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. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

In the United States, only approximately one-third of students read at or above proficiency level. Moreover, the difference in reading proficiency of students is severely disproportionate for students with disabilities compared to students without disabilities. Reading fluency is a precursor for academic success and one of the six aspects of reading that contributes to effective reading skills. Many studies have examined the effectiveness of repeated reading to improve reading fluency. However, existing literature has mixed evaluations of whether repeated reading can be considered evidence-based reading intervention practice for students with disabilities. The current study examined the effects of a repeated reading intervention on reading fluency for three middle school students with learning disabilities. To address limitations of traditional single-case experimental design analytical methods such as visual analysis and nonoverlap indices, our study provided empirical researchers with a step-by-step procedure of using an advanced statistical method for single-case experimental designs, namely, generalized linear mixed models (GLMM) to analyze data. The results presented by GLMMs showed that repeated reading intervention can significantly improve reading fluency for some students with learning disabilities. Implications, limitations, and future directions from both empirical and methodological perspectives were also discussed.

Generalized linear mixed models (GLMMs) have great potential to deal with count and rate data in single-case experimental designs (SCEDs). However, applied researchers face challenges to apply such an advanced approach in their own studies. Hence, our study aimed to provide a tutorial and demonstrate a step-by-step procedure of using GLMMs to handle SCED count and rate outcomes. We utilized an empirical examplewith a purpose to examine the effect of prelinguistic milieu teaching (PMT) on prelinguistic intentional communication for six school-age children with autism. The outcomes were sustained intentional communication (frequency count) and initiated intentional communication (rate). A step-by-step analytical approach with GLMMs was illustrated and associated R and SAS code was provided. The results overall supported the original conclusions of the effectiveness of PMT, whereas additional evidence regarding the precise estimate of the individual treatment effect and between-case variation of the treatment effect were also interpreted. The implications of the similarities and differences between the findings based on GLMMs and from the original study were discussed.