Analyzing Count Data in Single Case Experimental Designs with Generalized Linear Mixed Models: Does Serial Dependency Matter?

Single-case experimental designs (SCEDs) involve repeated measurements of a small number of cases under different experimental conditions, offering valuable insights into treatment effects. However, challenges arise in the analysis of SCEDs when autocorrelation is present in the data. Recently, generalized linear mixed models (GLMMs) have emerged as a promising statistical approach for SCEDs with count outcomes. While prior research has demonstrated the effectiveness of GLMMs, these studies have typically assumed error independence, an assumption that may be violated in SCEDs due to serial dependency. This study aims to evaluate two possible solutions for autocorrelated SCED count data: 1) to assess the robustness of previously introduced GLMMs such as Poisson, negative binomial, and observation-level random effects models under various levels of autocorrelation, and 2) to evaluate the performance of a new GLMM and a linear mixed model (LMM), both of which incorporate an autoregressive error structure. Through a Monte Carlo simulation study, we have examined bias, coverage rates, and Type I error rates of treatment effect estimators, providing recommendations for handling autocorrelation in the analysis of SCED count data. A demonstration with real SCED count data is provided. The implications, limitations, and future research directions are also discussed.