title: Identification of the 1PL model with guessing parameter: parametric and semi-parametric results.
abstract: 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.
authors.affiliation: Faculty of Mathematics, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile, esanmart@mat.puc.cl.
authors.forename: Ernesto
authors.initials: E
authors.lastname: San Martín
authors.forename: Jean-Marie
authors.initials: JM
authors.lastname: Rolin
authors.forename: Luis M
authors.initials: LM
authors.lastname: Castro
mesh_terms: D006801:Humans; D015233:Models, Statistical; D011594:Psychometrics / Q000379:methods*
references.citation: Psychol Methods. 2006 Sep;11(3):253-70
references.pmid: 16953704
references.citation: J Appl Meas. 2009;10(2):196-207
references.pmid: 19564699
references.citation: Br J Math Stat Psychol. 2009 Feb;62(Pt 1):1-20
references.pmid: 17903345
references.citation: Psychometrika. 2006 Jun;71(2):281
references.pmid: 28197961
references.citation: Stat Med. 2000 Sep 15-30;19(17-18):2279-94
references.pmid: 10960853