I am fitting a generalised linear model on binomial data. Although I know overdispersion is much more common, I am pretty sure that my data are actually underdispersed. My two clues for this are that, in 99.8% of replications, the generated data had greater variance than the dataset; and also, plots of the residuals by the number of successes show a decreasing linear trend, indicating that for a low number of predicted successes, the number of successes is actually higher, and vice versa.
For overdispersed data, I have previously used the beta binomial, but I am unsure what to do with this underdispersed data. Does anyone have any advice for how to do this in Stan?
Please let me know if you need any additional information!