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:


where is the likelihood of the intercept-only model, is the likelihood of the specified model, and is the sample size. The quantity achieves a maximum of less than 1 for discrete models, where the maximum is given by


Nagelkerke (1991) proposes the following adjusted coefficient, which can achieve a maximum value of 1:


Properties and interpretation of and are provided in Nagelkerke (1991). In the "Testing Global Null Hypothesis: BETA=0" table, is labeled as "RSquare" and is labeled as "Max-rescaled RSquare."  Use the RSQUARE option to request and .