18 Multidimensional Item Response Theory

This chapter describes the common forms of Multidimensional Item Response Theory (MIRT) models and the mathematical expressions for MIRT models. It also provides a general conceptual framework for the use of MIRT models. MIRT models are typically models for the relationship between the probability of a response to one item and the location of a person in the coordinate space. The model only contains parameters for the characteristics of one item and the location for one person. The item parameters are assumed to be constant. The probability of correct response to the item changes with the location of the person. The model is not for the sets of items, although a number of items are analyzed at the same time during the estimation of item parameters and tests of fit of the models to item response data. It is always possible to fit a model to the data from one item. The simultaneously fitting of the model to multiple items is a stringent test of the usefulness of the model.