Robust Estimation of Latent Ability in Item Response Models

Abstract

Because of response disturbances such as guessing, cheating, or carelessness, item response models often can only approximate the “true” individual response probabilities. As a consequence, maximum-likelihood estimates of ability will be biased. Typically, the nature and extent to which response disturbances are present is unknown, and, therefore, accounting for them by altering the model is not possible. Even if the nature of the response disturbances were known, accounting for them by increasing model complexity could easily lead to sample size requirements for estimation purpose that would be difficult to achieve. An approach based on weighting the contributions of the item responses to the log likelihood function has been suggested by Mislevy and Bock. This estimation approach has been shown to effectively reduce bias of ability estimates in the presence of response disturbances. However, this approach is prone to produce infinite ability estimates for unexpected response patterns in which correct answers are sparse. An alternative robust estimator of ability is suggested that does not appear to produce infinite estimates. Limited simulation studies show that the two estimators are equivalent when evaluated in terms of mean squared error.