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Bayesian Factor Analysis for Multilevel Binary Observations

Published online by Cambridge University Press:  01 January 2025

Asim Ansari  and
Kamel Jedidi
Asim Ansari*
Affiliation:
Columbia University
Kamel Jedidi
Affiliation:
Columbia University
*
Requests for reprints should be sent to Asim Ansaxi, 517 Uris Hall, Columbia University, 3022 Broadway, New York, NY, 10027. E-mail: [email protected]
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Abstract

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics.

Keywords

MCMC methodsbinary datamultilevel factor analysisGibbs samplingMetropolis-Hastings
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 4 , December 2000 , pp. 475 - 496
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The authors thank Ian Westbury, University of Illinois at Urbana Champaign for kindly providing the SIMS data for the application.

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