Analytical and graphical methods for understanding hierarchical models with an application to estimating state trends in death

One of the longest running questions that has been regularly included in Gallup’s national public opinion poll is “Do you favor or oppose the death penalty for persons convicted of murder?” Because the death penalty is governed by state laws rather than federal laws, it is of special interest to know how public opinion varies by state, and how it has changed over time within each state. In this paper we combine dozens of national polls taken over a fifty-year span and fit a Bayesian multilevel logistic regression model We thank the National Science Foundation, Institute of Education Sciences, Department of Energy, and National Security Agency for partial support of this work. AT&T Labs Research, Florham Park, NJ. [email protected], http://www.research.att.com/∼kshirley/. A portion of this work was done while the author was a postdoc at Columbia University. Department of Statistics and Department of Political Science, Columbia University, New York. [email protected], http://www.stat.columbia.edu/∼gelman/