ABSTRACT
This chapter discusses methods for evaluating the fit of individual response patterns to an item response theory (IRT) model. These methods are based on so-called person-fit tests, which can be used to identify respondents that do not fit the IRT model, for instance, because their ability changes during test taking or because their item responses are not locally independent. The chapter starts with giving an overview of person-fit tests for dichotomously scored items, then tests for polytomously scored items are discussed, and finally, some examples pertaining to the application of the test statistics are given.
The sections on dichotomously scored items include a description of nonparametric tests, such as a uniformly most powerful test for the Rasch model, and parametric tests that can be computed both in a frequentist and in a Bayesian framework.
The sections on polytomously scored items focus on Lagrange-multiplier test statistics. It is shown that these statistics are very flexible because they can be focused on various model violations.
The sections with examples give an impression of the detection rates of model violations.
