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Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling

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  • James H. Albert

Abstract

The problem of estimating item parameters from a two-parameter normal ogive model is considered. Gibbs sampling (Gelfand & Smith, 1990) is used to simulate draws from the joint posterior distribution of the ability and item parameters. This method gives marginal posterior density estimates for any parameter of interest; these density estimates can be used to judge the accuracy of normal approximations based on maximum likelihood estimates. This simulation technique is illustrated using data from a mathematics placement exam.

Suggested Citation

  • James H. Albert, 1992. "Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 17(3), pages 251-269, September.
    • Handle: RePEc:sae:jedbes:v:17:y:1992:i:3:p:251-269
    DOI: 10.3102/10769986017003251
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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. Eijffinger, Sylvester & Mahieu, Ronald & Raes, Louis, 2018. "Inferring hawks and doves from voting records," European Journal of Political Economy, Elsevier, vol. 51(C), pages 107-120.
    3. 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.
    4. de Jong, M.G., 2006. "Response bias in international marketing research," Other publications TiSEM 5d4031be-97b5-4db3-962b-2, Tilburg University, School of Economics and Management.
    5. Spruk, Rok & Kovac, Mitja, 2019. "Replicating and extending Martin-Quinn scores," International Review of Law and Economics, Elsevier, vol. 60(C).
    6. 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.
    7. Azevedo, Caio L.N. & Andrade, Dalton F. & Fox, Jean-Paul, 2012. "A Bayesian generalized multiple group IRT model with model-fit assessment tools," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4399-4412.
    8. Vinícius Diniz Mayrink & Flávio Bambirra Gonçalves, 2017. "A Bayesian hidden Markov mixture model to detect overexpressed chromosome regions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 387-412, February.
    9. Steven Andrew Culpepper, 2019. "An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 921-940, December.
    10. Steven Andrew Culpepper, 2019. "Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 333-357, June.
    11. Maria Bolsinova & Jesper Tijmstra, 2019. "Modeling Differences Between Response Times of Correct and Incorrect Responses," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1018-1046, December.

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