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Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results

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San Martín, Ernesto [Faculty of Mathematics, Pontificia Universidad Católica de Chile, Santiago, Chile] Rolin, Jean-Marie [UCL] Castro, Luis M. [Department of Statistics, Universidad de Concepción, Barrio Universitario, Concepción, Chile]

In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution G generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution G is not identified. It is finally shown that, after introducing two identification restrictions, either on the distribution G or on the item parameters, the distribution G and the item parameters are identified provided an infinite quantity of items is available. © 2013 The Psychometric Society.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2013
Language Anglais
Journal information "Psychometrika" - Vol. 78, no. 2, p. 341-379 (2013)
Peer reviewed yes
Publisher Springer New York LLC
e-issn 1860-0980
issn 0033-3123
Publication status Publié
Affiliation UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
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Bibliographic reference San Martín, Ernesto ; Rolin, Jean-Marie ; Castro, Luis M.. Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results. In: Psychometrika, Vol. 78, no. 2, p. 341-379 (2013)
Permanent URL http://hdl.handle.net/2078.1/160515