# beta binomial to reduce overdispersion for binomial data (zero inflation)

I know that a negative binomial model is often use to solve the problem of overdispersion in count data (poisson regression). Now, someone said that a beta binomial model can also be used to solve the problem of overdispersion in binomial data (e.g. if you use logistic regression). Can someone explain why this is?

Also, I know that zero-inflation is a problem when you have count data and want to fit a poisson model. Can zero-inflation be a problem when you want to fit a logistic model for binary data? And what if I fit a beta binomial model to solve the problem of overdispersion? I notice that there exist a zero inflated beta binomial model, but not a zero inflated logistic model?

In the case of a binomial distribution $$Y_i \sim \text{Bin}(n, \pi)$$, adding zero inflation (e.g. average proportion of $$\xi$$ being zeros) is actually just the same thing as $$Y_i \sim \text{Bin}(n, \pi(1-\xi))$$. I.e. you stay within the binomial distribution family and you just end up estimating $$\pi' := \pi(1-\xi)$$.