Confirmatory factor analysis of items with a dichotomous response format using the multidimensional Rasch model

Two models that can be used for exploratory factor analysis of items with a dichotomous response format are discussed: threshold models and multidimensional item response models. The models arise from different traditions: The threshold model is rooted in the factor analytic tradition, the multidimensional item response model had its foundation in item response theory. Despite the different origins, it can be proved that both models are the same. Subsequently, the generalized multidimensional Rasch model is introduced. This model can be used for confirmatory factor analysis of items with a dichotomous response format Stated otherwise, it is the confirmatory counterpart of the (exploratory) threshold and multidimensional item response models.