On the Bayesian nonparametric generalization of IRT-type models
(2011) Psychometrika — (2011)
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- Authors
- Abstract
- 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 properties of the genral 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.
- Affiliations
Pontificia Universidad Católica de Chile Department of Statistics and Measurement Center MIDE UC Pontifica Universidad Católica de Chile Department of Statistics and Measurement Center MIDE UC
Citations
San Martin, E., Jara, A., Rolin, J.-M., & Mouchart, M. (2011). On the Bayesian nonparametric generalization of IRT-type models. Psychometrika. Published. https://doi.org/10.1007/s11336-011-9213-9 (Original work published 2011)