Fitting Multilevel Models When Predictors and Group Effects Correlate

14 Pages Posted: 3 Sep 2007

See all articles by Joseph Bafumi

Joseph Bafumi

Dartmouth College - Department of Government

Andrew Gelman

Columbia University - Department of Statistics and Department of Political Science

Abstract

Random effects models (that is, regressions with varying intercepts that are modeled with error) are avoided by some social scientists because of potential issues with bias and uncertainty estimates. Particularly, when one or more predictors correlate with the group or unit effects, a key Gauss-Markov assumption is violated and estimates are compromised. However, this problem can easily be solved by including the average of each individual-level predictors in the group-level regression. We explain the solution, demonstrate its effectiveness using simulations, show how it can be applied in some commonly-used statistical software, and discuss its potential for substantive modeling.

Suggested Citation

Bafumi, Joseph and Gelman, Andrew, Fitting Multilevel Models When Predictors and Group Effects Correlate. Available at SSRN: https://ssrn.com/abstract=1010095 or http://dx.doi.org/10.2139/ssrn.1010095

Joseph Bafumi

Dartmouth College - Department of Government ( email )

Hanover, NH
United States

Andrew Gelman (Contact Author)

Columbia University - Department of Statistics and Department of Political Science ( email )

New York, NY 10027
United States
212-854-4883 (Phone)
212-663-2454 (Fax)

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