VIF test after negative binomial regression

[Changhyeon Song]

Hi, I have something to ask about vif test after negative binomial regression.

After finishing negative binomial regression, (nbreg y x1 x2 .....)

command 'vif' doesn't work.

STATA shows that

not appropriate after regress, nocons;
use option uncentered to get uncentered VIFs
r(301);

I didn't choose the option ', nocons'


Should I remove constant term when doing negative binomial regression?

Sincererly

[Clyde Schechter]

It seems that Stata has confused its error messages here. I can replicate your problem here, and the error message is inappropriate: it has nothing to do with -nocons-. But, -vif- does not run after -nbreg- in any case. It is designed only to run after -regress- (and, at that, -regress- with a constant term.) The reason for this is that multicolinearity among predictors does not inflate coefficient standard errors in the same way in non-linear models that it does in ordinary linear regression, so the -vif- output statistics cannot be interpreted at face value.

If you really want to run -vif- anyway, you can do so by re-doing the regression analysis with the -regress- command instead of -nbreg-. Then run -vif-. Since -vif- is calculated only from the regressors, not the outcome variable you will get results that reflect the degree of multicolinearity among your predictors (though the results will not correctly identify the effect of that multicolinearity on standard errors in models other than -regress-.)

All of that said, why are you wasting your time on this? See Arthur Goldberger's A Course in Econometrics, Harvard University Press, 1991 (there may be more recent editions) for a takedown of this misguided approach. At the end of the day, multi-colinearity in an analysis is either not a problem at all, or an unsolvable problem, and when it is a problem, its presence is easily recognized without any special tests. When it is an unsolvable problem, it means your data are inadequate to your research goals and you have to gather a much larger data set or use a different design altogether.

The simple way to tell if multicolinearity is a problem in your results is to just look at the standard error(s) or the confidence interval(s) of the variable(s) that represent(s) the key predictor(s) in your model (not the variables you are including just to adjust/control for their effects.) If the standard error(s) or confidence interval(s) are satisfactory, then whatever multicolinearity might be present is not causing you a problem, so there is no point in going on a hunt for it.
If, on the other hand, those measures of the uncertainty of your predictions show an unacceptably wide range of uncertainty, then you have too small a sample, or multicolinearity involving your key predictor(s), or too much error variance in your outcome to satisfactorily answer your research question(s). It is pretty easy to see what your error variance is and what your sample size is. If those are ruled out, then it's multicolinearity. But there is nothing you can do about the multicolinearity within that same data set anyway.

[Changhyeon Song]

Thank you so much, Mr. Schechter

It really helped me a lot.

[Richard Williams]

I can reproduce the weird error message. It would be better to just say vif does not work after nbreg.

In general I agree with Clyde about multicollinearity. However I think there are some situations where you could take corrective steps. For example, you may want to create a scale out of several items that are all meant to tap the same thing. See p. 4 of

https://www3.nd.edu/~rwilliam/stats2/l11.pdf

[Liza]

Dear Clyde,

I found your above discussion of multicollinearity among predictors very useful. However, what do you consider satisfactory in terms of standard error or confidence interval(s)?

Many Thanks

[Clyde Schechter]

A satisfactory confidence interval is one that enables me to answer the research question, so it depends on the question. Suppose I am testing the effect of drug X on reduction of symptoms (as measured quantitatively in some way) of disease Y. Suppose I have determined that a reduction 3.5 points is clinically meaningful. Then if my confidence interval for the amount of symptom reduction attributable to X excludes 3.5, I have answered my research question. If the confidence interval lies entirely above 3.5, then the drug produces a clinically meaningful improvement in symptoms If the confidence interval lies entirely below 3.5, it does not. If the confidence interval contains 3.5, then my question remains unanswered, and additional research is required to answer the question.

(I am, of course, oversimplifying here to focus on the role of the confidence interval. Of course, interpreting any study also requires looking for sources of error other than sampling--so, in the clinical context, was the population studied representative of the target population for the disease, was there much dropout from the study, did people follow their treatment consistently, etc., etc.)

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[Liza]

Dear Clyde,

many thanks for your response.

Liza Viiera