Bhati, Avinash (2007): Learning from multiple analogies: an Information Theoretic framework for predicting criminal recidivism.

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Abstract
If recidivism is defined as rearrest within a finite period following release from prison, then the kinds of outcomes typically available to researchers include: (i) whether or not the individual was rearrested within the followup period; (ii) how many times the individual was rearrested; and (iii) what was the duration from release to first (or subsequent) rearrest. Since these outcomes are all different manifestations of the same underlying stochastic process, they provide multiple analogies from which to recover information about it. This paper develops a semiparametric approach for utilizing information in these, and several other related outcomes, to predict criminal recidivism and presents preliminary findings.
Item Type:  MPRA Paper 

Original Title:  Learning from multiple analogies: an Information Theoretic framework for predicting criminal recidivism 
Language:  English 
Keywords:  information theory; criminal recidivism; predictive modeling; multiple analogies 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics 
Item ID:  11850 
Depositing User:  Avinash Bhati 
Date Deposited:  02. Dec 2008 06:37 
Last Modified:  12. Feb 2013 08:20 
References:  Allison, P. (1982). Discretetime methods for the analysis of event histories. Sociological Methodology 13:61–98. Allison, P. (1984). Event history analysis: Regression for Longitudinal Data. Newbury Park: Sage. Alt, J.E., King, G., and Signorino, C.S. (2001). Aggregation among binary, count, and duration models: Estimating the same quantity from different levels. Political Analysis 9(1):21–44. Asadi, M., Ebrahimi, N., Hamedani, G. G., and Soofi, E. (2005). Minimum Dynamic Discrimination information models. Journal of Applied Probability 42(3):643660. Bhati, A.S. (in press). Estimating the number of crimes averted by incapacitation: An Information Theoretic approach.” Journal of Quantitative Criminology. Bhati, A.S. (2007). Studying the effects of incarceration on offending trajectories: An Information Theoretic approach. Washington, DC: The Urban Institute. Bhati, A.S., and Piquero, A.R. (under review). On the effect of incarceration on subsequent individual criminal offending: Deterrent, criminogenic, or null effects. Beck, N. (1998). Modelling space and time: The event history approach. Pg. 191–213 in E. Scarbrough and E. Tanenbaum eds. Research strategies in the social sciences. New York, NY: Oxford University Press. BoxSteffensmeier, J.M., and Jones, B.S. (2004). Event history modeling: A guide for social scientists. Cambridge, UK: Cambridge University Press. Bureau of Justice Statistics. (2002). Recidivism of prisoners released in 1994, Codebook for dataset 3355. Downloaded from NACJD in April 2007. Cameron, C., and Trivedi, P. (1998). The analysis of count data. New York, NY: Cambridge University Press. Dean, C.B., and Balshaw, R. (1997). Efficiency lost by analyzing counts rather than event times in Poisson and overdispersed Poisson regression models. Journal of the American Statistical Association 92(440):1387–1398. Diamond, S. (1959). Information and error: An introduction to statistics. New York, NY: Basic Books. Donoho, D.L., Johnstone, I. M., Joch, J. C., and Stern, A. S. (1992). Maximum entropy and nearly black objects. Journal of the Royal Statistical Society B54:4181. Ebrahimi, N., Habibullah, M., and Soofi, E. (1992). Testing exponentiality based on KullbackLeibler information. Journal of the Royal Statistical Society B 54(3):739748. Ebrahimi, N., and Kirmani, S. N. U. A. (1996). A characterization of the proportional hazard model through a measure of discrimination between two residual life distributions. Biometrika 83(1):233235. Ebrahimi, N., and Soofi, E. (2003). Static and dynamic information for duration analysis. Invited presentation given at A conference in honor of Arnold Zellner: Recent developments in the theory, method, and application of information and entropy econometrics. Washington, D.C. Accessed February, 2007 from http://www.american.edu/cas/econ/faculty/golan/golan/Papers/8_20soofi.pdf Ezell, M.E., Land, K.C., and Cohen, L.E. (2003). Modeling multiple failure time data: A survey of variancecorrected proportional hazard models with applications to arrest data. Sociological Methodology 33(1):111167. Glaser, D. (1955). The efficacy of alternate approaches to parole prediction. American Sociological Review 20:283–287. Gottfredson, S.D., and Gottfredson, D.M. (1986). Accuracy of prediction models. Pg. 212–290 in eds. Blumstein, Cohen, Roth, and Visher Criminal careers and “career criminals” volumes II. Washington, DC: National