Performance of mixed effects for clustered binary data models

Abstract

Clustered binary responses are very common in many practical applications, as binary data are naturally grouped by sampling techniques or some property of the sampling units. Clusters may be balanced, which means they have an equal number of observations, or they may be unbalanced. Mixed effects models are appropriate in practice since, the random effects account for the variation across clusters. When using mixed effects models for clustered data with binary outcomes, a preferred model is the Hierarchical Generalized Linear Model (HGLM). This article compares the performance of Restricted Pseudo Likelihood estimation (RPL) of the mixed effects clustered binary data models with equal and unequal cluster sizes. This was evaluated in terms of Type I error rate, power, and standard error through computer simulation. The simulation is performed by using different numbers of clusters and different cluster sizes. The results show that the performance of the mixed effects clustered binary data model is similar, regardless of inequality in cluster size.