Examination of differential item functioning under different conditions using MIMIC methods

The aim of this study is to investigate the performance of the standard MIMIC method (M-ST) and the MIMIC method with a pure anchor (M-PA) methods in determining DIF under different conditions. The study was conducted on simulation datasets generated under different conditions and a real dataset obtained from the PISA 2012 mathematics test. The conditions considered in the simulation study were IRT model (2PLM and 3PLM), sample size (2000, 1000, and 600), focal/reference group ratio (1/1 and 1/3), DIF magnitude (0.3, 0.5, and 0.7), and the proportion of items with DIF (20% and 40%). Analyses were conducted on each of the 100 repetitions of 36 conditions generated for each dataset. The data were generated for a 20-item test. In analyses conducted on the real dataset, sample size (900 and 450) and focal/reference group ratio (350/550, 450/450, 225/225, and 150/300) conditions were considered. DIF analyses were performed using M-ST and M-PA methods. Type I error rates and power ratios were calculated to examine the performance of the methods in analyses conducted with simulation data. Factorial ANOVA analyses were applied to examine how Type I error rates and power ratios changed according to the conditions considered. It was found that Type I error rates and power ratios showed significant differences depending on sample size, focal/reference group ratio, the proportion of items with DIF, and DIF magnitude. M-PA method exhibited superior performance to M-ST method in terms of Type I error rates. In analyses conducted with real data, it was observed that the number of items identified with DIF using the M-PA method was lower than the number identified using the M-ST method for all conditions.