# Item response theory

## 1 Definition

“In psychometrics, item response theory (IRT: also known as latent trait theory, strong true score theory, or modern mental test theory) is a body of theory describing the application of mathematical models to data from questionnaires and tests as a basis for measuring abilities, attitudes, or other variables. It is used for statistical analysis and development of assessments, often for high stakes tests such as the Graduate Record Examination. At its most basic level, it is based on the idea that the probability of getting an item correct is a function of a latent trait or ability. For example, a person with higher intelligence would be more likely to correctly respond to a given item on an intelligence test.” (Item response theory (Wikipedia, retrieved 14:58, 9 March 2009 (UTC)).

“ In many educational and psychological measurement situations, there is an underlying variable of interest. This variable is often something that is intuitively understood, such as "intelligence". [...] In academic areas, one can use descriptive terms such as reading ability and arithmetic ability. Each of these is what psychometricians refer to as an unobservable, or latent, trait.[...] A primary goal of educational and psychological measurement is the determination of how much of such a latent trait a person possesses.” [http://echo.edres.org:8080/irt/baker/chapter1.pdf Baker, 2001:5).

“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.” (L.M. Rudner, retrieved 16:41, 9 March 2009 (UTC)).

See also: Methodology tutorial - descriptive statistics and scales

## 2 Links

- Overviews

- Item response theory (Wikipedia).
- Item Response Theory by Lawrence M. Rudner, 2001.

- Online Tutorials

- Item Response Theory by Michael T. Brannick. I found this well writen and useful.
- A visual guide to item response theory by Ivailo Partchev, Friedrich-Schiller-Universität Jena (2004).

- Other

- Latent Structure Analysis web site. This site is a resource for social scientists and biostatisticians interested in latent class, latent trait, item response, and related models.

- Software

- Psychometric software (Wikipedia). Good list, including free/open source software.

## 3 Bibliography

- Baker, Frank (2001). The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation, University of Maryland, College Park, MD. The first edition is available as free on line book (chapters available as PDF)

- Partchev, Ivailo (2004). A visual guide to item response theory, Friedrich-Schiller-Universität Jena. PDF. Good tutorial, but
*not*easy.

- Thorpe, Geoffrey L. and Favia, Andrej, "Data Analysis Using Item Response Theory Methodology: An Introduction to SelectedPrograms and Applications." (2012).Psychology Faculty Scholarship.Paper 20. http://digitalcommons.library.umaine.edu/psy_facpub/20 (Abstract/PDF)