Lenore Fahrig writes,

I have two multinomial logistic models meant to explain the same data set. The two models have different predictor variables but they have the same number of predictor variables (2 each). Can I use the difference in deviance between the two models to compare them?

This sort of question comes up a lot. My quick answer is to include all four predictors in the model, or to combine them in some way (for example, sometimes it makes sense to reparameterize a pair of related predictors by considering their average and their difference). I can see why it can be useful to look at the improvement in fit from adding a predictor or two, but I don’t see the use in comparing models with different predictors. (I mean, I see how one can learn interesting things from this sort of comparison, but I don’t see the point in a formal statistical test of it, since I would think of your two original models as just the starting points to something larger.)