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A Bayesian Hierarchical Regression Approach to Clustered and Longitudinal Data in Empirical Legal Studies

Authors


  • The authors thank John Donohue and Steven Levitt for providing their data set, which is publicly available at <http://islandia.law.yale.edu/donohue/pubsdata.htm>. The authors are indebted to Ted Eisenberg for his encouragement on this project. The support of NIH Grant R01-GM083606-01 is gratefully acknowledged.

Direct correspondence to William Anderson, Visiting Assistant Professor, School of Operations Research and Information Engineering & Department of Statistical Science, Cornell University, Ithaca, NY 14853; email: wla6@cornell.edu. Well is Professor, Department of Statistical Science, Cornell University.

Abstract

The various forms of regression are a dominant feature of modern data analysis. This is hardly surprising since the basic premises of regression are well understood in many different areas of research, and basic regression analysis is a standard component in many statistical software packages. However, researchers do not have to venture very far in their applications of regression analysis to run into trouble from a computational and modeling point of view. This is especially apparent when modeling longitudinal or repeated measures data using classical regression. We introduce a Bayesian hierarchical modeling approach to clustered and longitudinal data. These hierarchical models overcome many of the limitations of classical regression and are well suited to handle longitudinal data. The intuitive concepts of hierarchical models are introduced via the Donohue and Levitt (DL) abortion-crime data set, using the statistical software package R. We show that when properly modeled, there is no empirical relationship between abortion and crime using the DL data set.

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