, Volume 76, Issue 3, pp 385-409
Date: 04 May 2011

On the Bayesian Nonparametric Generalization of IRT-Type Models

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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.

The first author was partially supported by CEPPE CIEO-01-CONICYT grant and PUENTE grant 08/2009 from the Pontificia Universidad Católica de Chile. The second author is supported by FONDECYT 3095003 and 11100144 grants. The last two authors were partially supported by the Interuniversity Attraction Poles Program P6/03 from the Belgian State Federal Office for Scientific, Technical and Cultural Affairs.