Is it appropriate to use a negative binomial regression with fixed effects when the dependent variable appears somewhat normally distributed within each group, but the overall distribution of the dependent variable appears more like a negative binomial distribution?
I'm using multilevel modeling to test hypotheses about "within group" relationships, without any need to make assumptions about variation between them. For that reason, I'm opting for a "fixed effects" model. Theory would lead us to use a multilevel count model, and overall analysis of the dependent variable supports the claim. The skew of the variable is 231.49 and its kurtosis is 77899.
Here's the log-transformed distribution of the dependent variable:
However, when we look at the within-group variation, the distributions have skewness closer to 0. Here is a histogram of the per-group skewness for a subset of groups:
Given this, when using a fixed effects model to estimate the within-group variation, should I try to fit a fixed effects count model or a fixed effects linear model?