Accounting for Heteroskedasticity Resulting from Between-Group Differences in Multilevel Models

• Published in: Multivariate behavioral research Vol. 58; no. 3; pp. 637 - 657
• Main Authors: Huang, Francis L., Wiedermann, Wolfgang, Zhang, Bixi
• Format: Journal Article
• Language: English
• Published: United States Routledge 01.05.2023; Taylor & Francis Ltd
• Subjects: assumptions; Clusters; Computer Simulation; heteroskedasticity; Homogeneity; homogeneity of variance; Models, Statistical; Monte Carlo Method; Monte Carlo simulation; Multilevel Analysis; multilevel models; Regression models; Robustness; Standard error; Statistical analysis; Variance; heteroskedasticity; multilevel models; assumptions; homogeneity of variance
• ISSN: 0027-3171; 1532-7906
• DOI: 10.1080/00273171.2022.2077290

Homogeneity of variance (HOV) is a well-known but often untested assumption in the context of multilevel models (MLMs). However, depending on how large the violation is, how different group sizes are, and the variance pairing, standard errors can be over or underestimated even when using MLMs, resulting in questionable inferential tests. We evaluate several tests (e.g., the H statistic, Breusch Pagan, Levene's test) that can be used with MLMs to assess violations of HOV. Although the traditional robust standard errors used with MLMs require at least 50 clusters to be effective, we assess a robust standard error adjustment (i.e., the CR2 estimator) that can be used even with a few clusters. Findings are assessed using a Monte Carlo simulation and are further illustrated using an applied example. We show that explicitly modeling the heterogenous variance structures or using the CR2 estimator are both effective at ameliorating the issues associated with the fixed effects of the regression model related to violations of HOV resulting from between-group differences.