Reversed Thresholds in Partial Credit Models : A Reason for Collapsing Categories?

Abstract

When questionnaire data with an ordered polytomous response format are analyzed in the framework of item response theory using the partial credit model or the generalized partial credit model, reversed thresholds may occur. This led to the discussion of whether reversed thresholds violate model assumptions and indicate disordering of the response categories. Adams, Wu, and Wilson showed that reversed thresholds are merely a consequence of low frequencies in the categories concerned and that they do not affect the order of the rating scale. This article applies an empirical approach to elucidate the topic of reversed thresholds using data from the Revised NEO Personality Inventory as well as a simulation study. It is shown that categories differentiate between participants with different trait levels despite reversed thresholds and that category disordering can be analyzed independently of the ordering of the thresholds. Furthermore, we show that reversed thresholds often only occur in subgroups of participants. Thus, researchers should think more carefully about collapsing categories due to reversed thresholds.