Risk of re imprisonment for parolees

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Risk of re imprisonment for parolees

  1. 1. Corrections’ VisionImproving public safety
  2. 2. Risk of Re-imprisonment for Parolees Statistical models by Arul Nadesu
  3. 3. PurposeThe purpose of this research is to improvecurrent offenders’ risk assessment practicein the Department.
  4. 4. Risk of Conviction and Risk of Imprisonment (RoC*RoI)In 1995, the Department developeda statistical model, which predictsthe risk of re-imprisonment of anoffender over 5 years.(based on Logistic Regressionmodelling)
  5. 5. ROC*ROI is one of the tools used formaking decisions every day about offenders• Pre-sentencing reports• Security classification• Eligibility for rehabilitation• Parole Board decisions
  6. 6. Our ResponsibilityIt is important that we make sure thatsuch a risk assessment tool in practice isof a very high standard in order tomanage the correctional systemeffectively.
  7. 7. The reconviction patterns of offenders are being influenced by:• Government crime reduction strategy• Police offence clearance rates (from 31% to 47%)• New sentencing legislation (eg: Sentencing Act and Parole Act, July 2002, Sentence and Parole Reform Act, Oct 2007)
  8. 8. The reconviction patterns of offenders are being influenced by:* Government crime reduction strategy* Police offence clearance rates (from 31% to 47%)* New sentencing legislation (eg: Sentencing Actand Parole Act, July 2002, Sentence and ParoleReform Act, Oct 2007)Accommodating all the above changes in the criminal justice system is very important for any risk assessment tool.
  9. 9. Prison Population by Year10000 100000 9500 95000 New Zealand England and Wales 9000 87147 90000 85400 83667 83900 8500 8793 85000 8662 80205 78454 8362 8000 76916 76673 80000 8100 73657 7500 71218 7744 75000 7632 7000 66403 70000 65727 65194 7046 64529 6500 61467 65000 6555 6000 60000 55256 6057 5973 5500 5739 5818 55000 51084 5677 5532 48929 5000 50000 5107 44246 4500 4706 4733 45000 4500 4413 4000 40000 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20
  10. 10. The New Zealand situation• Department of Corrections manages about 8500 prisoners in 19 prisons.• Department of Corrections manages more than 40,000 offenders in the community
  11. 11. Recidivism rates in New Zealand• 52% of released prisoners were convicted of a new offence returned to prison at least once during the 60 months follow-up period.
  12. 12. Re-imprisonment rates over 60 months Population (2002/03) Re-imprisoned (%) Prisoners 52% Community sentences 19% All sentences XX%
  13. 13. My Approach• Three models recommended (Parolees, Non Parolees, Community Offenders)• Outcome Reconviction Vs Re-imprisonment• Outcome Over 5 Years vs Over 2 Years
  14. 14. Model 1Parolees Re-imprisonment Over 5 Years
  15. 15. Model 2Short Term Prisoners Re-imprisonment Over 5 Years
  16. 16. Model 3Community Offenders Reconviction Over 5 Years
  17. 17. 14 Variables selected for model 1• Current Age• Age of first imprisonment• Age of first conviction• Age of first court appearance• First timer (Y/N)• Gang association (Y/N)• Gender (M/F)• Drug user (Y/N)
  18. 18. 14 Variables selected for model 1• Sentence length for the last sentence• Offence type for the last sentence (V/S/O)• Number of previous convictions (in the last 5 years)• Number of previous community sentences (in the last 5 years)• Number of previous imprisonments (in the last 5 years)• Time spent in prison (in the last 5 years)
  19. 19. Type of modelling considered• Logistic Regression (Stepwise, Backward, Forward, Full Model with 2- Way interactions)• Classification Trees (Gini, Entropy)• Memory Based Reasoning (MBR)• Neural Network (NN)• Hybrid Model
  20. 20. Multicollinearity in Logistic Regression• …..is a results of strong correlations between independent variables• …..creates incorrect conclusions about relationships between independent and dependent variables
  21. 21. Multicollinearity in Logistic RegressionBy examining the Variance Inflation Factor (VIF) forall variables we can remove the Multicollinearity(Variables with VIF values more than 5 are removed)
  22. 22. SAS EM DiagramTransformed Logistic Regression Gini Tree Test Data MBR ScoreSource NNData NN T Assess Transformed NN PCA Principal Component Hybrid
  23. 23. ROC Chart Hybrid NNT NN MBR TreeReg
  24. 24. Area Under Curve (AUC) A guide for assessing the accuracy of a predictive model• .90- 1 = Excellent model• .80-.90 = Good model• .70-.80 = Fair model• .60-.70 = Poor model• .50-.60 = Fail
  25. 25. ROC Chart Hybrid NNT NN MBR TreeReg
  26. 26. Area Under CurveModel Type AUCLogistic Reg. 2-Way Interactions 0.83CL Tree Gini Tree 0.81MBR 4 Neighbours 0.85Neural Net. 14 Neurons 0.92Neural Net. Transformed 14 Neurons 0.91Hybrid Using the above 2 models 0.95AUC sited for RoC*RoI = 0.78
  27. 27. False PositivePredicting low risk offenders as high risk
  28. 28. False NegativePredicting high risk offenders as low risk
  29. 29. Misclassification error ratesModel Type Training TestLogistic Reg. 2-Way Interactions 24.8CL Tree Gini Tree 24.1MBR 4 Neighbours 22.2Neural Net. 14 Neurons 11.4Neural Net. Transformed 14 N 11.3Hybrid Using the above 2 7.2
  30. 30. Misclassification error ratesModel Type Training TestLogistic Reg. 2-Way Interactions 24.8 22.1CL Tree Gini Tree 24.1 25.8MBR 4 Neighbours 22.2 27.5Neural Net. 14 Neurons 11.4 19.4Neural Net. Transformed 14 N 11.3 18.4Hybrid Using the above 2 7.2 14.7
  31. 31. Parolees (Hybrid model)The Distribution of Risk of Re-imprisonment, Released Prisoners 25 20 15 10 5 0 Less 0.1 - 0.2 0.2 - 0.3 0.3 - 0.4 0.4 - 0.5 0.5 - 0.6 0.6 - 0.7 0.7 - 0.8 0.8 - 0.9 0.9 or than 0.1 More
  32. 32. Parolees (RoC*RoI)25201510 5 0 Less 0.1 - 0.2 0.2 - 0.3 0.3 - 0.4 0.4 - 0.5 0.5 - 0.6 0.6 - 0.7 0.7 - 0.8 0.8 - 0.9 0.9 or than 0.1 More
  33. 33. Overall error rate of Hybrid Model False positive = 14.1 False negative = 15.3 Overall error rate = 14.7
  34. 34. Findings• New Hybrid model has a superior prediction• The proportion of offenders’ risk score lying between 0.4 and 0.6 is reduced from 22% to 10%

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