Analyzing latent variables is becoming more and more important in several fields, such as clinical research, psychology, educational sciences, ecology, and epidemiology. The item response theory allows analyzing latent variables measured by questionnaires of items with binary or ordinal...

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...