compare model fit logistic regression negative two times log likelihood I'm trying to decide between two logistic regression models.  I think I've used the negative two times log likelihood criterion before.  My two models are not nested - can I still use that approach? If so, please point me to a resource for how to use -2LogL to make the decision.  If not, what do you recommend?

If the models are not nested, as you are writing, the log-likelihood ratio test doesn't have the usual limiting $\chi^2$ distribution, so you have to use other methods.
One way could be to use information criteria such as AIC or BIC. In this approach, roughly speaking, the winner is the model that leads to the smallest AIC or BIC.
Another way is to compute the distribution of the test statistic via bootstrap. You could use (i) a parametric bootstrap approach in which data are generated from the estimated model or (ii) a nonparametric bootstrap approach in which the 'new' data are generated by extracting at random and with replacement from the observed dataset. See, for instance, Davison and Hinkley (1997) Bootstrap Methods and their Application, Cambridge University Press
