Identification in sifted mixture models with an application to item response models
(2000) , 46 pages
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- Abstract
- After introducing, at the level of model specication, three basic distinctions {the rst one between structurals and incidentals, the second one between incidentals and the third one between observables and unobservables{ this paper establishes that, in the presence of incidentals, a sifting condition ensures that the identication of a conditional model corresponding to a given sample size may be obtained from the identication of the corresponding individual conditional submodels. Using these results, sucient conditions are given for the identicafition of the statistical model obtained after integrating out the unobservables; the problem of minimal predictive sucency is also analysed.The second part of this paper illustrates the use of the main results in the class of IRT models; this class is specied by introducing a double sifting structure in the conditional model generating the observables conditionally on the unobservables, and an hypothesis of exchangeability in the marginal model generating the unobservables. Under such a specication, the identiability of the statistical model in IRT models for psychomotor assesment as well as for a Rasch model are analysed.
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Citations
Mouchart, M., & San Martin, E. (2000). Identification in sifted mixture models with an application to item response models (STAT Discussion Papers 0001). https://hdl.handle.net/2078.5/28679