Academy Press. Greene, W. (2000). Models with discrete dependent variables. Pg. 811–895 in Econometric analysis (4th edition). Upper Saddle River, NJ: Prentice Hall. Gull, S.F. (1989). Developments in maximum entropy data analysis. in Maximum entropy and Bayesian statistics ed. Skilling, J. Boston, MA: Kulwer. Gull, S.F., and Danielle, G.J. (1978). Image reconstruction from incomplete and noisy data. Nature 272:686690. Heckman, J., and Singer, B. (1984a). Econometric duration analysis. Journal of Econometrics 24:63–132. Heckman, J., and Singer, B. (1984b). Amethod for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52:271–320. Jaynes, E.T. (1957a). Information Theory and Statistical Mechanics. Physics Review 106:620–630. Jaynes, E.T. (1957b). Information Theory and Statistical Mechanics II. Physics Review 108:171–190. Jaynes, E.T. (1979). Where do we stand on maximum entropy? Pg. 15–118 in R.D. Levine and M. Tribus (eds.) The maximum entropy formalism. Cambridge, MA: MIT Press. Jaynes, E.T. (1986). Bayesian methods: An introductory tutorial. Pg. 1–25 in J.H. Justice (ed.) Maximum entropy and Bayesian methods in applied statistics. Cambridge, UK: Cambridge University Press. Jaynes, E.T. (1988). Discussion. American Statistician. 42:280–281. Justice, J.H. ed. (1986). Maximum entropy and Bayesian methods in applied statistics. Cambridge, UK: Cambridge University Press. Kalbfleisch, J.D., and Prentice, R.L. (1980). The statistical analysis of failure time data. New York: Wiley. King, G. (1977). A solution to the ecological inference problem. Princeton, NJ: Princeton University Press. King, G. (1989). Variance specification in event count models: From restrictive assumptions to a generalized estimator. American Journal of Political Science 33(3):762–784. King, G., Rosen, O., and Tanner, M.A. eds. (2004). Ecological inference: New methodological strategies. Cambridge, UK: Cambridge University Press. Kullback, S. (1959). Information theory and statistics. New York, NY: John Wiley. Lancaster, T. (1990). The analysis of transition data. New York, NY: Cambridge University Press. Langan, P.A., and Levin, D.J. (2002). Recidivism of prisoners released in 1994. Special report. Washington, DC: Bureau of Justice Statistics. Levine, R.D. and Tribus, M. eds. The maximum entropy formalism. Cambridge, MA: MIT Press. Lin, D.Y., Wei, L.J., and Ying, Z. (1998). Accelerated failure time models for counting processes. Biometrika 85(3):605–618. Lipton, D., Martinson, R., and Wilks, J. (1975). The effectiveness of correctional treatment: A survey of treatment valuation studies. New York, NY: Praeger Press. Maltz, M.D. (1984). Recidivism. Orlando, FL: Academic Press, Inc. Mathai, A.M. (1975). Basic concepts in Information Theory and statistics: Axiomatic foundations and applications. New York, NY: JohnWiley. Mayer, K.U. and Tuma, N.B. ed. (1990). Event history analysis in life course research. Madison, WI: The University ofWisconsin Press. Michell, S.M., and Moore, W.H. (2002). Presidential uses of force during the Cold War: Aggregation, truncation, and temporal dynamics. American Journal of Political Science 46(2):438–452. Mittelhammer, R. C., Judge, G. G., and Miller, D. J. (2000). Econometric Foundations. Cambridge, UK: Cambridge University Press. Ryu, H.K. (1993). Maximum entropy estimation of density and regression functions. Journal of Econometrics 56:397–440. Schmidt, P., and Witte, A.D. (1988). Predicting recidivism using survival models. New York, NY: SpringerVerlag. Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal 27:379423. Sherman, L.W., Gottfredson, D., MacKenzie, D., Eck, J., Reuter, P., and Bushway, S. (1997). Preventing crime: What works, what doesn’t, and what’s promising? A Report to the United States Congress. Washington, DC: National Institute of Justice. (http://www.ncjrs.gov/works) Skilling, J. (1989). Maximum entropy and Bayesian methods. Dordrecht, the Netherlands: Kluwer. Soofi, E.S. (1994). Capturing the intangible concept of information. Journal of the American Statistical Association 89(428):1243–1254. Soofi, E.S. (2000). Principal Information Theoretic approaches. Journal of the American Statistical Association 95(452):1349–1353. Soofi, E.S., Ebrahimi, N., and Habibullah, M. (1995). Information distinguishability with application to analysis of failure data. Journal of the American Statistical Association 90(430):657–668. Winkelmann, R. (1995). Duration dependence and dispersion in countdata models. Journal of business & economic statistics 13(4):467–474. Yamaguchi, K. (1991). Event history analysis. Newbury Park, CA: Sage Publications. Zellner, A. (1988). Optimal information processing and Bayes’ theorem. American Statistician 42:278–284. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/11850 