Investigating diagnostics for generalized linear mixed models

Abstract

Generalized linear mixed models (GLMMs) are extensions of linear mixed models that enable non-normal distributional assumptions on the response of interest. Effective diagnostic metrics and tools to assess GLMM fit and performance are limited. The objective of this study was to develop and explore potential diagnostics to assess GLMM fit and performance to ultimately inform model choice, specifically for discrete count responses. We conducted a simulation study whereby a count response variable was generated by three realistic data generation processes (DGP) under a 2x2 factorial treatment structure in randomized complete blocks. Simulated data were fitted with competing models, including various GLMM specifications and normal approximations with and without transformations. For each DGP, model performance was assessed for accuracy of estimation of treatment means, as well as for Type I error and power for inference on differential treatment effects. Models were evaluated and compared using the Pearson Chi-Square over degrees of freedom statistic for overdispersion and information criteria. Further, we developed an array of potential diagnostic metrics based on model point predictions and used them to assess the ability of competing models to recreate selected features of count data, specifically skewness and dispersion. Overall, the diagnostic metrics evaluated failed to identify the corresponding true model for each DGP. Meanwhile, regardless of DGP, a Poisson-Unit GLMM outperformed other model specifications in fitting selected features of count data. An entomological dataset was used for proof-of-concept application. Further study is warranted to best inform GLMM specification for count response variables.