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Abstract
Multidimensional item response theory (MIRT) models or mixture IRT (MixIRT) models are available for the multidimensional data analyses. The difference of these two IRT models is a type of characteristics used to capture multidimensionality of data. Multidimensionality is explained based on the characteristics of items in MIRT models, while MixIRT models explain multidimensionality as the characteristics of a group of examinees. Sometimes, however, the results of the MIRT or MixIRT models might not be enough to understand multidimensionality of data because it is the results of interaction between examinees and items. The purpose of this study is to propose a multidimensional and mixture random item model (MMixRIM) as an alternative IRT model for multidimensional data analyses. This proposed model is a combination of MIRT model, MixIRT model, and the random item model, and can provide information about both examinees and items to understand multidimensionality of data. One empirical study and one simulation study were conducted to compare the performances of the multidimensional two-parameter logistic (M2PL) model, two-parameter MixIRT (Mix2PL), and two-dimensional MMixRIM (2DMMixRIM) for the multidimensional data analysis. Results of the empirical study indicated that 2DMMixRIM detected some items that measure different latent trait between latent classes, whereas these items measure the same latent traits based on the analysis by using the M2PL model. Further, results of the simulation study suggested that the Mix2PL model and 2DMMixRIM showed better performances than the M2PL model for the correct model selections based on AIC, BIC, CAIC, AICc, and ABIC. On the other hand, recovery of item parameters and class memberships estimated by the M2PL and Mix2PL models were better than MMixRIM.