Direction Dependence Modeling: a Diagnostic Framework to Test the Causal Direction of Effects in Linear Models

• Activity Number: 510 - Recent Development in the Assessment and Modeling of Asymmetric Dependence
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Wolfgang Wiedermann* and Xintong Li
• Companies: University of Missouri and University of Missouri
• Keywords: direction of dependence; causal inference; linear regression; non-normality

Abstract

In non-experimental data, at least three possible explanations exist for the relation of two variables x and y: 1) x causes y, 2) y causes x, or 3) a common cause u is present. The Pearson correlation and ordinary least square estimates do not adjudicate regarding the model which best represents the data-generating mechanism. However, statistical methods to identify which of the three explanatory models fits best would be a useful adjunct to the use of theory alone. The present paper introduces one such statistical method, Direction Dependence Analysis (DDA). DDA assesses the relative plausibility of the three explanatory models by making use of asymmetry properties of 1) observed variable distributions, 2) residual distributions of competing models, and 3) the independence of predictors and errors of competing models. Under non-normality of variables, these asymmetry properties can be used to uniquely identify each explanatory model. Significance tests compatible with DDA are discussed and an empirical example is given for illustrative purposes. Implementations of DDA in R and SPSS are available from www.ddaproject.com.