Abstract
Previous research applying multilevel models to single-case data has made a critical assumption that the level-1 error covariance matrix is constant across all participants. However, the level-1 error covariance matrix may differ across participants and ignoring these differences can have an impact on estimation and inferences. Despite the importance of this issue, the effects of modeling between-case variation in the level-1 error structure had not yet been systematically studied. The purpose of this simulation study was to identify the consequences of modeling and not modeling between-case variation in the level-1 error covariance matrices in single-case studies, using Bayesian estimation. The results of this study found that variance estimation was more sensitive to the method used to model the level-1 error structure than fixed effect estimation, with fixed effects only being impacted in the most extreme heterogeneity conditions. Implications for applied single-case researchers and methodologists are discussed.
Highlights
Previous research applying multilevel models to single-case data has made a critical assumption that the level-1 error covariance matrix is constant across all participants
A Monte Carlo simulation study was conducted to examine the performance of the proposed Bayesian analysis of single-case design data, which allows between case varia‐ tion in the level-1 error variances and autocorrelation
This study developed a method for estimating between case heterogeneity in level-1 var‐ iances and provides insight into how different modeling approaches for the level-1 error
Summary
A Monte Carlo simulation study was conducted to examine the performance of the proposed Bayesian analysis of single-case design data, which allows between case varia‐ tion in the level-1 error variances and autocorrelation. Baek et al (2019) examined the impact of estimation methods in multilevel SCED using noninformative priors for variance parameters, and their study yielded similar results with the previous study that constructed weakly informative priors. Based on these suggestions, noninformative prior distributions for the SD of the level-2 errors (σu0j, σu1j, σu2j, σu3j) and the level-1 errors (σe) were assigned to be the uniform distribution (lower limit = 0 and upper limit = 100) in this study. The priors for μρ and σρ were further defined as a normal distribution and a uniform distribution, respectively
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