Updating Statistical Measures of Causal Strength

Abstract

We address Northcott’s (2005) criticism of Pearson’s correlation coefficient ‘r’ in measuring causal strength by replacing Pearson’s linear regressions by nonparametric nonlinear kernel regressions. Although new proof shows that Suppes’ intuitive causality condition is neither necessary nor sufficient, we resurrect Suppes’ probabilistic causality theory by using nonlinear tools. We use asymmetric generalized partial correlation coefficients from Vinod [2014] as our third criterion (denoted as Cr3) in addition to two more criteria (denoted Cr1 and Cr2). We aggregate the three criteria into one unanimity index, UI in [-100; 100], quantifying causal strengths associated with causal paths: Xi -> Xj , Xj -> Xi, and Xi Xj .

Keywords

• generalized correlation, kernel regression, unanimity index, stochastic dominance, fuzzy inequality