Unidimensional IRT Models
R. Darrell Bock, Robert D. Gibbons · 2021
Item response theory (IRT) deals with the statistical analysis of data in which responses of each of a number of respondents to each of a number of items or trials are assigned to defined mutually exclusive categories. If exogenous quantitative measurements of the respondents are available, IRT can be further extended to include estimation of relationships between the latent variables and external variables. All of these applications are amenable to a likelihood-based approach in estimation and hypothesis testing. This chapter presents a general formulation of IRT that supports these applications. It also presents the best-known item response models specifying the probability of response in each category as a function of parameters attributed to items and of a latent value attributed to the respondent. Their roles in item parameter estimation and respondent scoring are discussed.