Item response theory is a test theory, in contrast to classical test theory, that focuses on the individual items of an exam in order to analyze test accuracy amd reliability, and evaluate examinee ability levels. Developed in the mid 20th century, item response theory, or IRT, is consider superior in a number of ways to many other test theory approaches. Provided here is an overview of basic IRT models using the a test theory approach, as well as the development of IRT models in the context of generalized linear models. Binary, correct/incorrect, response and polytomous, or multiple, response items are considered for item response theory models developed here in the context of generalized linear models. Applications of IRT are also explored using the statistical software R.

Date of publication

Spring 5-7-2012

Document Type




Persistent identifier


Included in

Mathematics Commons