Modifications of REML algorithm for HGLMs

Hierarchical generalized linear models (HGLMs) have become popular in data analysis. However, their maximum likelihood (ML) and restricted maximum likelihood (REML) estimators are often difficult to compute, especially when the random effects are correlated; this is because obtaining the likelihood function involves high-dimensional integration. Recently, an h-likelihood method that does not involve numerical integration has been proposed. In this study, we show how an h-likelihood method can be implemented by modifying the existing ML and REML procedures. A small simulation study is carried out to investigate the performances of the proposed methods for HGLMs with correlated random effects.