Negative binomial vs zero-inflated NB

[Andry Haja]

Dear all,

I need some advice relative to the choice between nbreg and zinb.

My dependent variable is the number of patent registered by companies (N=200). About 50% of the sample have no registered patent. The mean is 1.86 and sd=4.71.
This indication of overdispersion is confirmed by a significant alpha (LR test of alpha=0: chibar2(01) = 196.74 Prob>=chibar2 = 0.000).
According to the Vuong test ( z =1.98 Pr>z = 0.0237), the zero-inflated NB is more appropriate. AIC and BIC also confirm the conclusion of the Vuong test
NBREG: AIC=660.345 BIC= 693.575
ZINB: AIC=649.385 BIC= 689.261.

At the same time, Desmarais and J. J. Harden. (2013) suggest that the Vuong test needs some correction (*). Applying their proposed correction with the command "zinbcv" (**), I have to choose the standard negative binomial as indicated by the AIC and BIC

Vuong test of zinb vs. standard negative binomial: z = 2.04 Pr>z = 0.0208
Pr<z = 0.9792
with AIC (Akaike) correction: z = 1.27 Pr>z = 0.1027
Pr<z = 0.8973
with BIC (Schwarz) correction: z = -0.02 Pr>z = 0.5068
Pr<z = 0.4932

Would you tell me which test should I follow: the usual Vuong test or the corrected one?

Thank you in advance.

Andry

(*) Testing for zero inflation in count models: Bias correction for the Vuong test
B. A. Desmarais and J. J. Harden. 2013.
Stata Journal Volume 13 Number 4.
(**) package st0319 from http://www.stata-journal.com/software/sj13-4

[Joao Santos Silva]

Dear Andry,

The version of Vuong's test that is reported using the option -vuong- in the -zip- and -zinb- commands is invalid. The reason for this is that this version of the test is valid only when comparing non-nested models and the models being compared here are overlapping. So, you should not trust the results of the standard test.

I am not very familiar with the corrected version you mentioned, but it appears to be based on the same test statistic and therefore I suspect it may also be invalid, but I am not at all sure about this.

One test that you can certainly use for this purpose is the one implemented in the -hpc- command, which is available from SSC; please see the help file for the references.

All the best,

Joao

[Andry Haja]

Dear Joao

Thank you for your response.
I use hpc command after reading you comments on Stata forum...and it suggests that the zinb is more appropriate.
Best regards.

Andry