Cross-level Two-way Differential Item Functioning Analysis by Multilevel Rasch Modeling

Abstract

The objective of this study was to investigate the quality of parameter estimates for a differential item functioning (DIF) model, when the model was not correctly specified. This study focused on a model with two DIF factors, where one DIF factor was a cluster characteristic variable and the other DIF factor was an individual characteristic variable. Accordingly, the model is referred to as a cross-level two-way DIF model, in which a fully specified model has six fixed effect parameters and two random parameters. The multilevel Rasch modeling was utilized in the framework of a two-leve confirmatory factor analysis model with categorical indicators. Repeatedly simulated data were investigated, and it was found that some parameter estimates were adversely affected under incorrect model specifications, including the individuallevel DIF and three-way interaction effect.