Direction-dependence analysis

Abstract

The concept of direction dependence has attracted growing attention due to its potential to help decide which of two competing linear regression models (X → Y or Y → X) is more likely to reflect the correct causal flow. Several tests have been proposed to evaluate hypotheses compatible with direction dependence. In this issue, Thoemmes (2015) reports results of an empirical evaluation of direction-dependence tests using real-world data sets with known causal ordering and concludes that the tests (known to perform excellent in simulation studies) perform poorly in the real-world setting. The present article aims at answering the question how this is possible. First, we review potential conceptual issues associated with Thoemmes’ (2015) approach. We argue that direction dependence is best conceptualized as a confirmatory approach to test focused directional theories. Thoemmes’ (2015) evaluation is based on an exploratory use of direction dependence. It implicitly follows the tradition of causal search algorithms. Second, we discuss potential statistical issues associated with Thoemmes’ (2015) selection schemes used to decide whether a variable pair is suitable for direction-dependence analysis. Based on these issues, new tests of direction dependence as well as new guidelines for confirmatory direction-dependence analysis are proposed. An empirical example is given to illustrate the application of these guidelines.