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

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 x(2) 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.