Tell me more ×
Cross Validated is a question and answer site for statisticians, data analysts, data miners and data visualization experts. It's 100% free, no registration required.
up vote 6 down vote favorite
2

I am using a Poisson regression model for count data and am wondering whether there are reasons not to use the robust standard error for the parameter estimates? I am particularly concerned as some of my estimates without robust are not significant (e.g., p=0.13) but with robust are significant (p<0.01).

In SAS this is available by using the repeated statement in proc genmod (e.g., repeated subject=patid;). I've been using http://www.ats.ucla.edu/stat/sas/dae/poissonreg.htm as an example which cites a paper by Cameron and Trivedi (2009) in support of using robust standard errors.

share|improve this question

1 Answer

up vote 4 down vote

In general if you have any suspicion that your errors are heteroskedastic, you should use robust standard errors. The fact that your estimates become non-significant when you don't use robust SEs suggests (but does not prove) the need for robust SEs! These SEs are "robust" to the bias that heteroskedasticity can cause in a generalized linear model.

This situation is a little different, though, in that you're layering them on top of Poisson regression.

Poisson has a well known property that it forces the dispersion to be equal to the mean, whether or not the data supports that. Before considering robust standard errors, I would try a Negative Binomial regression, which does not suffer from this problem. There is a test (see the comment) to help determine whether the resultant change in standard errors is significant.

I do not know for sure whether the change you're seeing (moving to robust SEs narrows the CI) implies under-dispersion, but it seems likely. Take a look at the appropriate model (I think negative binomial, but a quick googling also suggests quasi-Poisson for under-disperion?) and see what you get in that setting.

share|improve this answer
Nice answer! Typically in OLS heteroskedasticity does not cause the parameters to be unbiased (merely inefficient). This is not true though for generalized linear models, see this post by Dave Giles about it for references. I don't think I've seen the Vuong test recommend for this though (for comparisons of non-nested zero inflated models I have seen it suggested). Poisson is nested within the Neg. Binomial model, so one can use a likelihood ratio test for the dispersion parameter. – Andy W Nov 2 '12 at 12:42
Thank for your answer. I did try Negative Binomial regression but ran into the warning: "The relative Hessian convergence criterion of 0.0046138565 is greater than the limit of 0.0001. The convergence is questionable." Note that my response variable is a count with values ranging from 0 to 4. Is there a transformation of the dependent or independent variable that would help convergence? Or what does one do in this case? – kara Nov 2 '12 at 13:36
Also, related to the non-robust SEs being smaller - in my analysis I see that it is the robust SEs that are smaller and this is where the significance lies (not in the non-robust results). This is why I want to be careful about whether or not to report the robust results - I don't want to choose this method just because of significant pvalues! Thanks again! – kara Nov 2 '12 at 13:42
@AndyW I checked my notes and Vuong is indeed for ZI vs Poisson. Updated post. kara I missed the reversal. You could have under-dispersed data, in which case the NBD is also potentially the solution :-) – Ari B. Friedman Nov 2 '12 at 13:58
@kara Hard to diagnose your non-convergence problem in comments. I'd try a new question just on that with as much information as you can provide. – Ari B. Friedman Nov 2 '12 at 14:24
show 1 more comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.