A Bayesian Robust IRT Outlier-Detection Model

Abstract

In psychometric practice, the parameter estimates of a standard item-response theory (IRT) model can become biased when item-response data, of persons’ individual responses to test items, contain outliers relative to the model. Also, the manual removal of outliers can be a time-consuming and difficult task. Besides, removing outliers leads to data information loss in parameter estimation. To address these concerns, a Bayesian IRT model that includes person and latent item-response outlier parameters, in addition to person ability and item parameters, is proposed and illustrated, and is defined by item characteristic curves (ICCs) that are each specified by a robust, Student’s t-distribution function. The outlier parameters and the robust ICCs enable the model to automatically identify item-response outliers, and to make estimates of the person ability and item parameters more robust to outliers. Hence, under this IRT model, it is unnecessary to remove outliers from the data analysis. Our IRT model is illustrated through the analysis of two data sets, involving dichotomous- and polytomous-response items, respectively.