Colignatus, Thomas (2007): A comparison of nominal regression and logistic regression for contingency tables, including the 2 × 2 × 2 case in causality.

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Abstract
Logistic regression (LR) is one of the most used estimation techniques for nominal data collected in contingency tables, and the question arises how the recently proposed concept of nominal correlation and regression (NCR) relates to it. (1) LR targets the cells in the contingency table while NCR targets only the variables. (2) Where the methods seem to overlap, such as in the 2 × 2 × 2 case, there still is the difference between the use of categories by LR (notably the categories Success, Cause and Confounder) and the use of variables by NCR (notably the variables Effect, Truth and Confounding). (3) Since LR looks for the most parsimonious model, the analysis might be helped by NCR, that is very parsimonious since it uses only the variables and not all the cells of the contingency table. (4) While LR may generate statistically significant regressions, NRC may show that the correlation still is low. (5) Risk difference regression may be a bridge to understand more about the difference between LR and NCR. (6) The use of LR and NCR next to each other may help to focus on the research question and the amount of detail required for it.
Item Type:  MPRA Paper 

Institution:  Thomas Cool Consultancy & Econometrics 
Original Title:  A comparison of nominal regression and logistic regression for contingency tables, including the 2 × 2 × 2 case in causality 
Language:  English 
Keywords:  Experimental economics; causality; cause and effect; confounding; contingency table; epidemiology; correlation; regression; logistic regression; 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General 
Item ID:  3615 
Depositing User:  Thomas Colignatus 
Date Deposited:  19. Jun 2007 
Last Modified:  16. Feb 2013 00:01 
References:  Colignatus is the name of Thomas Cool in science. Christensen, R. (1997), “LogLinear Models and Logistic Regression”, Springer, http://www.math.unm.edu/~fletcher/llm.html, see http://books.google.nl/books?id=7acdFD_eX24C&dq=LogLinear+Models+and+Logistic+Regression etcetera (only partly available on the web, nonretrievable) 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 Colignatus, Th. (2007c), “A measure of association (correlation) in nominal data (contingency tables), using determinants”, a earlier version (3rd publishable draft), http://ideas.repec.org/p/pra/mprapa/2662.html Colignatus, Th. (2007d), “Correlation in contingency tables. A measure of association or correlation in nominal data (contingency tables), using determinants”, the improved version of Colignatus (2007c), but useful to mention in this list of references if only an abridged version is eventually published, http://mpra.ub.unimuenchen.de/3394/ Colignatus, Th. (2007e), “Elementary statistics and causality”, work in progress, http://www.dataweb.nl/~cool/Papers/ESAC/Index.html Colignatus, Th. (2007f), “The 2 × 2 × 2 case in causality, of an effect, a cause and a confounder”, http://mpra.ub.unimuenchen.de/3351/, Retrieved from source Friendly, M. (2007), “Categorical Data Analysis with Graphics”, Retrieved from http://www.math.yorku.ca/SCS/Courses/grcat/grc6.html (citing the data from Koch & Stokes (1991)) Garson, D. (2007a), “Logistic Regression”, http://www2.chass.ncsu.edu/garson/pa765/logistic.htm, Retrieved from source Garson, D. (2007b), “LogLinear, Logit, and Probit Models”, http://www2.chass.ncsu.edu/garson/pa765/logit.htm, Retrieved from source Kleinbaum, D.G., K.M. Sullivan and N.D. Barker (2003), “ActivEpi Companion texbook”, Springer Lowry, R. (2007), “VassarStats. Simple logistic regression”, website, http://faculty.vassar.edu/lowry/logreg1.html, Retrieved from Source Social Research Methods (2007), “The 2*2*2 Contingency Table”, http://www.socialresearchmethods.net/tutorial/Cho/222table.htm, Retrieved from source Theil H. (1971), “Principles of econometrics”, NorthHolland Weisstein, Eric W. (2007) “Fisher's Exact Test.” From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/FishersExactTest.html 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/3615 