Using a Multidimensional IRT Framework to Better Understand Differential Item Functioning (DIF): A Tale of Three DIF Detection Procedures

The theoretical reason for the presence of differential item functioning (DIF) is that data are multidimensional and two groups of examinees differ in their underlying ability distribution for the secondary dimension(s). Therefore, the purpose of this study was to determine how much the secondary ability distributions must differ before DIF is detected. Two-dimensional binary data sets were simulated using a compensatory multidimensional item response theory (MIRT) model, incrementally varying the mean difference on the second dimension between reference and focal group examinees while systematically increasing the correlation between dimensions. Three different DIF detection procedures were used to test for DIF: (1) SIBTEST, (2) Mantel-Haenszel, and (3) logistic regression. Results indicated that even with a very small mean difference on the secondary dimension, smaller than typically considered in previous research, DIF will be detected. Additional analyses indicated that even with the smallest mean difference considered in this study, 0.25, statistically significant differences will almost always be found between reference and focal group examinees on subtest scores consisting of items measuring the secondary dimension.