Introduction to Generalized Linear Mixed Models

Abstract

Chapter 15 investigated linear mixed-effects models (LMMs). This chapter introduces generalized linear mixed models (GLMMs), which can be considered as an extension of linear mixed models to allow response variables from different distributions, such as binary responses. First, it reviews the brief history of generalized linear models (GLMs) and generalized nonlinear models (GNLMs). Then it describes the generalized linear mixed models (GLMMs). Next, it introduces model estimation in GLMMs and investigates the algorithms for parameter estimation in GLMMs and particularly the parameter estimation algorithms for specifically developed GLMMs for microbiome research. Finally, it describes the statistical hypothesis testing and modeling in GLMMs.