A measure of association (correlation) in nominal data (contingency tables), using determinants

Colignatus, Thomas (2007): A measure of association (correlation) in nominal data (contingency tables), using determinants. Unpublished.

Abstract

Nominal data currently lack a correlation coefficient, such as has already defined for real data. A measure is possible using the determinant, with the useful interpretation that the determinant gives the ratio between volumes. With M a m × n contingency table and n ≤ m the suggested measure is r = Sqrt[det[A'A]] with A = Normalized[M]. With M an n1 × n2 × ... × nk contingency matrix, we can construct a matrix of pairwise correlations R so that the overall correlation is f[R]. An option is to use f[R] = Sqrt[1 - det[R]]. However, for both nominal and cardinal data the advisable choice for such a function f is to take the maximal multiple correlation within R.

• Item Type: MPRA Paper
• Additional Information: The March 27 version corrects a formula and introduces the term NominalCorrelation. The April 10 version gives the correct f[R] = Sqrt[1 - det[R]] and explains this measure also for real data. But advisable is the maximal multiple correlation.
• Institution: Thomas Cool Consultancy & Econometrics
• Language: English
• Keywords: association; correlation; contingency table; volume ratio; determinant; nonparametric methods; nominal data; nominal scale; categorical data; Fisher’s exact test; odds ratio; tetrachoric correlation coefficient; phi; Cramer’s V; Pearson; contingency coefficient; uncertainty coefficient; Theil’s U; eta; meta-analysis; Simpson’s paradox; causality; statistical independence
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C10 - General

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