H-Likelihood Estimation Method for Varying Clustered Binary Mixed Effects Model

Abstract

Clustered or hierarchical data structures with binary responses are prevalent in various practical applications. These structures can involve an equal or unequal number of observations, leading to the analysis of data exhibiting intricate variability patterns. Mixed models, incorporating fixed effects of interest and random effects to address clustering, are commonly employed due to their appropriateness in practice. Random effects in these models account for multiple error structures. In the domain of clustered binary mixed effects models, the Hierarchical Generalized Linear Model (HGLM) stands out as a preferred model. This study assesses the performance of the h-Likelihood estimation method for clustered binary mixed effects models with both balanced and unbalanced cluster sizes. Evaluation through computer simulations considers parameters such as unbiasedness, Type I error rate, power, and standard error. The simulations encompass varying numbers of clusters and cluster sizes, revealing nuances in the performance of the mixed effects clustered binary data model based on the cluster sizes.