The Performance of Maximum Likelihood and Weighted Least Square Mean and Variance Adjusted Estimators in Testing Differential Item Functioning With Nonnormal Trait Distributions

Abstract

The relative performance of the maximum likelihood (ML) and weighted least square mean and variance adjusted (WLSMV) estimators was investigated by studying differential item functioning (DIF) with ordinal data when the latent variable () was not normally distributed. As the ML estimator, ML with robust standard errors (labeled MLR in Mplus) was chosen and implemented with 2 link functions (logit vs. probit). The Type I error and power of χ2 tests were evaluated under various simulation conditions including the shape of the distributions for the reference and focal groups. Type I error was better controlled with MLR estimators than WLSMV. The error from WLSMV was inflated when there was a large difference in the shape of the distribution between the 2 groups. In general, the power remained quite stable across different distribution conditions regardless of the estimators. WLSMV and MLR-probit showed comparable power, whereas MLR-logit performed the worst.