When compensating for overdispersion in count data, is it more appropriate to use a negative binomial model or a quasi-Poisson model? What are the advantages and disadvantages of using either?
Thank you in advance for your help.
George.
Both the models were found useful depending on the type of research question and context, sometimes one was more "fitting" than the other. Here is a good paper that demonstrates this issue and slightly preferred the quasi poisson in their research context. Again, it depends on context of research and scientific reasoning and not merely based on data at hand. Hope it helps.
Another (simpler?) option is to use a mixture of Poissons. I don't belive the quasi-Poisson has a defined distribution so inference is difficult. With a mixture you can evaluate improvement in fit with a test based on likelihoods. Also, it may make substantive sense if there is a reasonable interpretation of the (latent) subgroups.
Have you looked at your scaled residual versus fit plot? Does it show homogeneity? There is much to be said for getting the error model right- first step is visual diagnosis. Poisson error model rarely adequate for count data - variance = mean too rigid, and hence fan shaped residual vs fit plot. Quasi poisson error estimates a single additional parameter that can sometimes put the overdispersion into the error model. Negative binomial is next step, if quasi poisson does not produce acceptable residual vs fit plot.. If negative binomial fails, next step is zero inflated model or hurdle model to deal with undue number of zero counts, which is often a problem.
I have bike crash data, I developed both Poisson and Negative binomial for my count data. However , both shows under-dispersion. which model do I have to fit for my data to get good result and best fit?
This should be useful
https://stats.stackexchange.com/questions/67385/what-is-the-appropriate-model-for-underdispersed-count-data
The Poisson QMLE will assume that Var(Y|X) is linearly proportional to the E(Y|X), while Negative Binomial allows for a quadratic relationship which could give more flexibility and allow a better fitting. However, it would depend in the problem you are analyzing. You can try to diagnostic your results using a qqplot for the residuals.
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