Birnbaum, A. "Some latent trait models and their use in inferring an examinee’s ability." Part 5 in F.M. Lord and M.R. Novick. Statistical Theories of Mental Test Scores. Reading, MA: Addison-Wesley, 1968.

Hambleton, R.K., and Swaminathan, H. Item Response Theory: Principles and Applications. Hingham, MA: Kluwer, Nijhoff, 1984.

Hulin, C. L., Drasgow, F., and Parsons, C.K. Item Response Theory: Application to Psychological Measurement. Homewood, IL: Dow-Jones, Irwin: 1983.

Lord, F.M. Applications of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: Erlbaum, 1980.

Mislevy, R.J., and Bock, R.D. PC-BILOG 3: Item Analysis and Test Scoring with Binary Logistic Models. Mooresville, IN: Scientific Software, Inc, 1986.

Wright, B.D., and Mead, R.J. BICAL: Calibrating Items with the Rasch Model. Research Memorandum No. 23. Statistical Laboratory, Department of Education, University of Chicago, 1976.

Wright, B.D., and Stone, M.A. Best Test Design. Chicago: MESA Press, 1979.

NOTE: See ( for more information about the BILOG program. See ( ) for more information about BICAL and its successors, WINSTEPS and BIGSTEPS.


Web Sites and Online Resources

Institute for Objective Measurement

The host of this site draws a careful distinction between IRT and Rasch measurement, but those interested in IRT will likely find items of interest here, including the full text of Rasch Measurement Transactions, the quarterly publication of the Rasch Measurement SIG of the American Educational Research Association.

Interactive CAT & IRT Mini-Tutorial

Part of an online, interactive tutorial on computer adaptive testing developed, this mini-tutorial introduces the three-parameter IRT model and allows users to experiment with varying the item parameter values and generating graphs of item response functions.

Item Response Theory Models for Unfolding

This Web site, maintained by James S. Roberts, Professor at Georgia Tech, explores unfolding models for predicting item scores where responses are obtained in a rating scale format such as a Thurstone or Likert scale. Users can download free modeling software and illustrative data sets on attitudes toward capital punishment or censorship.


Electronic Discussion Groups

Rasch Discussion Listserv

This unmoderated forum sponsored by the Australian Council for Educational Research has operated since 1966 to support "the exchange of news, questions and answers about the theory and practice of Rasch Measurement."

To join, send an e-mail with text subscribe rasch to

ERIC Database Search

Go to

Enter the term "item response theory" into the search box.

Print Classics (see ther IRT page for links)

Applications of Item Response Theory to Practical Testing Problems F. M. Lord. Lawrence Erlbaum, 1980

This classic text offers a thorough technical presentation of IRT models, including their limitations, as well as discussion of such practical problems as estimating ability and item parameters, equating, study of item bias, omitted responses and formula scoring. Flexilevel tests, multilevel tests, tailored testing, and mastery testing are also addressed.

Fundamentals of Item Response Theory R. K. Hambleton, H. Swaminathan, and H. J. Rogers. Sage, 1991

This introductory text draws on concepts from classical measurement methods and basic statistics to present the basics of IRT and its applications in test construction, identification of potentially biased test items, test equating, and computerized adaptive testing. Alternative procedures for estimating IRT parameters, including maximum likelihood estimation, marginal maximum likelihood estimation, and Bayesian estimation, are discussed. Step-by-step numerical examples are included throughout.

Item Response Theory: Parameter Estimation Techniques F.B. Baker. Marcell Dekker, 1992

This book presents the mathematical details of the parameter estimation procedures used in item response theory. The procedures maximum likelihood, marginal maximum likelihood, and Bayesian estimation are presented for binary, graded, and nominal response items. BASIC computer programs for these procedures are provided in the book.

Handbook of Modern Item Response Theory. W. J. van der Linden and R. K. Hambleton, eds. Springer, 1997

This reference work provides an introduction to item response theory and its application to educational and psychological testing. A comprehensive treatment of models and families of models is provided in 27 chapters, each of which is authored by person(s) who either proposed or contributed substantially to the development of the model discussed. Each chapter includes an introduction, presentation of the model, parameter estimation and goodness of fit, and a brief empirical example. Some chapters also offer discussion.