Robust Methods for Moderation Analysis with a Two-Level Regression Model.
Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.
a University of Notre Dame.
Miao
M
Yang
a University of Notre Dame.
Ke-Hai
KH
Yuan
D001741:Black or African American; D000367:Age Factors; D000465:Algorithms; D003198:Computer Simulation; D004522:Educational Status; D006801:Humans; D007182:Income; D016018:Least-Squares Analysis; D016013:Likelihood Functions; D009010:Monte Carlo Method; D055361:Multilevel Analysis / Q000379:methods*; D015999:Multivariate Analysis; D012044:Regression Analysis; D012737:Sex Factors; D012984:Software; D044465:White People
Complete moderation; partial moderation; robust methods; sandwich-type standard errors