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A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Michael C. Edwards
Michael C. Edwards*
Affiliation:
The Ohio State University
*
Requests for reprints should be sent to Michael C. Edwards, 1827 Neil Avenue, Columbus, OH 43210, USA. E-mail: edwards.134@osu.edu
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Abstract

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show that these methods can be implemented in a flexible way which requires minimal technical sophistication on the part of the end user. After providing an overview of item factor analysis and MCMC, results from several examples (simulated and real) will be discussed. The bulk of these examples focus on models that are problematic for current “gold-standard” estimators. The results demonstrate that it is possible to obtain accurate parameter estimates using MCMC in a relatively user-friendly package.

Keywords

item factor analysismultidimensional item response theoryMarkov chain Monte Carlo
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 3 , September 2010 , pp. 474 - 497
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

I would like to thank Li Cai, David Thissen, and R.J. Wirth for comments on earlier versions of this draft. I would like to thank Roger Millsap and the reviewers for their guidance on revisions. The resulting paper is better for all of your efforts. Any remaining faults are my own.

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