Noninformative priors for one-parameter item response models

We present a unified Bayesian approach for the analysis of one-parameter item response models. A necessary and sufficient condition is given for the propriety of posteriors under improper priors with nonidentifiable likelihoods. Posterior distributions for item and subject parameters may be improper when the sum of the binary responses for an item or subject takes its minimum or maximum possible value. When the item parameters have a flat prior but the item totals do not fall at a boundary value, we prove the propriety of the Bayesian joint posterior under some sufficient conditions on the joint (proper) distribution of the subject parameters. The methods are implemented using Markov chain Monte Carlo and illustrated with an example from a cross-over study comparing three medical treatments. (C) 2000 Elsevier Science B.V. All rights reserved. MSG: primary 62F15; secondary 62P15.