Simulating Clustered and Dependent Binary Variables

Dependent binary data can be simply simulated using the multivariate normal- and multinomial sampling-based approaches. We extend these methods to simulate dependent binary data with clustered random effect structures. Several distributions are considered for constructing random effects among cluster-specific parameters and effect sizes, including the normal, uniform and beta distributions. We present results from simulation studies to show proof of concept for these two methods in creating data sets of repeated-measure binary outcomes with clustered random effect structures in various scenarios. The simulation studies show that multivariate normal- and multinomial sampling approaches can be successfully adapted to simulate dependent binary data with desired random effect structures.