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.
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