tem Response Theory




Item Response Theory is the study of test and item scores based on assumptions concerning the mathematical relationship between abilities (or other hypothesized traits) and item responses. Other names and subsets include Item Characteristic Curve Theory, Latent Trait Theory, Rasch Model, 2PL Model, 3PL model and the Birnbaum model.

In the following figure, the x-axis represents student ability and the y-axis represents the probability of a correct response to one test item. The s-shaped curve, then, shows the probabilities of a correct response for students with different ability (theta) levels.

Modeling  the relationships between ability and a set of items provides the basis for numerous practical applications, most of which have advantages over their classical measurement theory counterparts. 

The goal of this page is to provide resources to help you learn more about this class of measurement models. The main feature of this page is Frank Baker's exceptional book, The Basics of Item Response Theory, which we have made available, in its entirely, on-line, at no cost. This delightful book will allow you to acquire the basic concepts of the theory without becoming enmeshed in the underlying mathematics and computational complexities. We hope you will take advantage of this important contribution by Dr. Baker.


December 2001
Lawrence M. Rudner



The Basics of Item Response Theory (by Frank Baker)
Chapter 1 - The Item Characteristic Curve
Chapter 2 - Models
Chapter 3 - Estimation of item parameters
Chapter 4 - Test Characteristic Curve
Chapter 5 - Ability Estimation
Chapter 6 - Information function
Chapter 7 - Test Calibration
Chapter 8 - Test Characteristics
References & Resources
Complete book
(800K) pdf
Computer Adaptive Testing by Lawrence Rudner, ERIC
IRT Modeling by University of Illinois IRT Modeling Lab
Generate ICC's and Information functions, interactive
IRT Overview by Penn State University testing Services
Other IRT sites
Institute for Objective Measurement, Inc.Excellent comprehensive site for the Rasch model
University of Illinois IRT Modeling Lab website. Good tutorial.
UMD. Under development featuring an unfolding model.
Paper Collections on IRT 
Rash Measurement Transactions
MD Assessment Archive
Software (free)
PARAM-3PL Calibration for the 3PL IRT Model - Via Larry Rudner, GMAC
IRT Programs and Datasets - Via IRT Modeling Lab, UIUC
Rasch  - Via Winsteps
Unfolding - Via Jim Roberts, UMD
Some source code
Software (via Assessment Systems Inc)
PARSCALE Performs IRT scaling, item analysis, and scoring of rating scale data.
BILOG-MG Estimates IRT parameters for multiple groups, allowing detection of differential item functioning. 
MULTILOG Provides versatile multiple-category IRT analysis for polytomous IRT models.
XCALIBRE Marginal maximum-likelihood IRT parameter estimation with small numbers of examinees or short tests, for the 2- and 3-parameter IRT model.
Books (via amazon.com)
Item Response Theory: Parameter Estimation Techniques, Second Edition  -- by Frank Baker and Seock-Ho Kim
Item Response Theory for Psychologists  -- by Susan E. Embretson and others
Essays on Item Response Theory 
by Anne Boomsma (Editor)
Handbook of Modern Item Response Theory
by Wim J. Van Der Linden & Ron Hambleton (Editors)
Computerized Adaptive Testing
by Howard Wainer and others
Fundamentals of Item Response Theory by Ronald Hambleton
Error Free Mental Measurements by Robert M. Hashway (in press)
Test Scoring by David Thissen & Howard Wainer (Editors)
Applying the Rasch Model by Trevor G. Bond, Christine M. Fox