Empirical Comparison Between Factor Analysis and Multidimensional Item Response Models

Many factor analysis and multidimensional item response models for dichotomous variables have been proposed in literature. The models and various methods for estimating the item parameters are reviewed briefly. In a simulation study these methods are compared with respect to their estimates of the item parameters both in terms of an item response theory formulation and in terms of a factor analysis formulation. It is concluded that for multidimensional data a common factor analysis on the matrix of tetrachoric correlations performs at least as well as the theoretically appropriate multidimensional item response models.