Bias and the effect of priors in Bayesian estimation of parameters of item response models

The effectiveness of a Bayesian approach to the es-timation problem in item response models has been sufficiently documented in recent years. Although re-search has indicated that Bayesian estimates, in gen-eral, are more accurate than joint maximum likelihood (JML) estimates, the effect of choice of priors on the Bayesian estimates is not well known. Moreover, the extent to which the Bayesian estimates are biased in comparison with JML estimates is not known. The ef fect of priors and the amount of bias in Bayesian esti-mates is examined in this paper through simulation studies. It is shown that different specifications of prior information have relatively modest effects on the Bayesian estimates. For small samples, it is shown that the Bayesian estimates are less biased than their JML counterparts. Index terms: accuracy, Bayesian estimates, bias, item response models, joint maximum likelihood estimates, priors. Item response theory has the potential for sig-nificantly improving educational and psychological measurement. However, the successful application of this theory relies heavily on the existence of adequate estimation techniques. The effectiveness of a Bayesian approach to the estimation problem in the one-, two-, and three-parameter item re-sponse models has been demonstrated (Mislevy