__Vuong test is not appropriate for testing zero inflation__

Greene (1994) proposed using the Vuong test for nonnested models (Vuong
1989) to test for zero inflation. Despite many earlier citations, recent
work by Wilson (2015) has shown that the Vuong test is inappropriate for
testing zero inflation. Nesting occurs when the probability of zero
inflation is 0, which is on the boundary, and this violates the
regularity conditions of the Vuong test for nonnested models. So the
distribution of the test statistic is not standard normal. The actual
distribution is unknown and thus cannot be used for inference.

You may consider using information criteria to choose between the
standard and the zero-inflated models; see example 2 in **[R] zip**.

__References__

Greene, W. H. 1994. Accounting for excess zeros and sample selection in
Poisson and negative binomial regression models. Working paper
EC-94-10, Department of Economics, Stern School of Business, New York
University. https://ideas.repec.org/p/ste/nystbu/94-10.html.

Vuong, Q. H. 1989. Likelihood ratio tests for model selection and
non-nested hypotheses. *Econometrica* 57: 307-333.

Wilson, P. 2015. The misuse of the Vuong test for non-nested models to
test for zero-inflation. *Economics Letters* 127: 51-53.