A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

A framework is described for exploiting auxiliary information about test items within item response theory models to enhance parameter estimates. The method also provides diagnostic information about items' operating characteristics. An empirical Bayesian estimation of Rasch item difficulty is used to illustrate the principles involved. (TJH)

Standard procedures for estimating item parameters in Item Response Theory models make no use of auxiliary information about test items, such as their format or content, or the skills they require for solution. This paper describes a framework for exploiting this information, thereby enhancing the precision and stability of item parameter…