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

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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 

Institution:  Thomas Cool Consultancy & Econometrics 
Original Title:  A measure of association (correlation) in nominal data (contingency tables), using determinants 
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; metaanalysis; Simpson’s paradox; causality; statistical independence 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General 
Item ID:  2662 
Depositing User:  Thomas Colignatus 
Date Deposited:  10. Apr 2007 
Last Modified:  07. Jan 2014 18:38 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/2662 