Generalized Linear Mixed Models in the Analysis of Alternating Treatment Designs

Alternating treatments designs (ATDs) are single-case experimental designs (SCEDs) characterized by the rapid alternation of conditions, with the sequence of conditions typically determined at random. Outcomes in ATDs are often recorded as count data with repeated measurements nested within cases. Although generalized linear mixed models (GLMMs) have been systematically examined for analyzing nonnormal outcomes in multiple-baseline designs, their application and statistical properties for ATDs remain unclear. In this study, we conducted a large-scale Monte-Carlo simulation to evaluate the performance of GLMMs in terms of bias, mean square error, coverage rate and type I error rate for estimating immediate effects and trend changes in two prototypical ATDs. In addition, we present two empirical demonstrations using real ATD datasets with a focus on illustrating design-matrix coding, interpretation of parameter estimates, and reporting practices that jointly consider immediate effects and trend changes. Finally, we provide recommendations for analytic procedures for applied researchers based on findings from the simulation study and empirical demonstrations. We hope this article equips SCED researchers with essential guidance for appropriately analyzing count data from ATDs using GLMMs and outlines directions for future methodological work exploring the full potential of GLMMs and their extensions for the analysis and meta-analysis of ATD data.