The Accuracy of Significance Tests for Slope Variance Components in Multilevel Random Coefficient Models

Abstract

This study examines the behavior of three tests for significant slope variance in multilevel random coefficient (MRC) models: the Hierarchical Linear Modeling chi-square test, the likelihood ratio test (LRT), and the corrected LRT. Monte Carlo simulations are conducted varying the numbers of groups, group size, and effect size. Results suggest that neither the number of groups nor group size influenced Type I errors. Group size has a stronger effect on power compared with the number of groups. The one-tailed LRT demonstrates the best balance between power and Type I errors. Recommendations for conducting MRC analyses are presented.