A Bayesian Robust IRT Outlier Detection Model

In the context of psychometric practice, the parameter estimates of a standard item-response theory (IRT) model may become biased when item-response data, of persons’ individual responses to test items, contain outliers relative to the model. Further, 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 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 in the presence of outliers. Hence, under this IRT model, it is unnecessary to remove outliers from the data analysis. The Bayesian IRT model is illustrated through the analysis of two real-world, and two simulated datasets involving dichotomous- and polytomous-response items. Additionally, the model is applied to a simulated skewed dichotomously scored assessment to more closely understand how the model performs under realistic testing conditions.