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

Type I error rates for the likelihood ratio test for detectingdifferential item functioning (DIF) were investigatedusing monte carlo simulations. Two- andthree-parameter item response theory (IRT) modelswere used to generate 100 datasets of a 50-item test forsamples of 250 and 1,000 simulated examinees foreach IRT model. Item parameters were estimated bymarginal maximum likelihood for three IRT models: thethree-parameter model, the three-parameter model witha fixed guessing parameter, and the two-parametermodel. All DIF comparisons were simulated by randomlypairing two samples from each sample size andIRT model condition so that, for each sample size andIRT model condition, there were 50 pairs of referenceand focal groups. Type I error rates for the two-parametermodel were within theoretically expected values ateach of the α levels considered. Type I error rates forthe three-parameter and three-parameter model with afixed guessing parameter, however, were differentfrom the theoretically expected values at the α levelsconsidered. Index terms: bias, differential item functioning,item bias, item response theory, likelihood ratiotest for DIF.