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

Type I error rates of Lord’s X² chi; test for differentialitem functioning were investigated using monte carlosimulations. Two- and three-parameter item responsetheory (IRT) models were used to generate 50-itemtests for samples of 250 and 1,000 simulated examinees.Item parameters were estimated using two algorithms(marginal maximum likelihood estimation andmarginal Bayesian estimation) for three IRT models (thethree-parameter model, the three-parameter modelwith a fixed guessing parameter, and the two-parametermodel). Proportions of significant X²s at selectednominal α levels were compared to those from jointmaximum likelihood estimation as reported byMcLaughlin & Drasgow (1987). Type I error rates forthe three-parameter model consistently exceeded theoreticallyexpected values. Results for the three-parametermodel with a fixed guessing parameter and for thetwo-parameter model were consistently lower than expectedvalues at the a levels in this study. Indexterms: differential item functioning, item responsetheory, Lord’s X².