Bayes modal estimation in item response models

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.This research was supported by a grant from the Spencer Foundation, Chicago, IL. Comments and suggestions on earlier drafts by Charles Lewis, Frederic Lord, Rosenbaum, James Ramsey, Hiroshi Watanabe, the editor, and two anonymous referees are gratefully acknowledged.