Solved – Zero-inflated Poisson regression Vuong test: Raw, AIC- or BIC-corrected results

aicbicgoodness of fitzero inflation

I'm analyzing count data for a set of ten species and found that for the five species with highest detection rate, the zero-inflated poisson (ZIP) regression fits the data significantly better than the regular poisson regression using glm in R. I found this using the vuong test to compare the two models, using the following code (ZP = zone/phase combination, as the data is separated into before/after phases, control/impact zones)

summary(m2 <- zeroinfl(Squirrel ~ ZP|ZP, data = bact))
summary(p2 <- glm(Squirrel ~ ZP, family = poisson, data = bact))
vuong(p2, m2)

However, for the next five species, the vuong test shows somewhat contradicting results for the fit of the ZIP regression and glm poisson regression. I'm wondering what the difference is between the raw, AIC-corrected BIC-corrected p-values is, and which I should be most concerned about (i.e. which p-value I should pay attention to). For example, the vuong results for sixth most common species is shown below: 

Vuong Non-Nested Hypothesis Test-Statistic: 
(test-statistic is asymptotically distributed N(0,1) under the
null that the models are indistinguishible)
-------------------------------------------------------------
              Vuong z-statistic             H_A    p-value
Raw                  -0.3378267 model2 > model1    0.36775
AIC-corrected         4.5566296 model1 > model2  2.599e-06
BIC-corrected        19.4932729 model1 > model2 < 2.22e-16

If I use the Raw results, I'd conclude that the ZIP model is not better than the glm poisson model. However, using the AIC- or BIC-corrected results, I'd conclude that the ZIP model is better than the glm poisson model.

What is the difference between these three values, and how should I decide which to use as the result? Thanks!

Best Answer

I am convinced that it is incorrect to use the Vuong test -- in any of its forms -- as a test for zero-inflation. I have had a paper "The misuse of the Vuong test for non-nested models to test for zero-inflation" published that explains why. See http://cybermetrics.wlv.ac.uk/paperdata/misusevuong.pdf. I have also presented the paper at major statistics conferences and no one disagreed with me.

If you are still working on this, or zero-inflation in general, get in touch if you wish.

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