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Priors in Bayesian Estimation under the Rasch Model.

Seock-Ho Kim1, Allan S Cohen, Minho Kwak

  • 1Seock-Ho Kim, Department of Educational Psychology, The University of Georgia, 325 Aderhold Hall, Athens, GA 30602-7143, USA, shkim@uga.edu.

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Summary
This summary is machine-generated.

Bayesian estimation using Gibbs sampling under the Rasch model closely matches maximum likelihood methods for item parameters. However, priors in Bayesian estimation can cause a shrinkage effect on ability estimates.

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Educational measurement

Background:

  • The Rasch model is a widely used item response theory model.
  • Bayesian estimation offers an alternative to traditional frequentist methods.
  • Understanding the impact of prior distributions is crucial for accurate parameter estimation.

Purpose of the Study:

  • To review priors used in Bayesian estimation for the Rasch model.
  • To compare Bayesian estimation (Gibbs sampling) with maximum likelihood methods.
  • To investigate the shrinkage effect of priors on parameter estimates.

Main Methods:

  • Review of hierarchical prior distributions in Bayesian estimation.
  • Comparison of Gibbs sampling with conditional, marginal, and joint maximum likelihood estimation.
  • Application to Knox Cube Test data and a mathematics test dataset.
  • Utilized OpenBUGS software for Gibbs sampling implementation.

Main Results:

  • Bayesian and maximum likelihood methods produced similar item parameter estimates.
  • A notable shrinkage effect was observed in ability estimates from Gibbs sampling.
  • The study analyzed item response data from 765 examinees on a 14-item mathematics test.

Conclusions:

  • Gibbs sampling is a viable method for Rasch model analysis, comparable to maximum likelihood for item parameters.
  • The choice of priors in Bayesian estimation can influence ability parameter estimates due to shrinkage.
  • Further research may explore optimal prior selection for specific applications.