Some Posterior Standard Deviations in Item Response Theory

Abstract

The procedures required to obtain the approximate posterior standard deviations of the parameters in the three commonly used item response models for dichotomous items are described and used to generate values for some common situations. The results were compared with those obtained from maximum likelihood estimation. It is shown that the use of priors may reduce the instability of estimates of the item parameters, assuming the choice of priors is reasonable. The sample size required for acceptable accuracy for the purposes of practical applications of item response theory may be inferred from tables or computer programs. It is suggested that the careful selection of priors be exercised to obtain the required precision when three-parameter models are applied in these situations.