Browsing by Author "Rolin, Jean-Marie"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Identification of Parametric Rasch-type Models
    (2013) San Martín, Ernesto; Rolin, Jean-Marie
  • No Thumbnail Available
    Item
    Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results
    (2013) San Martin, Ernesto; Rolin, Jean-Marie; Castro, Luis M.
    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.
  • No Thumbnail Available
    Item
    On the Bayesian Nonparametric Generalization of IRT-Type Models
    (2011) San Martín Gutiérrez, Ernesto Javier; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel
    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.