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Activity Number:
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360
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #304109 |
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Title:
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On the Analysis of Bayesian Semiparametric IRT-Type Models
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Author(s):
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Alejandro Jara*+ and Ernesto San Martin
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Companies:
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Universidad de Concepción and Department of Statistics and Measurement Center MIDE UC Pontificia Universidad Católica de Chile
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Address:
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Barrion Universitario S/N, Concepción, 4030000, Chile
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Keywords:
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Bayesian nonparametrics ; Bayesian identification ; Rasch model ; Generalized Linear Mixed Models ; Dirichlet processes ; Polya trees
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Abstract:
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Motivated by the characteristics of two educational data sets, we study the Bayesian identification and consistency of semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We establish sufficient conditions for the identification and consistency in the Bernoulli and Poisson versions of the model. For unbounded count (resp. binary) responses, the parameters are identified when a finite (resp. infinite) number of probes are available and are consistently estimated when the number of subjects tends (resp. subjects and probes tend) to infinite. The implications of the sufficient identification restrictions are evaluated using simulated data.
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