Asymptotic properties of the Bayes and pseudo Bayes estimators of ability in item response theory

Haruhiko Ogasawara

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 359-377

Abstract: Asymptotic cumulants of the Bayes and pseudo Bayes estimators of ability in item response theory are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. Typical estimators are treated as special cases of the (pseudo) Bayes estimator with the general weight. The asymptotic cumulants of the estimators after studentization are also derived. From the comparison of the mean square errors, the Bayes modal estimator with the standard normal prior is recommended for point estimation. For interval estimation, however, the maximum likelihood estimator is appropriate considering its small bias after studentization.

Keywords: IRT; Asymptotic cumulants; Bayes modal; Mean square error; Jeffreys prior; Bias; Higher-order asymptotic variance; Model misspecification (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:114:y:2013:i:c:p:359-377

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DOI: 10.1016/j.jmva.2012.08.013

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