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Applications and Extensions of MCMC in IRT: Multiple Item Types, Missing Data, and Rated Responses

Author

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  • Richard J. Patz
  • Brian W. Junker

Abstract

Patz and Junker (1999) describe a general Markov chain Monte Carlo (MCMC) strategy, based on Metropolis-Hastings sampling, for Bayesian inference in complex item response theory (IRT) settings. They demonstrate the basic methodology using the two-parameter logistic (2PL) model. In this paper we extend their basic MCMC methodology to address issues such as non-response, designed missingness, multiple raters, guessing behavior and partial credit (polytomous) test items. We apply the basic MCMC methodology to two examples from the National Assessment of Educational Progress 1992 Trial State Assessment in Reading: (a) a multiple item format (2PL, 3PL, and generalized partial credit) subtest with missing response data; and (b) a sequence of rated, dichotomous short-response items, using a new IRT model called the generalized linear logistic test model (GLLTM).

Suggested Citation

  • Richard J. Patz & Brian W. Junker, 1999. "Applications and Extensions of MCMC in IRT: Multiple Item Types, Missing Data, and Rated Responses," Journal of Educational and Behavioral Statistics, , vol. 24(4), pages 342-366, December.
    • Handle: RePEc:sae:jedbes:v:24:y:1999:i:4:p:342-366
    DOI: 10.3102/10769986024004342
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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. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    3. Steven Andrew Culpepper & James Joseph Balamuta, 2017. "A Hierarchical Model for Accuracy and Choice on Standardized Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 820-845, September.
    4. Santos, Vera Lúcia F. & Moura, Fernando A.S. & Andrade, Dalton F. & Gonçalves, Kelly C.M., 2016. "Multidimensional and longitudinal item response models for non-ignorable data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 91-110.
    5. Michela Battauz, 2019. "On Wald tests for differential item functioning detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 103-118, March.
    6. Yang Liu & Jan Hannig, 2016. "Generalized Fiducial Inference for Binary Logistic Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 290-324, June.
    7. 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.

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