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Estimation of Incarceration and Criminal Careers Using Hierarchical Models

NCJ Number
Date Published
June 1986
Mark J. Schervish, Carnegie-Mellon University; John P. Lehoczky, Carnegie-Mellon University
Publication Type
This report contains the results of a statistical analysis of the 1979 Survey of Inmates of State Correctional Facilities. The statistical analysis was undertaken to gain insight into the prison population, the criminal careers of prisoners, and the nature of the offender population.

The analysis is complicated for three major reasons. First, the survey does not represent a random sample from the offender population. This means that a variety of statistical adjustments are needed to overcome the sampling bias. Second, the survey was not adjusted for the length-biasing effect of sentence lengths. This problem requires adjustments to properly interpret the nature of the criminal careers of those in prison. Third, both the prisoner and offender populations are very heterogeneous, exhibiting a wide range of offending behavior (crime types) and rates. It is crucial to use statistical models which can capture this heterogeneity rather than using traditional models and methods in which the populations are treated as homogeneous. This report is organized in several sections. Section HIERMODEL contains a discussion of hierarchical modeling, a simple approach that incorporates heterogeneity into the offender population. The associated estimation technique, empirical Bayes methodology, is described and illustrated by an example. Section LENGTHBIAS contains an introduction of the problem of length-biased sampling and its impact on proper statistical inference (length-biased sampling is a particular problem for proper analysis of prison survey data). Section EXPLOR contains an exploratory analysis of the prison survey data. Section MODELFIT contains results of model fitting using the techniques outlined in earlier sections. Conclusions are also presented in Section MODELFIT. In Section FURTHER, further analyses are discussed which could be performed with this data set. Figures and 8 references. (Author abstract modified)

Date Created: January 17, 2012