Multilevel Modeling in Single-Case Studies with Zero-Inflated and Overdispersed Count Data

Abstract

Count outcomes are frequently encountered in single-case experimental designs (SCEDs). Previous studies have shown that generalized linear mixed models (GLMMs) are a promising method to deal with overdispersed count data. For low rates behaviors, however, excessive zeros were not uncommon in the baseline phase in SCEDs, leading to a more complex data issue called zero-inflation that many researchers simply ignore. This study simulated zero-inflated and overdispersed count data in a multiple baseline design (MBD) in single-case studies and examined the performance of a series of GLMMs including Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) models in terms of the estimators and inferential statistics of treatment effects. The study also provided a demonstration of how to analyze zero-inflated and overdispersed count data from a real example.

Two simulation studies were conducted. The primary simulation study examined zero-inflated and overdispersed count data while the additional simulation study examined whether aforementioned models are robust to overdispersed count data without zero-inflation. It was found that the ZINB model yielded accurate estimates for treatment effects while the other three models led to biased estimates. The inferential statistic obtained from the ZINB model was reliable when the baseline level rate is low. However, when the data were overdispersed but not zero-inflated, ZINB and ZIP models had poor performance in terms of the accuracy of treatment effects estimation.

The finding of the dissertation enhanced our understanding of GLMMs to handle zero-inflated and overdispersed count data in SCEDs. To explore the full potential of GLMMs to handle SCED count data, future studies are needed to address relevant issues including but not limited to model selection, inferential statistics, and Bayesian estimation.