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A bayesian analysis using multilevel covariates
December 13, 2007 - 09:03 PM
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aDepartment of Decision Sciences, Charles H. Lundquist College of Business, 1208 University of Oregon, Eugene, OR 97403-1208, USA
bDepartment of Sociology Anthropology, University of Minnesota Duluth, Duluth, MN 55812, USA
Received 20 June 2003; accepted 28 September 2004. Available online 18 November 2004.
Abstract
Imprisonment levels vary widely across the United States, with some state imprisonment rates six times higher than others. Imposition of prison sentences also varies between counties within states, with previous research suggesting that covariates such as crime rate, unemployment level, racial composition, political conservatism, geographic region, and sentencing policies account for some of this variation. Other studies, using court data on individual felons, demonstrate how type of offense, demographics, criminal history, and case characteristics affect sentence severity. This article considers the effects of both county-level and individual-level covariates on whether a convicted felon receives a prison sentence rather than a jail or non-custodial sentence. We analyze felony court case processing data from May 1998 for 39 of the nation's most populous urban counties using a Bayesian hierarchical logistic regression model. By adopting a Bayesian approach, we are able to overcome a number of challenges. The model allows individual-level effects to vary by county, but relates these effects across counties using county-level covariates. We account for missing data using imputation via additional Gibbs sampling steps when estimating the model. Finally, we use posterior samples to construct novel predictor effect plots to aid communication of results to criminal justice policy-makers.
Keywords: Gibbs sampling; Hierarchical model; Logistic regression; Missing data; Predictor effect plot; Random effect
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