Bayesian item selection criteria for adaptive testing

R.J. Owen (1975) proposed an approximate empirical Bayes procedure for item selection in adaptive testing. The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity, involved in a fully Bayesian approach, but is no longer necessary given the computational power currently available in adaptive testing. This paper suggests several item selection criteria for adaptive testing that are all based on the use of the true posterior. Some of the statistical properties of the ability estimator produced by the secriteria are discussed and empirically characterized. An empirical study with 300 test items showed that the maximum predicted posterior expected information criterion had excellent mean-squared error for more extreme values of theta, and is the criterion elect for application in short adaptive tests. An appendix presents Owen's equations.