An Evaluation of California's Inmate Classification System Using a GeneralizedRegression Discontinuity DesignRichard A. Berk; Jan de LeeuwJournal of the American Statistical Association, Vol. 94, No. 448. (Dec., 1999), pp. 1045-1052.Stable URL:http://links.jstor.org/sici?sici=0162-1459%28199912%2994%3A448%3C1045%3AAEOCIC%3E2.0.CO%3B2-VJournal of the American Statistical Association is currently published by American Statistical Association.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/astata.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact [email protected]://www.jstor.orgFri Sep 14 18:31:21 2007An Evaluation of California's Inmate Classification System Using a Generalized Regression Discontinuity Design Richard A. BERKand Jan de LEEUW Published studies using the regression discontinuity design have been limited to cases in which linear regression is applied to a categorical treatment indicator and an equal interval outcome. This is unnecessarily narrow. We show here how a generalization the usual regression discontinuity design can be applied in a wider range of situations. We focus on the use of categorical treatment and response variables, but we also consider the more general case of any regression relationship. We also show how a resampling sensitivity analysis may be used to address the credibility of the assumed assignment process. The broader formulation is applied to an evaluation of California's inmate classification system, which is used to allocate prisoners to different kinds of confinement. KEY WORDS: Regression discontinuity design; Program evaluation; Sensitivity analysis. 1. INTRODUCTION With the rapid growth of prison populations and firm bud- get constraints imposed by state legislatures, prison systems across the country have been looking for measures to im- prove their efficiency. California is no different, and the Cal- ifornia Department of Corrections (CDC) has been under pressure to seek to new ways to get more for less. Among the strategies being considered are methods to house pris- oners so that more costly higher-security beds are allocated only to prisoners who truly need them. A first step would be an evaluation of how well the system currently allocates inmates to incarceration facilities. In July 1996, we were asked by the CDC to provide an analysis of how inmates are currently screened and placed. The key criterion for effective placement was defined by CDC as inmate misconduct in prison. Serious misconduct can substantially disrupt prison operations and put inmates and prison staff in harm's way. We were not asked to ad- dress later misconduct in the community outside of prison, because the issues are quite different and require rather dif- ferent research designs. Two specific questions naturally followed: 1. How well do current placement methods sort inmates by their potential for misconduct? 2. How effective currently are different placements in controlling prisoner misconduct? Although these questions might seem simple enough, we had access only to observational data with which to provide answers. We raised the possibility of randomized experi- ments, but for various practical reasons, randomized exper- iments were at the time out of the question. But because inmates were most often placed through a computed "clas- Richard A. Berk is Professor and Jan de Leeuw is Professor, Depart- ment of Statistics, University of California, Los Angeles, CA 90095 (E-mail: [email protected]).The research reported in this article would have been impossible to undertake without the full cooperation the California Department of Corrections. Indeed, key staff were more like collaborators than clients, and the authors learned an enormous amount working with them on a regular basis. Thanks also go to the students and staff of the UCLA Statistical Consulting Center who at various times worked on the project. sification score," there was the real prospect of using a re- gression discontinuity design (Berk and Rauma 1983; Cook and Campbell 1979; Trochim 1984). That is, CDC's most common placement procedures assigned inmates to differ- ent kinds of housing on the basis of a known covariate. Under such circumstances, it is now well understood that conditioning on the assignment covariate alone can lead to unbiased estimates of treatment effects (Rubin 1977). Un- fortunately, the outcome of interest was binary, and past applications of the regression discontinuity design had been limited to equal interval outcomes. In response, we generalized in the usual regression dis- continuity design to any regression function that is invariant across different interventions (in the categorical treatment case) or different doses (in the quantitative treatment case). We also developed a resampling sensitivity test to consider assumptions made about the assignment process. We report on these efforts as part of our evaluations of CDC's inmate classification and placement system. A number of other is- sues and details can be found in our full report to the CDC (Center for Statistics 1997a). 2. CALIFORNIA'S INMATE CLASSIFICATION SYSTEM 2.1 Summary of the Classification and Placement System Each inmate is sent after sentencing to a CDC reception center. There information is collected on a standardized form,