Robust Estimation of Ability in Multidimensional Item Response Theory

Aberrant responses (e.g., careless responses, miskeyed items, etc.) often contaminate psychological assessments and surveys. Previous robust estimators for unidimensional dichotomous item response theory (IRT) models have demonstrated more accurate latent trait estimates with data containing response disturbances. However, for multidimensional dichotomous items, a robust estimator for estimating latent traits does not exist. We propose a robust estimator for the multidimensional IRT (MIRT) model. Two weighting mechanisms for downweighting ''suspicious" responses are considered: the Huber and the bisquare weight functions. Simulations reveal the estimator reduces bias and MSE for different test lengths, dimensions, and types of response disturbances. The robust estimation is applied to real, aberrant data from a high school science aptitude test, demonstrating the improved accuracy of latent trait scores in the presence of response disturbances. Overall, the reduction in bias suggests that the robust estimator for the MIRT is effective in counteracting the harmful effects of response disturbances and providing more accurate scores on psychological assessments.