An investigation of Lord's procedure for the detection of differential item functioning

Abstract

Type I error rates of Lord’s X² chi; test for differential item functioning were investigated using monte carlo simulations. Two- and three-parameter item response theory (IRT) models were used to generate 50-item tests for samples of 250 and 1,000 simulated examinees. Item parameters were estimated using two algorithms (marginal maximum likelihood estimation and marginal Bayesian estimation) for three IRT models (the three-parameter model, the three-parameter model with a fixed guessing parameter, and the two-parameter model). Proportions of significant X²s at selected nominal α levels were compared to those from joint maximum likelihood estimation as reported by McLaughlin & Drasgow (1987). Type I error rates for the three-parameter model consistently exceeded theoretically expected values. Results for the three-parameter model with a fixed guessing parameter and for the two-parameter model were consistently lower than expected values at the a levels in this study. Index terms: differential item functioning, item response theory, Lord’s X².