Asymptotic approximations to the distributions of the ability estimator and its transformations in item response theory are derived beyond the usual normal one when associated item parameters are given as in tailored testing. For the approximations, the asymptotic cumulants of the estimators up...

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...

Asymptotic expansions of the distributions of thirteen fit indexes used in covariance structure analysts in practice are obtained. The fit indexes include the usual log likelihood ratio statistic for a posited model and the functions of this statistic and the corresponding statistic of the...