Prior distribution for item response curves

The paper examines the use of the ordered Dirichlet prior for binary logistic item response models. This prior is based on the investigator's prior information about the probabilities of correct response to items from examinees at several ability levels. The effect of the prior is examined in terms of the posterior mode of the item parameters computed via the EM algorithm. An illustration is used to explore the application of a 1981 ACT math test to form a prior that is then used on a similar 1987 test. A novel feature of the paper is the emphasis placed on the entire item response curves, rather than the item parameters per se . Detailed computational expressions for the three‐parameter logistic model are summarized in an Appendix.