Multilevel Modeling in Single-Case Studies With Count and Proportion Data: A Demonstration and Evaluation

The outcomes in single-case experimental designs (SCEDs) are often counts or proportions. In our study, we provided a colloquial illustration for a new class of generalized linear mixed models (GLMMs) to fit count and proportion data from SCEDs. We also addressed important aspects in the GLMM framework including overdispersion, estimation methods, statistical inferences, model selection methods by detecting overdispersion, and interpretations of regression coefficients. We then demonstrated the GLMMs with two empirical examples with count and proportion outcomes in SCEDs. In addition, we conducted simulation studies to examine the performance of GLMMs in terms of biases and coverage rates for the immediate treatment effect and treatment effect on the trend. We also examined the empirical Type I error rates of statistical tests. Finally, we provided recommendations about how to make sound statistical decisions to use GLMMs based on the findings from simulation studies. Our hope is that this article will provide SCED researchers with the basic information necessary to conduct appropriate statistical analysis of count and proportion data in their own research and outline the future agenda for methodologists to explore the full potential of GLMMs to analyze or meta-analyze SCED data.