MCMC estimation of multidimensional IRT models

Anton Beguin, Cornelis A.W. Glas

Research output: Book/ReportReportProfessional

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Abstract

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization to a model with multidimensional ability parameters are discussed. The procedure is a generalization of a procedure by J. Albert (1992) for estimating the two-parameter normal ogive model. The procedure will support multiple samples from multiple populations and restrictions on the factor matrix for testing specific hypotheses about the ability structure. The technique is illustrated using simulated and real data. A Markov chain Monte Carlo (MCMC) procedure is used to sample the posterior distributions of interest and needed chains are constructed using the Gibbs sampler (A. Gelfand and A. Smith, 1990).
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty Educational Science and Technology
Publication statusPublished - 1998

Publication series

NameOMD Reseach Report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.98-14

Fingerprint

Multidimensional Model
Markov Chain Monte Carlo
Gibbs Sampler
Posterior distribution
Two Parameters
Model
Restriction
Testing
Estimate

Keywords

  • Simulation
  • Estimation (Mathematics)
  • Item Response Theory
  • Bayesian Statistics
  • IR-103766
  • Markov Processes
  • Monte Carlo Methods
  • METIS-136530
  • Ability

Cite this

Beguin, A., & Glas, C. A. W. (1998). MCMC estimation of multidimensional IRT models. (OMD Reseach Report; No. 98-14). Enschede: University of Twente, Faculty Educational Science and Technology.
Beguin, Anton ; Glas, Cornelis A.W. / MCMC estimation of multidimensional IRT models. Enschede : University of Twente, Faculty Educational Science and Technology, 1998. (OMD Reseach Report; 98-14).
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Beguin, A & Glas, CAW 1998, MCMC estimation of multidimensional IRT models. OMD Reseach Report, no. 98-14, University of Twente, Faculty Educational Science and Technology, Enschede.

MCMC estimation of multidimensional IRT models. / Beguin, Anton; Glas, Cornelis A.W.

Enschede : University of Twente, Faculty Educational Science and Technology, 1998. (OMD Reseach Report; No. 98-14).

Research output: Book/ReportReportProfessional

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N2 - A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization to a model with multidimensional ability parameters are discussed. The procedure is a generalization of a procedure by J. Albert (1992) for estimating the two-parameter normal ogive model. The procedure will support multiple samples from multiple populations and restrictions on the factor matrix for testing specific hypotheses about the ability structure. The technique is illustrated using simulated and real data. A Markov chain Monte Carlo (MCMC) procedure is used to sample the posterior distributions of interest and needed chains are constructed using the Gibbs sampler (A. Gelfand and A. Smith, 1990).

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KW - Item Response Theory

KW - Bayesian Statistics

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KW - Markov Processes

KW - Monte Carlo Methods

KW - METIS-136530

KW - Ability

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Beguin A, Glas CAW. MCMC estimation of multidimensional IRT models. Enschede: University of Twente, Faculty Educational Science and Technology, 1998. (OMD Reseach Report; 98-14).