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

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dc.contributor.authorSan Martin, Ernesto
dc.contributor.authorRolin, Jean-Marie
dc.contributor.authorCastro, Luis M.
dc.date.accessioned2025-01-24T00:04:12Z
dc.date.available2025-01-24T00:04:12Z
dc.date.issued2013
dc.description.abstractIn 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.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s11336-013-9322-8
dc.identifier.eissn1860-0980
dc.identifier.issn0033-3123
dc.identifier.urihttps://doi.org/10.1007/s11336-013-9322-8
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/101796
dc.identifier.wosidWOS:000316344000009
dc.issue.numero2
dc.language.isoen
dc.pagina.final379
dc.pagina.inicio341
dc.revistaPsychometrika
dc.rightsacceso restringido
dc.subject2PL model
dc.subject3PL model
dc.subjectlocation-scale distributions
dc.subjectfixed effects
dc.subjectrandom effects
dc.subjectidentified parameter
dc.subjectparameters of interest
dc.subjectHilbert space
dc.subjectGibbs sampler
dc.subjectmeasurable separability
dc.titleIdentification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results
dc.typeartículo
dc.volumen78
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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