I am looking to model some data, but I am not sure what type of model I can use. I have count data, and I want a model that will give parametric estimates of both the mean and the variance of the data. That is, I have various predictive factors and I want to determine if any of them influence the variance (not just the group mean).
I know that Poisson regression will not work because the variance is equal to the mean; this assumption is not valid in my case, so I know there is overdispersion. However, a negative binomial model only generates a single overdispersion parameter, not one that is a function of the predictors in the model. What model can do this?
Additionally, a reference to a book or paper which discusses the model and/or an R package which implements the model would be appreciated.