Abstract
We use a simple example to show that Pearson’s correlation matrix R can underestimate the true dependence between two variables when nonlinearities are present by as much as 83%, compared to the newer and easy to compute \(R^*\) in Vinod (Commun Statist Simul Comput 46(6):4513–4534, 2017, https://doi.org/10.1080/03610918.2015.1122048). We include intuitive expository discussion of nonparametric kernel methods needed by \(R^*\) with graphs and examples. We illustrate how partial correlation coefficients based on R can underestimate the nonlinear effect of a confounding variable, compared to those from the newer \(R^*\). This paper develops an entirely new generalization of Hotelling’s canonical correlations based on nonlinear nonparametric pairwise dependencies of \(R^*\). An example illustrates how traditional methods can underestimate the joint dependence by 266%.
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20 March 2022
A Correction to this paper has been published: https://doi.org/10.1007/s10614-022-10236-8
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Vinod, H.D. Generalized, Partial and Canonical Correlation Coefficients. Comput Econ 60, 1479–1506 (2022). https://doi.org/10.1007/s10614-021-10190-x
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DOI: https://doi.org/10.1007/s10614-021-10190-x