Issues on item response theory modelling

Item response theory (IRT) models have been developed in order to study the individual responses to a set of items designed to measure latent abilities. IRT is a measurement theory that was first formalized in the sixties with the fundamental work of Lord and Novick (1968) and it has a predominant role in educational assessment. An IRT model describes the relationship between the observable examinee’s performance in the test, typically in the form of responses to categorical items, and the unobservable latent ability. Therefore, IRT models can be included in the more general framework of latent variable modelling . IRT is used in all phases of test administration, from the test calibration to the estimation of individual abilities, in which the estimated item parameters are used to characterize the examinees. After a brief presentation of the main assumptions of IRT models, several aspects related to specific problems in the context of test administration are treated. Many advances have been introduced over the last few years, that allow both to support more complex models and to improve the esti-mation algorithms. In particular, issues on multidimensionality incomplete design and the inclusion of prior information are discussed, referring both to current literature and to some contributions of the authors. Particular attention is given to the use of the Gibbs sam-pler, in the Markov Chain Monte Carlo (MCMC) methods, for the estimation of IRT models. Finally, an application related to one of this topics is presented in the context of educational assessment