Risk of Re-imprisonment for Parolees Statistical models by Arul Nadesu
PurposeThe purpose of this research is to improvecurrent offenders’ risk assessment practicein the Department.
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)
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
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.
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)
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.
Model 2Short Term Prisoners Re-imprisonment Over 5 Years
Model 3Community Offenders Reconviction Over 5 Years
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)
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)
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
Multicollinearity in Logistic Regression• …..is a results of strong correlations between independent variables• …..creates incorrect conclusions about relationships between independent and dependent variables
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)
SAS EM DiagramTransformed Logistic Regression Gini Tree Test Data MBR ScoreSource NNData NN T Assess Transformed NN PCA Principal Component Hybrid
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
False PositivePredicting low risk offenders as high risk
False NegativePredicting high risk offenders as low risk
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
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
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
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
Overall error rate of Hybrid Model False positive = 14.1 False negative = 15.3 Overall error rate = 14.7
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%