About a week ago I wrote about how to estimate congressional district level opinion from the Cooperative Congressional Election Survey, which is a large national opinion poll. I sent the post to Andrew Gelman, a statistician and political scientist, who gave me some great feedback on the methodology I used. In this post, I've revised my opinion model based on that feedback, and have made a few other additional enhancements as well. Compared to the previous model, this iteration produces very similar point estimates, but with reduced variance. Here I'll explain the changes and the reasoning behind them.
In the original post, I used a hierarchical student T distribution to model district level regression intercepts, with the standard deviation and degrees of freedom estimated from the data. I did not use a state or regional level regression as is typically done in the literature. There were two main reasons for this, the first is that I tended to get inefficient inferences when I included the state and regional level variation, which I blamed on correlations between the district level predictors and the state/regional regression indicators. However, at Andrew's suggestion I tried using more informative priors for the variance parameters in the model (which for example represent the standard deviation of the group distribution for the district level intercepts) and this problem resolved instantly.Read More