Item Response Theory

by

Anthony D. Albano, Tzu-Yun Chin, Kurt Geisinger

• LAST REVIEWED: 30 August 2016
• LAST MODIFIED: 30 August 2016
• DOI: 10.1093/obo/9780199828340-0182

Introduction

Item response theory (IRT) is arguably one of the most influential developments in the field of educational and psychological measurement. IRT provides a foundation for statistical methods that are utilized in contexts such as test development, item analysis, equating, item banking, and computerized adaptive testing. Its applications also extend to the measurement of a variety of latent constructs in a variety of disciplines. The success and influence of IRT over its predecessor, classical test theory, comes primarily from the focus in IRT on the individual components that make up a measure; that is, on the test items themselves. By modeling outcomes at the item level, rather than at the test level as in classical test theory, IRT is more complex but also more comprehensive in terms of the information it provides about test performance. The purpose of this article is to give a broad overview of the published research on and applications of IRT since its origins in the 1950s. The first part of this article introduces some General Overviews and more Specific Overviews of IRT. Sections then present journal articles that introduce IRT Model Formulations, topics in Estimation and Fit and Related Issues, and, finally, some common Applications of IRT.

General Overviews

The general overviews listed here are a subset of the many book-length treatments of IRT published since the 1960s. They were chosen because of their comprehensiveness in dealing broadly with the essential theory and applications of IRT. They all provide a thorough introduction to the traditional IRT models; however, they differ in their emphasis on the theory and statistical underpinnings upon which IRT is built and the testing applications that IRT supports. De Ayala 2009 provides a nice balance of theory, statistical foundations, and application, making it most suitable as a graduate-level textbook or general reference book. Embretson and Reise 2000, van der Linden and Hambleton 1997, and Lord 1980 are also balanced and serve as good general references, but they are less comprehensive and somewhat outdated. Baker 2001 and Hambleton, et al. 1991 both emphasize conceptual explanations and applications over equation and derivations, making them less authoritative but also simpler and more accessible to a broader audience of beginning users.

• Baker, F. B. 2001. The basics of item response theory. 2d ed. College Park, MD: ERIC Clearinghouse on Assessment and Evaluation.

  Second edition of a simple conceptual introduction to IRT with limited emphasis on the underlying mathematics. Includes a list of recommended readings, online resources, and exercises that can be completed in companion software. Content covers fundamentals of IRT, statistical theory, numerical methods, and the mechanics of computer programs for estimation.

• de Ayala, R. J. 2009. The theory and practice of item response theory. New York: Guilford.

  A comprehensive and balanced presentation of the theory and application of IRT, written for professionals and advanced graduate students. Covers the traditional unidimensional models with additional chapters on estimation approaches, multidimensional IRT, and differential item functioning. Demonstrations are provided throughout.

• Embretson, S. E., and S. P. Reise. 2000. Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum.

  A readable introduction to IRT for psychologists and others having some background in testing. Traditional dichotomous and polytomous models are introduced, with details on applications in test construction (especially for noncognitive measures), person measurement, item calibration, and computerized adaptive testing, as well as cognitive, developmental, personality, and attitude measurement.

• Hambleton, R. K., H. Swaminathan, and H. J. Rogers. 1991. Fundamentals of item response theory. Newbury Park, CA: SAGE.

  Classic introduction to IRT. Less reliance on mathematical formulae makes it more accessible, but less authoritative. Topics include the application of IRT methods to problems in test construction, identification of differentially functioning items, test equating, and adaptive testing.

• Lord, F. M. 1980. Applications of item response theory to practical testing problems. Mahwah, NJ: Lawrence Erlbaum.

  A complete introduction to IRT from a leading figure in the field. Provides a thorough overview of IRT, while covering important testing topics, including analysis of multiple-choice items, the optimal number of options in such items, flexilevel and multilevel tests, tailored testing, criterion-referenced testing, equating, and item bias.

• van der Linden, W. J., and R. K. Hambleton. 1997. Handbook of modern item response theory. New York: Springer.

  An authoritative handbook providing a broad overview of IRT while also stressing its application to educational and psychological testing. It is also the comprehensive reference volume for practitioners and researchers, at least as of the 1990s. It has six sections, each considering a class of models.