Generalized R2
Nagelkerke (1991) generalizes the definition of the coefficient of determination:
- A generalized coefficient of determination should be consistent with the classical coefficient of determination when both can be computed;
- Its value should also be maximised by the maximum likelihood estimation of a model;
- It should be, at least asymptotically, independent of the sample size;
- Its interpretation should be the proportion of the variation explained by the model;
- It should be between 0 and 1, with 0 denoting that model does not explain any variation and 1 denoting that it perfectly explains the observed variation;
- It should not have any unit.
The generalized R² has all of these properties.
where L(0) is the likelihood of the model with only the intercept, is the likelihood of the estimated model and n is the sample size.
However, in the case of a logistic model, where cannot be greater than 1, R² is between 0 and : thus, it is possible to define a scaled R² as R²/R²max.
Read more about this topic: Coefficient Of Determination
Famous quotes containing the word generalized:
“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”
—H.L. (Henry Lewis)