Bayesian Zero-inflated Generalized Linear Mixed Model for Single Case Experimental Design (Poster 4)

• In Event: Innovative Methodologies and Systematic Reviews in Analyzing Single-Case Experimental Design Data

Abstract

Single-case experimental design (SCED) is widely used in psychology, education, and behavior sciences to evaluate the effectiveness of an intervention or treatment on a single subject or a few. It involves repeated measurement of an outcome before, during, and after an intervention to observe any changes in subjects’ behavior or condition. In addition to continuous outcomes from SCEDs, count outcomes are also frequently encountered in these studies (Li et al., 2024). Examples include the number of words read correctly per minute in a reading intervention evaluation study and the number of off-task behaviors in a self-monitoring intervention evaluation.
Traditional methods to analyze SCED continuous data include visual analysis, various effect size estimators (Pustejovsky, 2015), and regression-based analysis (Shadish, 2014). However, these methods will encounter limited capability in addressing trend effects and heterogeneity across subjects. Linear mixed models (LMMs) were proposed and verified to be a promising method accounting for the time trend and the between-case variability. To account for both the clustering and the non-normal nature of count data in SCEDs, generalized linear mixed models (GLMMs) can be adopted as an alternative approach (Li et al., 2024). Recently, this method has been advanced by including the zero-inflation that often occurs in the count outcome (Li et al., 2024). Zero-inflation in frequency counts happens when there are more zeros in the data than would be expected if the data were generated by a Poisson or negative binomial distribution. This is often the case in SCEDs, as excessive zeros usually occur before the intervention. However, current GLMMs models with zero-inflation using frequentist estimation and optimization (e.g., restricted maximum likelihood (REML)) come with several limitations: (1) non-convergence in complex models, (2) unreliable inferential statistics (i.e., inflated type-I error), and (3) biased estimates of random effects. These issues arise due to REML's requirement for large sample sizes, which is unrealistic in SCEDs. Bayesian estimation could be a promising alternative and has not yet been used in analyzing SCED count data with GLMMs.
The proposed study has two objectives: (1) to propose a GLMM accounting for zero-inflation using a full Bayesian estimation, evaluate the performance via simulation studies, and compare it with frequentist results; and (2) to provide an empirical analysis to illustrate the merits of using Bayesian estimation. The simulation for this proposed study aims to evaluate the performance of GLMMs with zero-inflation in estimating fixed and random effects, inferential statistics, and convergence. Simulation conditions will vary across different numbers of subjects, numbers of measurements, effect sizes, and the existence and strength of zero inflation. Results will also be compared with pre-existing frequentist results. We expect to observe improved convergence rates, reliable estimation for inferential statistics, and reduced bias in random effects estimation.
Using Bayesian GLMMs to analyze SCED data addresses many of the statistical challenges - including the flexibility to model complex data structures, better convergence, and effectiveness in small sample sizes. By adopting Bayesian GLMMs, researchers can achieve more accurate, reliable, and interpretable results, leading to better-informed decisions and more effective interventions.

Authors

• Chendong Li, Texas A&M University

• Haoran Li, University of Minnesota