On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models

In item response theory, the classical estimators of ability are highly sensitive to response disturbances and can return strongly biased estimates of the true underlying ability level. Robust methods were introduced to lessen the impact of such aberrant responses onto the estimation process. The computation of asymptotic (i.e., large sample) standard errors (ASE) for these robust estimators, however, has not been fully considered yet. This paper focuses on a broad class of robust ability estimators, defined by an appropriate selection of the weight function and the residual measure, for which the ASE is derived from the theory of estimating equations. The maximum likelihood (ML) and the robust estimators, together with their estimated ASE, are then compared through a simulation study. It is concluded that both the estimators and their ASE perform similarly in absence of response disturbances, while the robust estimator and its estimated ASE are less biased and outperform their ML counterparts in presence of response disturbances with large impact on the item response process.