Comparing methods for estimating the abilities for the multidimensional models of mixed item types

The maximum likelihood (MLE), the weighted maximum likelihood (WMLE), and the maximum a posteriori (MAP or BMLE) have been widely used to estimate ability parameters in item response theory (IRT), and their precisions and biases have been studied and compared. Multidimensional IRT (MIRT) has been shown to provide better subscore estimates in both paper-and-pencil and computer adaptive tests; thus, it is very important to have an accurate score estimate for the MIRT model. The purpose of this article is to compare the performances of the three estimation methods in the MIRT framework for tests of mixed item types that have both dichotomous and polytomously scored items, and for tests of mixed structured items (simple structured and complex structured). It is found that all three methods perform well for all conditions. For all models studied (one-, two-, three-, and four- dimensional model), WMLE has smaller BIAS and higher reliabilities, but larger RMSE and SE. WMLE and MLE are closer to each other than to BMLE. However, for higher dimensions, BMLE is recommended, especially when there are correlations between the dimensions.