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On the Bayesian Nonparametric Generalization of IRT-Type Models

Published online by Cambridge University Press:  01 January 2025

Ernesto San Martín ,
Alejandro Jara ,
Jean-Marie Rolin  and
Michel Mouchart
Ernesto San Martín*
Affiliation:
Pontificia Universidad Católica de Chile
Alejandro Jara
Affiliation:
Pontificia Universidad Católica de Chile
Jean-Marie Rolin
Affiliation:
Université catholique de Louvain
Michel Mouchart
Affiliation:
Université catholique de Louvain
*
Requests for reprints should be sent to Ernesto San Martín, Department of Statistics & Measurement Center MIDE UC, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile. E-mail: esanmart@mat.puc.cl
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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

Information

Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 3 , July 2011 , pp. 385 - 409
Copyright
Copyright © 2011 The Psychometric Society

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Footnotes

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.

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