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%