An item response theory model of matching test performance

In a matching test, a test taker is presented with a list of test items and a list of response alternatives and asked to match each response alternative with a test item. The response alternatives can be given as a response to at most one test item. As a result, the response a test taker offers to one test item depends on his or her responses to all of the other test items. This violates the “local independence” assumption underlying most existing item response theory (IRT) methods, such as the Rasch model. Here we develop a framework for extending dichotomous IRT models to account for test taking behavior on matching tests. This model separates an individual’s knowledge of the correct responses to the items of a matching test from his or her responses to those items. In addition to developing the matching framework, we derive a number of important properties, including its item response function and score distribution. Finally, we demonstrate through an empirical example that our matching test framework provides a good account of behavior on matching tests.