On association in regression: The coefficient of determination revisited

Statistics

Volumn 42, Issue 1, 2008, Pages 1-24

  Van Der Linde, Angelika ^a   Tutz, Gerhard ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Coefficient of determination; Divergence; Mutual information; R2

Indexed keywords

EID: 39049166721     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880701529530     Document Type: Review

References (43)

1. 2 measures based on Wald and likelihood ratio joint significance tests. Journal of American, Statistical Association, 44, 250-253.
2. Nagelkerke, N.J.D., 1991, A note on a general definition of the coefficient of determination. Biometrika, 78, 691-692.
3. 2. The American Statistician, 39, 279-285.
4. Bell, C.B., 1962, Mutual information and maximal correlation as measures of dependence. Annals of Mathematical Statistics, 33, 587-595.
5. Cramer, E.M. and Nicewander, W.A., 1979, Some symmetric, invariant measures of multivariate association. Psychometrika, 44, 43-54.
6. Renyi, A., 1959, On measures of dependence. Acta Mathematica Academiae Scientiarum Hungarical, 10, 441-451.
7. Särndal, C.E., 1974, A comparative study of association measures. Psychometrika, 39, 165-187.
8. Silvey, S.D., 1964, On a measure of association. Annals Mathematical Statistics, 35, 1157-1166.
9. Kent, J.T., 1983, Information gain and a general measure of correlation. Biometrika, 70, 163-173.
10. Draper, N.R. and Smith, H., 1981, Applied Regression Analysis (New York: Wiley).
11. McKay, R.J., 1977, Variable selection in multivariate regression: an application of simultaneous test procedures. Journal of the Royal Statistical Society, B39, 371-380.
12. Kullback, S., 1968, Information Theory and Statistics (2nd edn) (Mineola, NY: Dover Publications).
13. Osius, G., 2004, The association between two random, elements: a complete characterization and odds ratio Models. Metrika, 60, 261-277.
14. Mardia, K. V., Kent, J.T. and Bibby, J.M., 1995, Multivariate Analysis (10th edn) (New York: Academic Press).
15. Hooper, J., 1959, Simultaneous equations and canonical correlation theory. Econometrica, 27, 245-256.
16. Glahn, H., 1969, Some relationships derived from canonical correlation theory. Econometrica, 37, 252-256.
17. 2 as a measure of goodness of fit. Journal of the Royal Statistical Society, A147, 608-609.
18. 2 : its use in weighted least-squares regression analysis. Journal of American Statistical Association, 42, 236-238.
19. Fahrmeir, L. and Tutz, G., 1994, Multivariate Statistical Modelling Based on. Generalized Linear Models (New York: Springer).
20. McCullagh, P. and Nelder, J.A., 1989, Generalized Linear Models (2nd edn) (London: Chapman and Hall).
21. Barnwal, R.K. and Paul, S.R., 1988, Analysis of one-way layout of count data withnegative binomial variation. Biometrika, 75, 215-222.
22. Soofi, E.S., Retzer, J.J. and Yasai-Ardekani, M., 2000, A framework for measuring the importance of variables with applications to management research and decision models. Decision Sciences, 31, 595-625.
23. Joe, H., 1989, Relative entropy measures of multivariate dependence. Journal of American Statistical, Association, 84, 157-164.
24. Cover, T.M. and Thomas, J.A., 1991, Information Theory (New York: Wiley).
25. Theil, H., 1987, How many bits of information does an independent variable yield in a multiple regression? Statistics and Probability Letters, 6, 107-108.
26. Stewart, D. and Love, W., 1968, A general canonical index. Psychological Bulletin, 70, 160-163.
27. Gleason, T.C, 1976, On redundancy in canonical analysis. Psychological Bulletin, 83, 1004-1006.
28. Jessop, A., 1995, Informed Assessments (New York: Ellis Horwood).
29. Cameron, A.C. and Windmeijer, A.G., 1997, An R-squared measure of goodness of fit for some common nonlinear regression models. Journal of Econometrics, 77, 329-342.
30. Darbellay, G.A., 1998, Predictability: an information-theoretic perspective. In: A. Procházka et al. (Eds) Signal Analysis and Prediction (Boston: Birkhäuser), pp. 249-262.
31. Soofi, E.S. and Retzer, J.J., 2002, Information indices: unifications and applications. Journal of Econometrics, 107, 17-40.
32. van der Linde, A., 2005, DIC in variable selection. Statistica Neeriandica, 59, 45-56.
33. Simon, G., 1973, Additivity of information in exponential family probability laws. Journal of American Statistical Association, 68, 478-482.
34. Bjerve, S. and Doksum, K., 1993, Correlation curves: measures of association as functions of covariate values. Annals of Statistics, 21, 890-902.
35. Doksum, K., Blyth, S., Bradlow, E., Meng, X.-L. and Zhao, H., 1994, Correlation curves as local measures of variance explained by regression. Journal of American Statistical Association, 89, 571-582.
36. Doksum, K. and Samarov, A., 1995, Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in Regression. Annals of Statistics, 23, 1443-1473.
37. Hardie, W., 1990, Applied Nonparametric Regression (Cambridge: Cambridge University Press).
38. Lavergne, P. and Vuong. Q.H., 1998, An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression. Journal of Nonparametric Statistics, 9, 363-380.
39. van der Linde, A., 2004, On the association between a random, parameter and an observable. Test, 13, 85-111.
40. Rao, C.R., 1973, Linear Statistical Inference and Its Applications (New York: Wiley).
41. Rao, C.R. and Toutenburg, H., 1995, Linear Models (New York: Spinger).
42. Spiegelhalter, D.J., Best, N.G., Carlin, B.P. and van der Linde, A., 2002, Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, B64, 583-639.
43. Theil, H. and Chung, C., 1988, Information-theoretic measures of fit for univariate and multivariate regression, The American Statistician, 42, 249-252.