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Corrections’ Vision
Improving public safety
Risk of Re-imprisonment for
Parolees
Statistical models
by Arul Nadesu
Purpose
The purpose of this research is to improve
current offenders’ risk assessment practice
in the Department.
Risk of Conviction and Risk of
Imprisonment (RoC*RoI)
In 1995, the Department developed
a statistical model, which predicts
the risk of re-imprisonment of an
offender over 5 years.
(based on Logistic Regression
modelling)
ROC*ROI is one of the tools used for
making decisions every day about offenders
• Pre-sentencing reports
• Security classification
• Eligibility for rehabilitation
• Parole Board decisions
Our Responsibility
It is important that we make sure that
such a risk assessment tool in practice is
of a very high standard in order to
manage the correctional system
effectively.
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:
Accommodating all the above changes in the criminal justice
system is very important for any risk assessment tool.
* 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)
Prison Population by Year
4706
44134500
4733
5107
5532
5739 5677
59735818
6057
6555
7046
7632
8100
7744
8362
87938662
44246
48929
51084
55256
61467
6572764529 65194
66403
71218
73657
76916 7667378454
80205
83667 8390085400
87147
4000
4500
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
2011
40000
45000
50000
55000
60000
65000
70000
75000
80000
85000
90000
95000
100000
New Zealand England and Wales
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
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.
Re-imprisonment rates over 60 months
Population (2002/03) Re-imprisoned (%)
Prisoners 52%
Community sentences 19%
All sentences XX%
My Approach
• Three models recommended (Parolees, Non Parolees, Community Offenders)
• Outcome Reconviction Vs Re-imprisonment
• Outcome Over 5 Years vs Over 2 Years
Model 1
Parolees Re-imprisonment Over 5 Years
Model 2
Short Term Prisoners Re-imprisonment
Over 5 Years
Model 3
Community 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 Regression
By examining the Variance Inflation Factor (VIF) for
all variables we can remove the Multicollinearity
(Variables with VIF values more than 5 are removed)
SAS EM Diagram
Gini Tree
Principal Component
Transformed
Source
Data
Logistic Regression
MBR
NN
NN T
NN PCA
Test Data
Transformed
Score
Assess
Hybrid
ROC Chart
Hybrid
Reg
MBR
Tree
NN
NNT
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
ROC Chart
Hybrid
Reg
MBR
Tree
NN
NNT
Area Under Curve
Model Type AUC
Logistic Reg. 2-Way Interactions 0.83
CL Tree Gini Tree 0.81
MBR 4 Neighbours 0.85
Neural Net. 14 Neurons 0.92
Neural Net. Transformed 14 Neurons 0.91
Hybrid Using the above 2 models 0.95
AUC sited for RoC*RoI = 0.78
False Positive
Predicting low risk offenders
as high risk
False Negative
Predicting high risk offenders
as low risk
Misclassification error rates
Model Type Training Test
Logistic Reg. 2-Way Interactions 24.8
CL Tree Gini Tree 24.1
MBR 4 Neighbours 22.2
Neural Net. 14 Neurons 11.4
Neural Net. Transformed 14 N 11.3
Hybrid Using the above 2 7.2
Misclassification error rates
Model Type Training Test
Logistic Reg. 2-Way Interactions 24.8 22.1
CL Tree Gini Tree 24.1 25.8
MBR 4 Neighbours 22.2 27.5
Neural Net. 14 Neurons 11.4 19.4
Neural Net. Transformed 14 N 11.3 18.4
Hybrid Using the above 2 7.2 14.7
The Distribution of Risk of Re-imprisonment, Released Prisoners
Parolees (Hybrid model)
0
5
10
15
20
25
Less
than 0.1
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
More
Parolees (RoC*RoI)
0
5
10
15
20
25
Less
than 0.1
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
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%