Detecting Differential Item Functioning: Item Response Theory Methods Versus the Mantel-Haenszel Procedure

Abstract

This Monte Carlo study assessed Type I error in differential item functioning analyses using Lord’s chi-square (LC), Likelihood Ratio Test (LRT), and Mantel-Haenszel (MH) procedure. Two research interests were investigated: item response theory (IRT) model specification in LC and the LRT and continuity correction in the MH procedure. This study enhances the literature by investigating LC and the LRT using correct and incorrect model-data fit and comparing those results to the MH procedure. There were three fixed factors (number of test items, IRT parameter estimation method, and item parameter equating) and four varied factors (IRT model used to generate data and fit the data, sample size, and impact). The findings suggested the MH procedure without the continuity correction is best based on Type I error rate.This Monte Carlo study assessed Type I error in differential item functioning analyses using Lord’s chi-square (LC), Likelihood Ratio Test (LRT), and Mantel-Haenszel (MH) procedure. Two research interests were investigated: item response theory (IRT) model specification in LC and the LRT and continuity correction in the MH procedure. This study enhances the literature by investigating LC and the LRT using correct and incorrect model-data fit and comparing those results to the MH procedure. There were three fixed factors (number of test items, IRT parameter estimation method, and item parameter equating) and four varied factors (IRT model used to generate data and fit the data, sample size, and impact). The findings suggested the MH procedure without the continuity correction is best based on Type I error rate.