Psychometrika

, Volume 76, Issue 3, pp 385–409

On the Bayesian Nonparametric Generalization of IRT-Type Models

Authors

    • Department of Statistics & Measurement Center MIDE UCPontificia Universidad Católica de Chile
  • Alejandro Jara
    • Department of StatisticsPontificia Universidad Católica de Chile
  • Jean-Marie Rolin
    • Institut de Statistique, Biostatistique et Sciences ActuariellesUniversité catholique de Louvain
  • Michel Mouchart
    • Institut de Statistique, Biostatistique et Sciences ActuariellesUniversité catholique de Louvain
Article

DOI: 10.1007/s11336-011-9213-9

Cite this article as:
San Martín, E., Jara, A., Rolin, J. et al. Psychometrika (2011) 76: 385. doi:10.1007/s11336-011-9213-9

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.

Keywords

Bayesian identificationBayesian consistencyRasch modelRasch Poisson counts modelDirichlet processesPólya tree processes

Copyright information

© The Psychometric Society 2011