likelihood ratio testing for overdispersion in negative binomial distributions

[Robyn Jones]

Hi,

I am using the following command to fit my data:

nbreg outcome i.exposure [pweight=weight], irr

I have used the prcounts command and twoway to plot my observed vs. predicted poisson vs. predicted negative binomial – I am confident my data fits a negative binomial distribution. However, when I use the command stated above I do not recieve a likelihood ratio test for alpha=0 in the output as I see in example outputs in the documentation for this command. I would like to see this, is there a way to obtain this output or any ideas as to why I am not receiving this output?

Thanks
Robyn

[Robyn Jones]

update: I have just taken out the survey weight and the output provides the LRT

[tlo9966]

I am having the same problem, I am using Version 18. Do you think the problem is an issue with the new version? I am not using weights so I could not resolve the issue as you did.

[Jeff Wooldridge]

I'll give the same advice I always give: If you're interested in the effects on the mean, which is the vast majority of applications, you're better off using Poisson regression with robust standard errors. It is completely robust in the presence of underdispersion, overdispersion, or any variance-mean relationship. NegBin requires a very specific type of overdispersion. If you use Poisson, you don't even test for overdispersion; you just live with it if it's there.

Having said that, is an estimate for alpha reported along with its confidence interval? Are you using vce(robust) by any chance?

We strongly encourage people to show the commands typed and the Stata output reported. You're much more likely to get a useful answer.

[Robyn Jones]

Hi, NegBin is the best fit to my data. I have v18 and the exact same issue occurs for me.

nbreg outcome i.exposure [pweight=weight], irr – no LRT
nbreg outcome i.exposure, irr – LRT alpha + CI

There is no error message only the presence/absence of the LRT

[Jeff Wooldridge]

"Fit" can be defined in different ways. If the estimation converges, NegBin has to give a higher log likelihood than Poisson even if the NegBin model is misspecified. That doesn't mean it gives better estimates of the mean parameters. Poisson is known to be fully robust to any distributional misspecification; NegBin is not. In practice, the estimates are often similar but one would have to choose Poisson based on statistical properties when they differ.

When you use weights, the weighted log likelihood cannot be used in the usual chi-square test. I'm not entirely sure the confidence interval is valid if the true value of alpha is zero. Another reason to avoid NegBin is because the LRT doesn't have the usual chi-square(1) distribution under the null (because of the boundary problem at zero). Many act as if it does, though.

[Jeff Wooldridge]

I finally found the description of the LRT for nbreg. It does appear that the p-values have been adjusted for the boundary problem. Unfortunately, that doesn't help when weights are used. There are score tests that can be applied, but that would require writing a lot more ....