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Underdispersion is when there is less variability than there 'ought' to be in the data. Eg, the variance of counts could be less than the mean, whereas the variance of a Poisson should equal the mean.
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Sampling from under/over-dispersed count data in R
Depending on the result, I switch to quasi-Poisson model when there is evidence of over- or underdispersion. … However, I have no idea how to do it in the cases of over/underdispersion. Any ideas? …