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Overdispersion is when there is greater variability than there 'ought' to be in the data. Eg, the variance of counts is often greater than the mean, whereas the variance of a Poisson should equal the mean.
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Very large theta values using glm.nb in R - alternative approaches?
It doesn't necessarily mean that there is overdispersion (though it could), just that a saturated model may be a better fit. … Thinking about overdispersion in a count model is always a good idea, but it does introduce complexity into the model. …