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A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models

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  • Richard J. Patz
  • Brian W. Junker

Abstract

This paper demonstrates Markov chain Monte Carlo (MCMC) techniques that are particularly well-suited to complex models with item response theory (IRT) assumptions. MCMC may be thought of as a successor to the standard practice of first calibrating the items using E-M methods and then taking the item parameters to be known and fixed at their calibrated values when proceeding with inference regarding the latent trait, in contrast to this two-stage E-M approach, MCMC methods treat item and subject parameters at the same time; this allows us to incorporate standard errors of item estimates into trait inferences, and vice versa. We develop a MCMC methodology, based on Metropolis-Hastings sampling, that can be routinely implemented to fit novel IRT models, and we compare the algorithmic features of the Metropolis- Hastings approach to other approaches based on Gibbs sampling. For concreteness we illustrate the methodology using the familiar two-parameter logistic (2PL) IRT model; more complex models are treated in a subsequent paper (Patz & Junker, in press).

Suggested Citation

  • Richard J. Patz & Brian W. Junker, 1999. "A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models," Journal of Educational and Behavioral Statistics, , vol. 24(2), pages 146-178, June.
    • Handle: RePEc:sae:jedbes:v:24:y:1999:i:2:p:146-178
    DOI: 10.3102/10769986024002146
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    Citations

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    Cited by:

    1. Steven Andrew Culpepper, 2016. "Revisiting the 4-Parameter Item Response Model: Bayesian Estimation and Application," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1142-1163, December.
    2. Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    3. Gonçalves, F.B. & Gamerman, D. & Soares, T.M., 2013. "Simultaneous multifactor DIF analysis and detection in Item Response Theory," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 144-160.
    4. Zhehan Jiang & Jonathan Templin, 2019. "Gibbs Samplers for Logistic Item Response Models via the Pólya–Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 358-374, June.
    5. Alexander Weissman, 2013. "Optimizing information using the EM algorithm in item response theory," Annals of Operations Research, Springer, vol. 206(1), pages 627-646, July.
    6. Federico Andreis & Pier Alda Ferrari, 2014. "Multidimensional item response theory models for dichotomous data in customer satisfaction evaluation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 2044-2055, September.
    7. Javier Revuelta, 2008. "The generalized Logit-Linear Item Response Model for Binary-Designed Items," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 385-405, September.
    8. Vitoratou, Silia & Ntzoufras, Ioannis & Moustaki, Irini, 2016. "Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions," LSE Research Online Documents on Economics 57685, London School of Economics and Political Science, LSE Library.

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