On the Bayesian Nonparametric Generalization of IRT-Type Models
No Thumbnail Available
Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general distribution generating the abilities, even for a finite number of probes. For the semiparametric Rasch model, only a finite number of properties of the general abilities' distribution can be identified by a finite number of items, which are completely characterized. The full identification of the semiparametric Rasch model can be only achieved when an infinite number of items is available. The results are illustrated using simulated data.
Description
Keywords
Bayesian identification, Bayesian consistency, Rasch model, Rasch Poisson counts model, Dirichlet processes, Pólya tree processes