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

PDF
MPRA_paper_2662.pdf Download (360kB)  Preview 
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 
References:  Colignatus is the name of Thomas Cool in science. Becker, L.A. (1999), “Measures of Effect Size (Strength of Association)”, http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm, Retrieved from source Cool, Th. (1999, 2001), “The Economics Pack, Applications for Mathematica”, http://www.dataweb.nl/~cool, ISBN 9080477419, JEL990820 Colignatus, Th. (2006), “On the sample distribution of the adjusted coefficient of determination (R2Adj) in OLS”, http://library.wolfram.com/infocenter/MathSource/6269/ Colignatus, Th. (2007a), “A logic of exceptions”, http://www.dataweb.nl/~cool, ISBN 9789080477445 Colignatus, Th. (2007b), “Voting theory for democracy”, 2nd edition, http://www.dataweb.nl/~cool, ISBN 9789080477452 Garson, D. (2007), “Nominal Association: Phi, Contingency Coefficient, Tschuprow's T, Cramer's V, Lambda, Uncertainty Coefficient”, http://www2.chass.ncsu.edu/garson/pa765/assocnominal.htm, Retrieved from source Johnston J. (1972), “Econometric methods”, McGrawHill Kleinbaum, D.G., K.M. Sullivan and N.D. Barker (2003), “ActivEpi Companion texbook”, Springer Losh, S.C. (2004), “Guide 5: Bivariate Associations and Correlation Coefficient Properties”, http://edf540001.fa04.fsu.edu/Guide5.html, Retrieved from Source Mood, A.M. and F.A. Graybill (1963), “Introduction to the theory of statistics”, McGrawHill Pearl, J. (2000), “Causality. Models, reasoning and inference”, Cambridge Simon, R. (2007), “Lecture Notes and Exercises 2006/07”, http://www.maths.lse.ac.uk/Courses/MA201/, Retrieved from source Takayama A. (1974), “Mathematical economics”, The Dryden Press Theil H. (1971), “Principles of econometrics”, NorthHolland UCLA ATS (2007), “SAS Textbook Examples. Econometric Analysis, Fourth Edition by Greene. Chapter 16: Simultaneous Equations Models”, http://www.ats.ucla.edu/stat/SAS/examples/greene/chapter16.htm, Retrieved from source (Other) websites http://en.wikipedia.org/wiki/Contingency_table http://post.queensu.ca:8080/SASDoc/getDoc/en/procstat.hlp/corr_sect26.htm http://en.wikipedia.org/wiki/Fisher%27s_exact_test 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/2662 