PROC SURVEYLOGISTIC: Generalized Coefficient of Determination

The SURVEYLOGISTIC 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:

$\text{[math]}$

where $\text{[math]}$ is the likelihood of the intercept-only model, $\text{[math]}$ is the likelihood of the specified model, and $\text{[math]}$ is the sample size. The quantity $\text{[math]}$ achieves a maximum of less than 1 for discrete models, where the maximum is given by

$\text{[math]}$

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

$\text{[math]}$

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

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