There is more than one solution for the problem of overdispersed count data. One is to use a quasipoisson model. One is to use a negative binomial model. One is to use a mixed-level model with subject-level random intercepts. Is there a rational and non-arbitrary way to choose among these? I ask because of a specific behavior I discovered for some overdispersed data. I have laid out all the details for this behavior in the following Kaggle notebook:

https://www.kaggle.com/bryanmaloney/dealing-with-overdispersion-which-model-to-use/