Asymptotic properties of the Bayes modal estimators of item parameters in item response theory

Haruhiko Ogasawara ()

Computational Statistics, 2013, vol. 28, issue 6, 2559-2583

Abstract: Asymptotic cumulants of the Bayes modal estimators of item parameters using marginal likelihood in item response theory are derived up to the fourth order with added higher-order asymptotic variances under possible model misspecification. Among them, only the first asymptotic cumulant and the higher-order asymptotic variance for an estimator are different from those by maximum likelihood. Corresponding results for studentized Bayes estimators and asymptotically bias-corrected ones are also obtained. It was found that all the asymptotic cumulants of the bias-corrected Bayes estimator up to the fourth order and the higher-order asymptotic variance are identical to those by maximum likelihood with bias correction. Numerical illustrations are given with simulations in the case when the 2-parameter logistic model holds. In the numerical illustrations, the maximum likelihood and Bayes estimators are used, where the same independent log-normal priors are employed for discriminant parameters and the hierarchical model is adopted for the prior of difficulty parameters. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Asymptotic cumulants; Higher-order asymptotic variances; Marginal maximum likelihood; Bayes modal; Logistic models; Mean square errors (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:28:y:2013:i:6:p:2559-2583

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DOI: 10.1007/s00180-013-0418-5

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