Model selection of GLMMs in the analysis of count data in single-case studies: A Monte Carlo simulation

Generalized linear mixed models (GLMMs) have great potential to deal with count data in single-case experimental designs (SCEDs). However, applied researchers have faced challenges in making various statistical decisions when using such advanced statistical techniques in their own research. This study focused on a critical issue by investigating the selection of an appropriate distribution to handle different types of count data in SCEDs due to overdispersion and/or zero-inflation. To achieve this, I proposed two model selection frameworks, one based on calculating information criteria (AIC and BIC) and another based on utilizing a multistage-model selection procedure. Four data scenarios were simulated including Poisson, negative binominal (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB). The same set of models (i.e., Poisson, NB, ZIP, and ZINB) were fitted for each scenario. In the simulation, I evaluated 10 model selection strategies within the two frameworks by assessing the model selection bias and its consequences on the accuracy of the treatment effect estimates and inferential statistics. Based on the simulation results and previous work, I provide recommendations regarding which model selection methods should be adopted in different scenarios. The implications, limitations, and future research directions are also discussed.