id, data = simulated_binary_dataset$simdata)
#> Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
#> running glm to get initial regression estimate
#> (Intercept)           x 
#>   0.1315121   0.2826005
# checking the estimated coefficients
summary(binary_gee_model)$coefficients
#>              Estimate Naive S.E.  Naive z Robust S.E. Robust z
#> (Intercept) 0.1315121 0.06399465 2.055048   0.1106696 1.188331
#> x           0.2826006 0.07191931 3.929412   0.1270285 2.224703