A short history of statistical association: From correlation to correspondence analysis to copulas

Carles M. Cuadras and Michael Greenacre

Journal of Multivariate Analysis, 2022, vol. 188, issue C

Abstract: We present in three parts different concepts of correlation and statistical association, with some historical notes, starting with Galton’s notion of correlation, subsequently improved by Pearson. Continuing in this first part, we discuss the correlation ratio, the intraclass correlation, multiple correlation, and redundancy analysis. Throughout we use the classic data set of Galton on the heights of parents and their children. In the second part we explain how these same data can be studied from a multivariate viewpoint, using canonical correlation analysis, Procrustes correlation and simple/multiple correspondence analysis. For correspondence analysis, we use the same data as categorized by Galton into intervals of heights for the parents and their children. In this part we also make an incursion into the continuous form of correspondence analysis. The third part is dedicated to bivariate distributions, where we give the main results of bivariate distributions with given marginals, commenting on the correlations of Spearman and Kendall. Seeing that a bivariate distribution can be generated using a copula, we fit Galton’s data to two copulas: the Gaussian copula and the copula which has the best fit.

Keywords: Canonical correlation; Copula; Correlation; Correlation ratio; Correspondence analysis; Intraclass correlation; Kendall’s tau; Multiple correlation; Procrustes correlation; Spearman’s rho (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104901

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