[PDF][PDF] A note on a general definition of the coefficient of determination

NJD Nagelkerke - biometrika, 1991 - cesarzamudio.com
NJD Nagelkerke
biometrika, 1991cesarzamudio.com
The use of R2, the coefficient of determination, also called the multiple correlation
coefficient, is well established in classical regression analysis (Rao, 1973). Its definition as
the proportion of variance'explained'by the regression model makes it useful as a measure
of success of predicting the dependent variable from the independent variables. It is
desirable to generalize the definition of R'to more general models, for which the concept of
residual variance cannot be easily defined, and maximum likelihood is the criterion of fit. The …
The use of R2, the coefficient of determination, also called the multiple correlation coefficient, is well established in classical regression analysis (Rao, 1973). Its definition as the proportion of variance'explained'by the regression model makes it useful as a measure of success of predicting the dependent variable from the independent variables. It is desirable to generalize the definition of R'to more general models, for which the concept of residual variance cannot be easily defined, and maximum likelihood is the criterion of fit. The following generalization, but with misprint lln replaced by 2/n here in (la) and (lb), was proposed by Cox & Snell (1989, pp. 208-9) and, apparently independently, by Magee (1990); but had been suggested earlier for binary response models by Maddala (1983), where I (;) and l (0)= log L (0) denote the log likelihoods of the fitted and the'null'= log~(6) model respectively.
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