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Item response theory (IRT) has become one of the most popular statisticalmodels for psychometrics, a field of study concerned with the theory andtechniques of psychological measurement. The IRT models are latent factormodels tailored to the analysis, interpretation, and prediction of individuals'behaviors in answering a set of measurement items that typically involvecategorical response data. Many important questions of measurement are directlyor indirectly answered through the use of IRT models, including scoringindividuals' test performances, validating a test scale, linking two tests,among others. This paper provides a review of item response theory, includingits statistical framework and psychometric applications. We establishconnections between item response theory and related topics in statistics,including empirical Bayes, nonparametric methods, matrix completion,regularized estimation, and sequential analysis. Possible future directions ofIRT are discussed from the perspective of statistical learning.

Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement