The mixed-coefficients multinomial logit model : a generalized form of the Rasch model

Since Rasch's introduction of his item response models, there has been a proliferation of extensions and alternatives, each of which has a different name and different matching software package. The proliferation of models has, in some ways, been a hindrance to practitioners. This paper presents a generalised item response model that provides a unifying framework for a large class of Rasch-type models. The advantages of a single framework include mathematical elegance, generality in a single software package, and a facilitation of the development, testing, and comparison of new models. The unified model is a multidimensional item response model, the specification of which is achieved through the use of design matrices chosen to represent the parametrisation of the model. In the paper the authors discuss the estimation of the parameters of the model, the testing of model fit, and they illustrate how standard models (such as the simple logistic, the rating scale, and facets models) and alternative user- defined models are specified.