ABSTRACT
In this chapter, the authors consider only situations where the one-to-one correspondence among task, work product, and observable holds. Accordingly, they present the terms "items" and "responses" from educational assessment, though the model applies to situations where this terminology does not apply. Item response theory (IRT) models employ continuous latent variables to model dichotomous or polytomous observables, as occur frequently in assessment and social and life science settings. The chapter provides conceptual aspects of several applications of IRT in assessment that are strongly aligned with Bayesian perspectives. In IRT the metric of each latent variable is often specified by fixing the mean and the variance of the latent variable, and the orientation of each latent variable is often specified by constraining the discriminations to be positive. Treatments and overviews of IRT from conventional perspectives can be found in De Ayala, Embretson and Reise, Hambleton and Swaminathan, Lord, McDonald, and van der Linden and Hambleton.
