An Investigation of Lord's Procedure for the Detection of Differential Item Functioning

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Abstract
Type I error rates of Lord's χ 2 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 examin ees. Item parameters were estimated using two algo rithms (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-param eter model). Proportions of significant χ 2s 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 theo retically expected values. Results for the three-param eter model with a fixed guessing parameter and for the two-parameter model were consistently lower than ex pected values at the a levels in this study. Index terms: differential item functioning, item response theory, Lord's χ2.