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Robust Moderation Analysis Using a Two-Level Regression Model

Moderation analysis has many applications in social and behavioral sciences. Classical estimation methods typically assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the conclusions from a classical moderation analysis can be misleading. A twolevel regression model (Yuan, Cheng, & Maxwell, 2014) has been proposed to allow for heteroscedasticity. However, existing study of the two-level regression model is limited to the normal-distribution-based maximum likelihood (NML). For more accurate parameter estimates and more powerful tests with real data when conducting moderation analysis using the two-level regression model, two robust methods are proposed in this study. One is based on maximum likelihood with Student’s t distribution, and the other is based on M-estimators with Huber-type weights. An iteratively reweighted least squares algorithm is developed for estimating the parameters of the two-level regression model based on the robust approaches. Consistent standard errors of the robust parameter estimates are obtained using the so-called sandwich-type covariance matrix. The robust approaches are compared against NML with respect to power and ac-