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I'm modelling overdispersed counts. I began using a GLM with Poisson error structure, then moved to quasi-Poisson, and then finally negative binomial. The residuals versus fitted values plot is still fan shaped and indicative of overdispersion. Is there a type of GLM that can handle this amount of overdispersion?

I've thought about using a hurdle-type approach, where smaller counts are modeled using Poisson or NB, and then the larger counts are modeled.

Any ideas for handling this amount of overdispersion?

Here is the code I've used:

glm.count.nb <- glm.nb(count ~ (year.range/year)*region*vegetation, data=data3)
plot(glm.count.nb)

With these model diagnostic plots:

enter image description here

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    $\begingroup$ are you sure you're looking at residuals that have been correctly standardized? Can you give some more detail (code, picture) of what you're doing? $\endgroup$ – Ben Bolker Jul 27 '15 at 14:07
  • $\begingroup$ No I'm not sure if they have been standardized! How would I standardize them? $\endgroup$ – smccain Jul 27 '15 at 14:16
  • $\begingroup$ good start. can you show the location-scale plot (sqrt(abs(resids)) vs fitted) too ? $\endgroup$ – Ben Bolker Jul 27 '15 at 17:13
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    $\begingroup$ I would take out the outlier (remembering to go back later to understand why it's an outlier) and redo the analysis before making any judgments. The names of the variables alone indicate the possibility of spatio-temporal correlation, which suggests looking at models designed to handle that explicitly. $\endgroup$ – whuber Jul 27 '15 at 17:30
  • $\begingroup$ agreed. at least on the basis of what's shown here, it looks like the actual degree of heteroscedasticity (represented by the red smoothing line in the scale-location plot) is marginal (some of the appearance of the 'fan' is driven by differential sampling across the range of the data; because there are more data points with medium-to-large than with smaller predicted values, the range of the data is larger there ... $\endgroup$ – Ben Bolker Jul 27 '15 at 18:12

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