Updating Statistical Measures of Causal Strength

Hrishikesh Vinod


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 .


generalized correlation, Kernel regression, unanimity index, stochastic dominance, fuzzy inequality

Full Text:



David E Allen and Vince Hooper. Generalized correlation measures of causality and forecasts of the VIX using non-linear models. Sustainability, 10((8): 2695):1–15, 2018. doi: 10.3390/su10082695. URL https://www.mdpi.com/2071-1050/10/8/2695.

Nancy Cartwright. Two theorems on invariance and causality. Philosophy of Science, 70(1):203–224, 2003.

Nancy Cartwright. Are RCTs the gold standard? BioSocieties, 2(1):1–20, 2007.

Ellery Eells. Probabilistic causal interaction. Philosophy of Science, 53(1):52–64, 1986.

Christopher Hitchcock. Probabilistic causation. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, fall 2018 edition, 2018. URL


Tjalling C Koopmans. When is an equation system complete for statistical purposes. Technical report, Yale University, 1950. URL http://cowles.econ.yale.edu/P/cm/m10/m10-17.pdf.

Q Li and J S Racine. Nonparametric Econometrics. Princeton University Press, 2007.

Bradford C. Lister and Andres Garcia. Climate-driven declines in arthropod abundance restructure a rainforest food web. Proceedings of the National Academy of Sciences, Oct. 15:1–10, 2018. URL http://www.pnas.org/content/early/2018/10/09/1722477115.full.pdf.

Igor Mandel. Troublesome dependency modeling: Causality, inference, statistical learning. SSRN eLibrary, 2017. URL https://ssrn.com/abstract=2984045.

Marcel Mlynczak and Hubert Krysztofiak. Cardiorespiratory temporal causal links and the differences by sport or lack thereof. Frontiers in Physiology, 10 (45):1–14, 2019. doi: 10.3389/fphys.2019.00045.

Robert Northcott. Pearson’s wrong turning: Against statistical measures of causal efficacy. Philosophy of Science, 72(5):900–912, 2005.

Judea Pearl. An introduction to causal inference. The International Journal of Biostatistics, pages 1–59, 2010. URL http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2836213/.

Joseph Lee Rodgers and W. Alan Nicewander. Thirteen ways to look at the correlation coefficient. The American Statistician, 42(1):59–66, 1988.

Wesley C. Salmon. An “at-at” theory of causal influence. Philosophy of Science, June, 44(2):215–224, 1977. URL ttp://www.unige.ch/lettres/baumgartner/docs/kausa/protect/salmon.Kenneth

M. Sayre. Statistical models of causal relations. Philosophy of Science, 44(2):203–214, 1977.

Elliott Sober. Apportioning causal responsibility. Journal of Philosophy, 85(6):303 – 318, 1988. URL https://www.jstor.org/stable/2026721.

Patrick Suppes. A probabilistic theory of causality. Amsterdam: North-Holland, 1970.

H. D. Vinod. Causal paths and exogeneity tests in generalCorr package for air pollution and monetary policy, 2017a. URL https://cloud.r- project.org/web/packages/generalCorr/vignettes/generalCorr-A vignette accompanying the package “generalCorr” of R.

Hrishikesh D Vinod. Matrix algebra topics in statistics and economics using R. In M. B. Rao and C. R. Rao, editors, Handbook of Statistics: Computational Statistics with R, volume 34, chapter 4, pages 143–176. North Holland, Elsevier Science, New York, 2014.

Hrishikesh D. Vinod. Generalized correlation and kernel causality with applications in development economics. Communications in Statistics - Simulation and Computation, 46(6):4513–4534, 2017b. URL https://doi.org/10.1080/03610918.2015.1122048. posted online: 29 Dec 2015.

DOI: http://dx.doi.org/10.23756/sp.v8i1.497


  • There are currently no refbacks.

Copyright (c) 2020 Hrishikesh Vinod

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Science & Philosophy - Journal of Epistemology, Science and Philosophy. ISSN 2282-7757; eISSN  2282-7765.