A Monte Carlo investigation of the likelihood-ratio procedure in the detection of differential item functioning
When items in an educational or psychological measurement instrument perform differentially in two or more groups of examinees, the ability of that measuring device to accurately measure the intended construct is negatively impacted. As a result, differential item functioning (DIF) contributes to test invalidity. The likelihood ratio (LR) procedure for detecting DIF in educational and psychological measurements, has been largely unstudied in the literature. Consequently, the ability of the LR procedure to accurately detect DIF, and the effects of extraneous variables on this accuracy remain unexamined. The present study examined the accuracy of the LR procedure and investigated the impact of several variables that have been demonstrated to impact other DIF detection procedures. The independent variables included in the present study were values of the a and b item parameters, amount of DIF in the a and b item parameters, ratio of reference group size to focal group size, and the congruence of the reference and focal group ability distributions. The dependent variables included were the percentage of items identified as differentially functioning and the value of the likelihood ratio statistic, G$\sp2$. Results of this study found that the LR procedure works well in a wide range of conditions, and that the procedure maintains good control over Type I error rates across all conditions in the study. It was found that a general relationship existed such that there was a higher probability of detecting DIF when there were large differences between the reference and focal group ICCs and when focal group examinees were located where those differences occured. As the differences between the ICCs decreased or the number of examinees located where those differences occured decreased, the probability of detecting DIF also decreased.
Sweeney, Kevin P, "A Monte Carlo investigation of the likelihood-ratio procedure in the detection of differential item functioning" (1997). ETD Collection for Fordham University. AAI9715510.