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When calculating the dispersion deviance/degrees freedom I get the value 1.8. Is it absolutly necessary to carry out the glm using quasipoisson? What is deemed 'significantly overdispersed' ?

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The Poisson model assumes equal mean and variance. If that doesn't hold, then the Poisson model isn't correct. Quasi-poisson is one possibility when there is overdispersion. Others include: Negative binomial regression (NBR) - similar to Poisson model, but using the negative binomial distribution instead, which has a dispersion parameter. Available in the MASS package in R, also integrated into Stata. Hurdle regression - for circumstances with more 0s than would be expected from the Poisson/NB model. It combines a logit/probit with Poisson/NB, where the logit/probit is used to estimate y=0 vs y>0, and a truncated Poisson/NB is used to estimate the cases where y>0. Available in the pscl package. Also available as a separate Stata add-on I cannot remember. Zero-inflated - zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZNB) models are similar to the hurdle model, but assume two mechanisms at work to generate 0s: never-takers, and potential takers who didn't take in this instance. Available in the pscl package, and available in Stata.

If your data are over-dispersed, try NBR, and compare the log-likelihoods (e.g. via AIC/BIC, etc.), and you can also get the statistical significance of the dispersion parameter from the NBR. From what I can tell, there is no disadvantage of using the NBR model relative to the Poisson model - so when I have overdispersion (in my limited experience, this has always been the case!), I simply use NBR and don't think twice. I could be wrong and would welcome others' thoughts. One of the downsides to the quasi-poisson is that it doesn't allow you to get likelihood-based stats, like the AIC/BIC. NBR uses MLE so it does.

This is a wonderful reference walking through how these models are used; it's an R vignette, but even if you don't use R it should be very useful.

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    $\begingroup$ If you want to carry out a formal test for overdispersion you can use the LR test of Poisson vs. NB but there are also many other tests (e.g. dispersiontest in AER). However, overdispersion can be relevant before it is significant. So in case of doubt I recommend to use NB or quasipoisson etc. $\endgroup$ – Achim Zeileis Jan 9 '15 at 20:26
  • $\begingroup$ I have used the automated model selection glmulti for my poisson model and can't work out how to do this for a negative binomial model. Is it likely the model selection will differ hugely e.g. will I have to run model selection again? If so what package do you recommend? $\endgroup$ – user13641 Jan 12 '15 at 12:06
  • $\begingroup$ Sorry I have limited experience with automated model selection, it's not something I do really. Do have so many independent variables that you cannot use Wald tests, LR tests, etc., to determine which to include? Part of model selection is the distribution you will use (for parametric regression), which you will determine based on the dispersion parameter (and it sounds like that is already decided you should use NB). $\endgroup$ – robin.datadrivers Jan 12 '15 at 17:03

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