From Linear to Generalized Linear Mixed Models: A Case Study in Repeated Measures (303276)

Keywords: designed experiments, repeated measures, linear mixed models, linear mixed effects models, generalized linear mixed models

Compared to traditional linear mixed models, generalized linear mixed models (GLMMs) can offer better correspondence between response variables and explanatory models, yielding more efficient estimates and tests in the analysis of data from designed experiments. Using proportion data from a designed experiment with repeated measures, results from several candidate GLMMs implemented with different distributions (binomial and beta), likelihood estimation methods (integral approximation and PL), covariance structures, and bias correction methods, are compared. The results show that constructing an appropriate GLMM is not trivial, especially the case of repeated measures. The numerical estimation procedures GLMMs utilize can easily produce intractable or nonsensical results that are difficult to diagnose and rectify. Many common adjustments and modeling decisions fundamentally change the model’s inference space and alter appropriate interpretations of model parameters. Modelers must also confront mean-variance dependency, important differences between conditional (“G-side”) and marginal (“R-side”) formulations of random effects, and how to implement bias correction.