Detecting Multidimensional DIF in Polytomous Items with IRT Methods and Estimation Approaches

The purpose of this study was to investigate multidimensional DIF with a simple and nonsimple structure in the context of multidimensional Graded Response Model (MGRM). This study examined and compared the performance of the IRT-LR and Wald test using MML-EM and MHRM estimation approaches with different test factors and test structures in simulation studies and applying real data sets. When the test structure included two dimensions, the IRT-LR (MML-EM) generally performed better than the Wald test and provided higher power rates. If the test included three dimensions, the methods provided similar performance in DIF detection. In contrast to these results, when the number of dimensions in the test was four, MML-EM estimation completely lost precision in estimating the nonuniform DIF, even with large sample sizes. The Wald with MHRM estimation approaches outperformed the Wald test (MML-EM) and IRT-LR (MML-EM). The Wald test had higher power rate and acceptable type I error rates for nonuniform DIF with the MHRM estimation approach.The small and/or unbalanced sample sizes, small DIF magnitudes, unequal ability distributions between groups, number of dimensions, estimation methods and test structure were evaluated as important test factors for detecting multidimensional DIF.