### What is Item Response Theory?

Item Response Theory (IRT) is a way to analyze responses to tests or questionnaires with the goal of improving measurement accuracy and reliability.

A common application is in testing a student’s ability or knowledge. Today, all major psychological and educational tests are built using IRT. The methodology can significantly improve measurement accuracy and reliability while providing potential significant reductions in assessment time and effort, especially via computerized adaptive testing. For example, the SAT and GRE both use Item Response Theory for their tests. IRT takes into account the number of questions answered correctly and the difficulty of the question.

In recent years, IRT models have also become increasingly popular in health behavior, quality of life, and clinical research. There are many different models for IRT. Three of the most popular are:

Early IRT models (such as the Rasch model and two-parameter model) concentrate mainly on dichotomous responses. These models were later extended to incorporate other formats, such as ordinal responses, rating scales, partial credit scoring, and multiple category scoring.

### Item Response Theory Models Using SAS

Ron Cody and Jeffrey K. Smith’s book, *Test Scoring and Analysis Using SAS*, uses SAS PROC IRT to show how to develop your own multiple-choice tests, score students, produce student rosters (in print form or Excel), and explore item response theory (IRT).

Aimed at non-statisticians working in education or training, the book describes item analysis and test reliability in easy-to-understand terms and teaches SAS programming to score tests, perform item analysis, and estimate reliability.

For those with a more statistical background, *Bayesian Analysis of Item Response Theory Models Using SAS* describes how to estimate and check IRT models using the SAS MCMC procedure. Written especially for psychometricians, scale developers, and practitioners, numerous programs are provided and annotated so that you can easily modify them for your applications.

Assessment has played, and continues to play, an integral part in our work and educational settings. IRT models continue to be increasingly popular in many other ﬁelds, such as medical research, health sciences, quality-of-life research, and even marketing research. With the use of IRT models, you can not only improve scoring accuracy but also economize test administration by adaptively using only the discriminative items.

Interested in learning more? Check out our chapter previews available for free. Want to learn more about SAS Press? Explore our online bookstore and subscribe to our newsletter to get all the latest discounts, news, and more.

### Further resources

**SAS Blogs**:

New at SAS: Psychometric Testing by Charu Shankar

SAS author’s tip: Bayesian analysis of item response theory models

**SAS Communities**:

SAS Communities: Custom Task Tuesday: SAS Global Forum/PROC IRT Edition!

**SAS Global Forum Paper**:

Item Response Theory: What It Is and How You Can Use the IRTProcedure to Apply It by Xinming An and Yiu-Fai Yung

**SAS Documentation**:

The IRT Procedure

SAS/STAT 14.1 User Guide: The IRT Procedure

SAS/STAT 14.2 User Guide: Help Center

Understanding Item Response Theory with SAS was published on SAS Users.