Modeling (in)congruence between dependent variables: The directional and nondirectional difference (DNDD) framework.

This paper proposes a new approach to modeling the antecedents of incongruence between two dependent variables.In this approach, incongruence is decomposed into two orthogonal components representing directional and non-directional difference (DNDD).Nondirectional difference is further divided into components representing shared and unique variability.We review previous approaches to modeling antecedents of difference, including the use of arithmetic, absolute and squared differences, as well as the approaches of Edwards (1995) and Cheung (2009).Based on two studies, we demonstrate the advantages of DNDD approach compared to other methods.In the first study, we use a Monte Carlo simulation to demonstrate the circumstances under which each type of difference arises, and we compare the insights revealed by each approach.In the second study, we provide an illustrative example of DNDD approach using a field dataset.In the discussion, we review the strengths and limitations of our approach and propose several practical applications.Our paper proposes two extensions to the basic DNDD approach, including modeling difference with a known target or "true" value, and using multilevel analysis to model non-directional difference with exchangeable ratings.