Poisson Regression for Complex Surveys: Applicable to Negative Binomial Models?

[lsr0820]

I am working with complex survey data with an over-dispersed count outcome, for which a negative-binomial model is appropriate. I found the following tutorial for conducting a Poisson regression with complex data:

https://support.sas.com/rnd/app/stat/examples/SurveyPoisson/surveypoisson.htm

The post contains the following 'caution' statement: 

"However, the log likelihood for the negative binomial model is [equation]. The weight, wi, cannot be factored out of the log likelihood, so you cannot use PROC GENMOD with a WEIGHT statement to obtain point estimates of the model parameters that account for the unequal weights. Whereas the weighted maximum likelihood point estimates that PROC GENMOD generates appropriately account for the unequal weights for distributions such as the Poisson, the weighted maximum likelihood variances and standard errors that PROC GENMOD computes do not account for the complex survey design. You must compute the variances and standard errors by using a different method. One such method is the delete-1 jackknife (resampling) method."

I am unclear as to whether this 'caution' statement means that the approach given in this example can or cannot be applied to a negative-binomial model. In the example, the delete-1 jackknife method is applied. Would this then be appropriate for extension to a negative-binomial case? Or, does this method only adjust the variances and standard errors, meaning that the point estimates from a negative-binomial model would be incorrect?

Also, if this example cannot be applied to a negative-binomial model, is there another available approach that can be implemented with complex-survey data? I am aware of the following macro -- any other options would also be appreciated.

https://support.sas.com/resources/papers/proceedings17/0268-2017.pdf

Thank you for your time and assistance.

[ger15xxhcker · Accepted solution]

The caution statement in that tutorial applies to both Poisson and negative binomial models. It is true that the weight can't be factored out of the log likelihood for the negative binomial, so you cannot use PROC GENMOD with a WEIGHT statement to obtain point estimates of the model parameters that account for the unequal weights. To account for the unequal weights when you are running a negative binomial model, you need to use a different method, like the delete-1 jackknife (resampling) method, to obtain the weighted maximum likelihood point estimates. This method will also adjust the variances and standard errors.

[lsr0820]

Thanks very much for clarifying! This is helpful.