Suppose the model contains s explanatory effects. For the jth observation, let be the estimated probability of the observed response. The three criteria displayed by the SURVEYLOGISTIC procedure are calculated as follows:
–2 log likelihood:
where and are the weight and frequency values, respectively, of the jth observation. For binary response models that use the events/trials syntax, this is equivalent to
where is the number of events, is the number of trials, and is the estimated event probability.
Akaike information criterion:
where p is the number of parameters in the model. For cumulative response models, , where k is the total number of response levels minus one, and s is the number of explanatory effects. For the generalized logit model, .
Schwarz criterion:
where p is the number of parameters in the model. For cumulative response models, , where k is the total number of response levels minus one, and s is the number of explanatory effects. For the generalized logit model, .
The –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 p-value for this statistic. The AIC and SC statistics give two different ways of adjusting the –2 log likelihood statistic for the number of terms in the model and the number of observations used.