A Review of Bayesian Item Response Modeling: Theory and Applications

Abstract

The primary reason Bayesian methods have become increasingly soughtafter in educational statistics is their flexibility in evaluating complex models.Bayesian estimation of item response models has been argued to be more advan-tageous than marginalized maximum likelihood or maximum likelihood becauseof their ability to estimate parameters for complex data structures, such as hier-archical data or data that violate the basic assumptions of item response theory(IRT), success with smaller samples, no parameter drift, and parameter estimationin extreme response patterns (Albert, 1992; Fox, 2010; Lord, 1986; SwaminathanGAlbert, 1992; Patz & Junker, 1999) and the availability of open-access softwareprogramssuchasRand BUGS that facilitateMCMCestimation.Asaresult,thereisprolificgrowthinthenumberofpublishedarticlesthatuseBayesianestimation.This in turn has created a real need for a comprehensive source of information onBayesian approaches to IRT.Some other, relatively isolated, works on the topic exist. The classicbook, Item response theory: Parameter estimation techniques by Baker andKim (2004) addressed Bayesian estimation in only one chapter. The recentlypublishedExplanatoryitemresponsemodels:Ageneralizedlinearandnonlinearapproach edited by De Boeck and Wilson (2004) provided some examples ofBayesianestimationofitemresponsemodels.However,thistext emphasizedtheformulation of IRT models as generalized linear and nonlinear models and notBayesian estimation procedures. A psychometrician or an advanced student ofpsychometrics did not have a comprehensive guide that focused on the Baye-sian estimation of all aspects of IRT in detail along with some practical