Item Response Theory clearly describes the most recently developed IRT models and furnishes detailed explanations of algorithms that can be used to estimate the item or ability parameters under various IRT models. Extensively revised and expanded, this edition offers three new chapters discussing parameter estimation with multiple groups, parameter estimation for a test with mixed item types, and Markov chain Monte Carlo methods. It includes discussions on issues related to statistical theory, numerical methods, and the mechanics of computer programs for parameter estimation, which help to build a clear understanding of the computational demands and challenges of IRT estimation procedures.The Item Characteristic Curve: Dichotomous Response Estimating the Parameters of an Item Characteristic Curve Maximum Likelihood Estimation of Examinee Ability Maximum Likelihood Procedures for Estimating Both Ability and Item Parameters The Rasch Model Marginal Maximum Likelihood Estimation and an EM Algorithm Bayesian Parameter Estimation Procedures The Graded Item Response Nominally Scored Items Markov Chain Monte Carlo Methods Parameter Estimation with Multiple Groups Parameter Estimation for a Test with Mixed Item Types