st: Fixed-effects models with skewed data and heteroskedasticity?

[Alex Borwein <aborwein@gmail.com>]

We are working with panel data, specifically a dataset of prescriptions nested within prescribers, Our dependent variable is a proportion (the proportion of quantity of all drugs prescribed in a class that are for a specific drug per month). We want to use fixed-effects models, as we are interested in the effect of a policy change on the change in prescribing over time within prescribers (we don't care about the differences between prescribers). We are looking at using the _xtreg_ command, but are worried by three things: 1) that we are using proportions as the dependent variable,  2) our data is very positively skewed and in any given month there is a high proportion of zeros (which are legitimate values) and 3) the denominator of the proportion is skewed, and variable between prescribers with about 50% of prescribers having very low prescribing volume. As a result, there is substantial heteroskedascticity (i.e. low volume prescribers have high variability in their proporti!
 ons). 

Logistic regression might seem logical, but is not really appropriate here. We are looking at the proportion of overall quantity prescribed, not the proportion of prescriptions. We are looking at a logistic transform, and then fitting models with xtreg.  To deal with heteroskedasticity , we are considering weighting prescribers by their average volume of prescribing.

Anyway, lots of messy problems in the data, and we are wondering if folks on this list have ideas of other modelling approaches that we should consider?
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