Model Fitting Information

The LOGISTIC Procedure

Model Fitting Information

Suppose the model contains s explanatory effects. For the jth observation, let $\hat{p}_j$ be the estimated probability of the observed response. The three criteria displayed by the LOGISTIC procedure are calculated as follows:

-2 Log Likelihood:
$-2{ Log L}=-2\sum_j w_j f_j\log(\hat{p}_j)$
where w_j and f_j are the weight and frequency values of the jth observation. For binary response models using events/trials syntax, this is equivalent to
$-2{ Log L}=-2\sum_j w_j f_j \{r_j \log(\hat{p}_j) + (n_j-r_j)\log(1-\hat{p}_j) \}$
where r_j is the number of events, n_j is the number of trials, and $\hat{p}_j$ is the estimated event probability.
Akaike Information Criterion:

AIC = -2 Log L+2(k+s)
where k is the total number of response levels minus one, and s is the number of explanatory effects.
Schwarz Criterion:

${SC}=-2{ Log L}+(k+s)\log(\sum_jf_j)$

where k and s are as defined previously.

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. These statistics should be used when comparing different models for the same data (for example, when you use the METHOD=STEPWISE option in the MODEL statement); lower values of the statistic indicate a more desirable model.

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