The use of multidimensional item response theory models in controlling differential item functioning

The purpose of this study is to investigate the effects of Unidimensional (UD) and Multidimensional Item Response Theory (MIRT) Estimations on controlling Variability of Differential Item Functioning (DIF) in tests where unidimensionality cannot be ensured due to tests with DIF in different simulation conditions. In line with the aim of the study, 24 different experimental conditions, alternatingly for the number of dimensions (2, 3), DIF percentage (10%, 20%, 30%), DIF size (small, large), and DIF type (Uniform_UDIF, Nonuniform_NUDIF) 2x3x2x2 = 24x100 repetitions = 2400 different data sets were generated. Depending on the changes in the number of dimensions, DIF percentage, DIF size, and DIF type; differences in the performance of DIF determination techniques (Logistic Regression-LR, Simultaneous item bias test-SIBTEST, Lord's χ2) in terms of Type I error and statistical power rates were examined. In the generation of data, estimating ability parameters based on Unidimensional and Multidimensional IRT, examining differences in Type I error and statistical power rates for performing DIF analyses, and drawing graphs R programming language were used. In line with IRT assumptions, dimensionality and model-data fit analyses were conducted for data generated under simulation conditions. In addition, for the validity of simulation data, cases providing the desired DIF percentage, DIF size, and DIF type -produced data were examined, and statistical and logical checks were performed. UDIF and NUDIF types, differences in Type I error and statistical power rates of DIF analyses for Unidimensional and Multidimensional IRT estimates in each simulation condition were separately examined. Factorial ANOVA analysis was used to determine the differences. As a result of the analysis, for UDIF and NUDIF types, lower Type 1 error values and higher statistical power values were obtained for the multidimensional estimation method compared to the unidimensional estimation method, and it was concluded that the obtained differences were significant and had a high level of effect. These results can be interpreted as indicating that multidimensional estimations are more effective in obtaining corrected scores compared to unidimensional estimations. In real data analysis, it was concluded that there were significant differences in favor of multidimensional estimations in terms of Type I error and statistical power rates for both unidimensional and multidimensional estimations. When the results are evaluated together, it is seen that multidimensional estimations are effective in controlling DIF compared to unidimensional estimations, and this result is supported by real data. In this context, in a test with multidimensional DIF, it is recommended to obtain corrected total scores by making multidimensional estimations without removing items. In addition, for UDIF and NUDIF DIF types; Increasing DIF size; For UDIF DIF type, increasing DIF percentage provides more correction in multidimensional estimation Type I error rates. For both UDIF and NUDIF DIF types; Increasing DIF size and the number of dimensions, and for NUDIF DIF type, increasing DIF percentage provide more correction in multidimensional estimation statistical power rates. In addition to these results, for UDIF and NUDIF DIF types; lower Type I error and higher statistical power rates were obtained in multidimensional estimation results for all DIF determination techniques compared to unidimensional estimation. Another result is that while the differences between the sub-levels determined in unidimensional estimation are prominent, the differences decrease and the levels work more similarly in the multidimensional estimation results.