LOGLINEAR MULTIDIMENSIONAL IRT MODELS FOR POLYTOMOUSLY SCORED ITEMS

A loglinear IRT model is proposed that relates polytomously scored ite m responses to a multidimensional latent space. The analyst may specif y a response function for each response, indicating which latent abili ties are necessary to arrive at that response. Each item may have a di fferent number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are de rived and the models may be tested generally or against alternative lo glinear IRT models.