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The LOGISTIC Procedure

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 one for discrete models, where the maximum is given by


To take the frequency and weight of observation into account, the sample size is replaced in and with . Specifying the NORMALIZE option in the WEIGHT statement makes these coefficients invariant to the scale of the weights.

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


Like the AIC and SC statistics described in the section Model Fitting Information, and are most useful for comparing competing models that are not necessarily nested—larger values indicate better models. More 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 .

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