Think about what a p value is--the probability that a null hypothesis is rejected is usually the answer given. But it has some assumptions, the first being that some sort of test exists. About the only test I can think of is a likelihood ratio test, comparing the log-likelihoods of the model that is fit, to the null model. It turns out, that for reasonably sized datasets and a limited number of model parameters, AICc is as good a comparator as you can find. However, the chi-square value from comparing the -2 log-likelihoods is the only "p value" generating test that I can think of.

Steve Denham