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

Area of Science:

• Statistics
• Multilevel Modeling
• Quantitative Psychology

Background:

• Homogeneity of variance (HOV) is a key assumption in multilevel models (MLMs).
• Violations of HOV can lead to inaccurate standard errors and unreliable inferential tests in MLMs.
• Existing methods for assessing HOV violations may be limited, especially with fewer than 50 clusters.

Purpose of the Study:

• To evaluate statistical tests for assessing HOV violations in MLMs.
• To assess the effectiveness of a robust standard error adjustment (CR2 estimator) for MLMs with few clusters.
• To demonstrate methods for mitigating the impact of HOV violations on MLM fixed effects.

Main Methods:

• Monte Carlo simulation to evaluate statistical tests and the CR2 estimator.
• Assessment of traditional HOV tests (H statistic, Breusch-Pagan, Levene's) within MLM frameworks.
• Application of findings to an illustrative real-world dataset.

Main Results:

• The CR2 estimator provides effective robust standard error adjustments even with a small number of clusters.
• Explicitly modeling heterogeneous variance structures is also effective in addressing HOV violations.
• Both methods successfully ameliorate issues with fixed effects caused by between-group variance heterogeneity.

Conclusions:

• Researchers should test for homogeneity of variance in MLMs.
• The CR2 estimator offers a viable solution for handling HOV violations, particularly when cluster counts are low.
• Explicitly modeling variance structures provides another robust approach to ensure the validity of MLM analyses.