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Is there a test that I can use for a logistic regression that is similar to the Vuong test for OLS?

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    $\begingroup$ Not clear what you are asking. What are the (non-nested) models that you are trying to compare? $\endgroup$ – tchakravarty Mar 17 '15 at 5:02
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    $\begingroup$ Why don't you just use the Vuong test? It is not an OLS-specific test. $\endgroup$ – Bill Mar 17 '15 at 13:37
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Indeed, there is a variety of goodness-of-fit (GoF) tests that can be applied to logistic regression as an alternative to the Vuong test (Vuong, 1989). I think that the following tests can be considered as relative equivalents in the above-mentioned context:

For some theory on GoF testing for categorical models (in particular, logistic regression models), deviance and LRT, as well as additional examples in R, Stata and SAS, see this nice presentation.

Note

It seems that there are some issues of significant importance, when considering logistic regression (LR) models. In particular, it appears to me that nested vs. saturated models, sample size, data grouping in cases with continuous predictors are specifically important in LR GoF testing context.

References

Hosmer D.W., & Lemeshow S. (1980). A goodness-of-fit test for the multiple logistic regression model, Communications in Statistics - Theory and Methods, 9(10), 1043-1069. doi:10.1080/03610928008827941

Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica, 57(2), 307–333. Retrieved from http://fisher.osu.edu/~schroeder.9/AMIS900/Vuong1989.pdf

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    $\begingroup$ @Billy: My pleasure! Consider upvoting and accepting my answer, if you're satisfied with it. $\endgroup$ – Aleksandr Blekh Mar 19 '15 at 3:53

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