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

作者：Ogasawara Haruhiko^*

来源：Computational Statistics, 2013, 28(6): 2559-2583.

DOI：10.1007/s00180-013-0418-5

• Asymptotic cumulants
• Higher-order asymptotic variances
• Marginal maximum likelihood
• Bayes modal
• Logistic models
• Mean square errors

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.

• 出版日期2013-12