An investigation of the likelihood ratio test for detection of differential item functioning

Type I error rates for the likelihood ratio test for detecting differential item functioning (DIF) were investigated using monte carlo simulations. Two- and three-parameter item response theory (IRT) models were used to generate 100 datasets of a 50-item test for samples of 250 and 1,000 simulated examinees for each IRT model. Item parameters were estimated by marginal maximum likelihood for three IRT models: the three-parameter model, the three-parameter model with a fixed guessing parameter, and the two-parameter model. All DIF comparisons were simulated by randomly pairing two samples from each sample size and IRT model condition so that, for each sample size and IRT model condition, there were 50 pairs of reference and focal groups. Type I error rates for the two-parameter model were within theoretically expected values at each of the α levels considered. Type I error rates for the three-parameter and three-parameter model with a fixed guessing parameter, however, were different from the theoretically expected values at the α levels considered. Index terms: bias, differential item functioning, item bias, item response theory, likelihood ratio test for DIF