The SURVEYLOGISTIC Procedure

Model Fitting Statistics

Suppose the model contains $\text{[math]}$ explanatory effects. For the $\text{[math]}$ th observation, let $\text{[math]}$ be the estimated probability of the observed response. The three criteria displayed by the SURVEYLOGISTIC procedure are calculated as follows:

$\text{[math]}$ log likelihood:

$\text{[math]}$

where $\text{[math]}$ and $\text{[math]}$ are the weight and frequency values, respectively, of the $\text{[math]}$ th observation. For binary response models that use the events/trials syntax, this is equivalent to

$\text{[math]}$

where $\text{[math]}$ is the number of events, $\text{[math]}$ is the number of trials, and $\text{[math]}$ is the estimated event probability.
Akaike information criterion:

$\text{[math]}$

where $\text{[math]}$ is the number of parameters in the model. For cumulative response models, $\text{[math]}$ , where $\text{[math]}$ is the total number of response levels minus one, and $\text{[math]}$ is the number of explanatory effects. For the generalized logit model, $\text{[math]}$ .
Schwarz criterion:

$\text{[math]}$

where $\text{[math]}$ is the number of parameters in the model. For cumulative response models, $\text{[math]}$ , where $\text{[math]}$ is the total number of response levels minus one, and $\text{[math]}$ is the number of explanatory effects. For the generalized logit model, $\text{[math]}$ .

The $\text{[math]}$ 2 log likelihood statistic has a chi-square distribution under the null hypothesis (that all the explanatory effects in the model are zero), and the procedure produces a $\text{[math]}$ -value for this statistic. The AIC and SC statistics give two different ways of adjusting the $\text{[math]}$ log likelihood statistic for the number of terms in the model and the number of observations used.