A General Approach for Assessing Person Fit and Person Reliability in Typical-Response Measurement

Abstract

In constant-θ IRT models, person unreliability is regarded as a source of person misfit. In Variable-θ IRT models, on the other hand, it is regarded as a relevant individual characteristic, which is modeled as an additional person parameter. As in any IRT application, person fit must be assessed when a variable-θ model is fitted to real data. This assessment aims to detect inconsistent response patterns once person unreliability has been taken into account. The present paper makes a general proposal for assessing person fit based on variable-θ models that are intended to be used with personality and attitude measures. For the three types of variable-θ IRT models developed to date—binary, graded, and (approximately) continuous response models—(a) graphical procedures, (b) global person-fit indices, and (c) residual indices at the item level are proposed and discussed. A multistage approach for using the indices and procedures is also proposed and illustrated using an empirical example.