Predictive Value of the Model

Before you start looking at the individual predictors in the model, you need to find out if the model gives adequate predictions. To answer this question, you can examine the Model-Fitting Information table. Here you see the -2 log-likelihood values for the intercept only (baseline) model and the final model (with the predictors). While the log-likelihood statistics themselves are suspect due to the large number of empty cells in the model, the difference of log-likelihoods can usually still be interpreted as chi-square distributed statistics ¹. The chi-square reported in the table is just that: the difference between -2 times the log-likelihood for the intercept-only model and that for the final model, within rounding error.

Model fitting table that shows -2 log-likelihood, chi-square, degrees of freedom, and significance. The significance value is less than .0005. — Figure 1. Model-fitting information

The significant chi-square statistic indicates that the model gives a significant improvement over the baseline intercept-only model. This basically tells you that the model gives better predictions than if you just guessed based on the marginal probabilities for the outcome categories. That's a good sign, but what you really want to know is how much better the model is.

¹ McCullagh, P., and J. A. Nelder. 1989. Generalized Linear Models, 2nd ed. London: Chapman & Hall.