## Item Response Models

Item response theory is a general term for a family of models, the item response or IRT models that share some fundamental ideas. These ideas are that IRT models persons’ responses on individual items. The response of a person on a test item is conceived of as a function of person characteristics and item characteristics. The response of a person (i.e., the performance of an examinee) is assumed to depend upon one or more factors called (latent) traits or abilities. Each item of a set of items is assumed to measure the underlying trait or traits. An example of a simple IRT model is that a person’s performance on an item depends only on one underlying trait, and that the relationship between persons’ performance on an item and the trait underlying item performance can be described by a monotonically increasing function. The latter function is commonly called

item trace line,

item characteristic function

(ICF), or

item characteristic curve

(ICC). It speciﬁes how the probability of a correct response to an item increases as the level of the trait increases. In contrast to classical test theory and generalizability theory discussed earlier, IRT consists of a class of mathematical models for which estimation procedures exist for model parameters (i.e., person and item parameters) and other statistical procedures for investigating to what extent the model at hand ﬁts the data or persons’ responses to a set of items.