Item Response Theory

Abstract

Item response theory (IRT) is a psychometric modeling framework for analyzing categorical data from questionnaires, tests, and other instruments that aim to measure underlying latent traits. Simply speaking, these models estimate a parameter for each item, as well as a parameter for each person. Depending on how many latent traits are involved, a core distinction in IRT is unidimensional vs. multidimensional IRT models. Hence, dimensionality assessment is important before fitting an IRT model, as elaborated in the first section. Subsequently, the focus is on various classical unidimensional models for dichotomous as well as polytomous input data. Afterward, three sections cover various special topics in IRT: item/test information, sample size determination, and differential item functioning, where differences in the item parameters are examined across person subgroups. Some modern IRT flavors are presented in final three sections on multidimensional IRT, longitudinal IRT, and Bayesian IRT.