Fitting Multilevel Models When Predictors and Group Effects Correlate

コロンビア大学のAndrew Gelman教授のブログを、少し前からしばしば読んでいる。

今日読んだのは下記の記事。
http://andrewgelman.com/2012/04/fixed-effects-and-identification/

この記事で紹介されている論文を読んでみたが面白かった。
http://www.stat.columbia.edu/~gelman/research/unpublished/Bafumi_Gelman_Midwest06.pdf

Can one fit a multilevel model with varying intercepts (or coefficients) when the units and predictors correlate? The answer is yes. And the solution is simple. The problem can usefully be viewed as an omitted variable bias. Once a model is as well specified as a researcher deems possible, and if the correlation between the units and the predictor still exists, one can remove the correlation with the predictor from the group-level error by calculating the mean of the predictor at each unit and including it as a group-level predictor.
[8]

共和党と民主党の投票の例もわかりやすい。