Multidimensional Rasch Measurement via Item Component Models and Faceted Designs

Abstract

A multidimensional Rasch model is presented here, which is a multidimensional extension of item component models. Relations to existing multidimensional item response theory models are discussed. Apart from other applications, it is also suitable for analyzing tests and questionnaires, which are designed according to two or more facets. An application to a 77-item questionnaire on students’ interest in physics with a two-facet structure demonstrates that the model parameters can even be estimated when 17 latent dimensions are to be measured simultaneously (by means of joint maximum likelihood methods).