Generalized Coefficient of Determination
Cox and Snell (1989, pp. 208 -209) propose the following generalization
of the coefficient of determination to a more general linear model:
![R^2 = 1 - \biggl\{\frac{L(0)}{L(\hat{{\beta}})}\biggr\}^
{\frac{2}n}](images/lgseq87.gif)
where L(0) is the likelihood of the intercept-only model,
is the likelihood of the specified model,
and n is the sample size. The quantity
R2 achieves a maximum of less than one for discrete models,
where the maximum is given by
-
Rmax2 = 1 - {L(0)}[2/n]
Nagelkerke (1991)
proposes the following adjusted coefficient, which can achieve a maximum
value of one:
![{\tilde{R}^2}= \frac{R^2}{R_{\max}^2}](images/lgseq89.gif)
Properties and interpretation of R2 and
are provided in
Nagelkerke (1991). In the "Testing Global Null Hypothesis: BETA=0"
table, R2 is labeled as "RSquare" and
is labeled as
"Max-rescaled RSquare." Use the RSQUARE option to request
R2 and
.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.