Comparing Differential Item Functioning Based on Multilevel Mixture Item Response Theory, Mixture Item Response Theory and Manifest Groups

Studies on the differential item functioning (DIF) are usually considered in the context of manifest groups. Recently, with the increase in the number of analyses conducted with mixture models, investigating the situations that cause differences between groups has come to the forefront. In addition, it is considered important to examine the DIF with mixture models in which levels are also handled. In this study, it is aimed to compare the results of the multilevel mixture item response theory (MMIRT) model and the mixture item response theory (MIRT) model and the results of the DIF analyses based on the manifest groups. The research sample consists of students who answered the second booklet in the electronic Trends in International Mathematics and Science Study (eTIMSS) 2019 and coded their gender. The answers given to 15 items were analyzed with the Mantel Haenszel (MH) method for the gender variable according to the manifest groups, and with the selection of the most appropriate models by varying the number of groups and the number of levels according to the MIRT model and the MMIRT model. DIF analyses of the obtained latent groups were also performed with the MH method. In the light of the findings, the number of items displaying DIF in both the MIRT model and the MMIRT model is higher than the manifest groups. While only one item displayed DIF in the analysis according to gender, 14 items displayed DIF according to the MIRT model and seven items displayed DIF according to the MMIRT model. There is not a complete overlap in the number of DIF items and DIF effect sizes found as a result of the MIRT model and MMIRT model analyses. For this reason, a level analysis should be conducted before the analyses and if there is multi -levelness, the analyses should be conducted by taking this situation into consideration.