Bayesian conditional inference for Rasch models

This paper is concerned with Bayesian inference in psychometric modeling. It treats conditional likelihood functions obtained from discrete conditional probability distributions which are generalizations of the hypergeometric distribution. The influence of nuisance parameters is eliminated by conditioning on observed values of their sufficient statistics, and Bayesian considerations are only referred to parameters of interest. Since such a combination of techniques to deal with both types of parameters is less common in psychometrics, a wider scope in future research may be gained. The focus is on the evaluation of the empirical appropriateness of assumptions of the Rasch model, thereby pointing to an alternative to the frequentists’ approach which is dominating in this context. A number of examples are discussed. Some are very straightforward to apply. Others are computationally intensive and may be unpractical. The suggested procedure is illustrated using real data from a study on vocational education.