Exploiting auxiliary information about items in the estimation of Rasch item difficulty parameters

Abstract

Standard procedures for estimating the item parameters in IRT models make no use of auxiliary information about test items, such as their format, their 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 estimates and providing diagnostic information about items’ operating characteristics. The principles are illustrated in a context for which a relatively simple approximation is available: empirical Bayesian estimation of Rasch item difficulty parameters. Index terms: Bayesian estimation, Collateral information, Empirical Bayesian estimation, Exchangeability, Hierarchical models, Item response theory, Linear logistic test model, Rasch model item parameters.