Using Item Scores and Distractors in Person-Fit Assessment

In order to detect a wide range of aberrant behaviors, it can be useful to incorporate information beyond the dichotomous item scores. In this paper, we extend the $l_z$ and $l_z^{\ast }$ person-fit statistics so that unusual behavior in item scores and unusual behavior in item distractors can be used as indicators of aberrance. Through detailed simulations, we show that the new statistics are more powerful than existing statistics in detecting several types of aberrant behavior, and that they are able to control the Type I error rate in instances where the model does not exactly fit the data. A real data example is also provided to demonstrate the utility of the new statistics in an operational setting.