Transcript Estimating (and Understanding) Individual Trajectories

In Search of the Intermittent
Offender:
A Theoretical and Statistical
Journey
Megan C. Kurlychek, Ph.D.
Assistant Professor
Shawn Bushway, Ph.D.
Associate Professor
School of Criminal Justice
University at Albany
Goals

Describe population of individual
trajectories underlying age crime curve

Identify process of desistance

Is intermittency real?

How do these different models
reflect/impact practice?
Starting Point

Lifecourse criminologists care about individual
lifecourse trajectory/criminal career


Descriptive: Age Crime Curve Debate
 What is the underlying distribution that determines the AgeCrime Curve
Explanatory: Thornberry 1987:
 “The manner in which reciprocal effects and developmental
changes are interwoven in the interactional model can be
explicated by the concept of behavioral trajectories.(p. 882)
What Has Happened Since?

Panel models



Growth Curve Models (GCM) HLM
Group-based Trajectories Model (GTM) Proc Traj
Generalized Mixture Models (GMM) Mplus
yi ,t  0,i  1,i Agei ,t  2,i Agei2,t  3,i Agei3,t  e i ,t

Much annoying banter about which model is
“Right”
Bushway, S., G. Sweeten, P.
Nieuwbeerta (2009)
Measuring Long Term Individual
Trajectories of Offending Using
Multiple Methods. Journal of
Quantitative Criminology 25:259–286
What Did We Do?




Compared individual trajectories from
three models:
1) Individual time series for every person
2) Growth Curve model (HLM)
3) Group Trajectory model (Traj)
Criminal Career and Life Course
Study (CCLS)
Sample:
 4.615 persons convicted in 1977






4% random sample of all persons convicted in 1977
Oversample of persons convicted for serious
offenses, undersample of persons convicted for
traffic incidents
500 women (10%)
20% non-native (Surinam, Indonesia)
Mean age in 1977: 27 years; youngest: 12; oldest
79
Data from year of birth until 2003: for most over 50
years.
CCLS Data
For all persons we have information on:

Full criminal conviction histories (Rap sheets)


Life course events:



Timing, type of offense, type of sentence, incarceration.
Various types: marriage, divorce, children, moving,
death (GBA & Central Bureau Heraldry) – incl. Exact
timing.
Cause of death (CBS)
Data = conviction for periods not dead or
incarcerated
Average Curves: Raw Data & ITM
Job 2: Compare Best estimates of
Individual paths
Desistors

An individual who has a period where
offending probability is statistically greater
than zero, followed by at least 5 years
when probability of offending is
statistically indistinguishable from zero.
Comparison of Desistors

MODEL
Desistors (% of sample)
ITM
GCM
GTM
60.8%
27.5%
36.4%
ITM more flexible, better captures change
(but with error).
Conclusion

Lots of “up and down”




Could be noise
Could be intermittency
Can’t tell with conviction data – even with
50 years!
Need another approach recidivism/survival models?
In Search of the Intermittent
Offender:
A Theoretical and Statistical
Journey
Megan C. Kurlychek, Ph.D.
Assistant Professor
Shawn Bushway, Ph.D.
Associate Professor
School of Criminal Justice
University at Albany
Criminal Career Research
 Traditional
Question:
 “When
does a criminal career start
and when does it end.”
 Traditional
Answer (Blumstein 1986)
Instantaneous Desistance


Go immediately to zero
Very consistent with parole/probation
models


Pragmatic
Fits qualitative work: Going (and staying)
straight (Maruna)
Hazards


Probability that you are going to offend in
this period given that you have not
offended yet
Used in latest round of reentry models

When does ex-offender “look like” non
offender in terms of offending
Test of desistance using hazards
Barnett et. al. (1989)
Full Sample Predicted and Actual Hazards:
Desistance = .33 P = .3
Predicted
Actual
0.250
Hazard Rate
0.200
0.150
0.100
0.050
0.000
1
2
3
4
5
6
7
8
9 10 11
Years of Follow-Up
12
13
14
15
16
17
Barnett Modification




Starting point
Active career
Ending point (instantaneous desistance)
A few people restart career (Intermittency)
Theoretical Intermittency

Matza (1964)


Horney, Osgood and Rowe (1995):



Drift: Offenders “flirt” with criminal activity.
“local-life circumstance”
“Relapse”
ZIP Parameter in Trajectory Models
Alternative: Glide Path
Desistance as a process: “glide” path
towards zero ( Bushway et al. 2001, Laub
and Sampson 2001)
Theoretical Glide Path


Differential Association Theory/Social
Learning Theory
Social Control Theory
“Social bonds do not arise intact and full-grown
but develop over time like a pension plan
funded by regular contributions” Laub, Nagin
and Sampson (1998)
In Hazard Model

Both can explain FAT Tail



People still at high(er) risk after many years
BUT – Glide Path should be smooth
declining hazard rate
Intermittency – bumpy declining hazard
Our Data

Crime Control Effects of Sentencing in Essex County
New Jersey, 1978-1997.

Judge questionnaires completed by 18 judges in Essex
County NJ on cases sentenced in 1976-77.

1.
2.
3.
Follow up information was collected through 1997
New Jersey Offender Based Transaction System
Computerized Criminal History
New Jersey Department of Corrections Offender based
Correctional Information System
US Department of Justice Interstate Identification Index
Sample and Methods



All offenders with probation or short jail
sentences (n=661)
Follow for 20 years
Apply parametric survival time
distributions and employ graphical
comparisons and goodness of fit statistics
Measures

Dependent Variable: New arrest

Independent Variables:



Age of offender
Prior Probations and Violations
Race, Gender, Type/Seriousness of Offense,
Judge’s perception of risk
Three Distributions

Exponential


Assumes constant rate of offending
Hazard drops fast


Weibull


High rate offenders – everyone who hasn’t
desisted offends quickly
Smoothly declining hazard rate
Lognormal

Allows hazard rate to go up and down
Three Distributions

Exponential = Original Criminal Career

Weibull = Glide path

Lognormal = Intermittency
Goodness of Fit Tests
Exponential
Weibull
Weibull
Lognormal
Dif. p Dif.
p
223.9 0.0000 284 0.0000
60.3 0.0000
0
.2
.4
.6
.8
1
Weibull regression
0
5
10
analysis time
15
20
0
.1
.2
.3
.4
Log-normal regression
0
5
10
analysis time
15
20
Why the Lognormal

“Upswing” in the beginning


OR
Fat Tail (intermittency)
Models t0 to t5
Weibull
-log l.
BIC
Full
n=661
After 1 year
n=464
After 2 years
n=374
After 3 years
n=328
After 4 years
N=300
After 5 years
n=278
Lognormal
-log l
BIC
-1217.37 2525.65 -1187.22
Diff -Loglp
2465.358 60.292 0.0000
-790.13 1666.21 -783.61
1653.16
13.04 0.0000
-563.86 1210.65 -558.01
1198.95
11.7 0.0000
-449.29
979.68 -441.25
963.61
16.08 0.0000
-394.97
869.7 -390.66
859.98
8.62 0.0033
777.85
3.72 0.0538
-351.36
781.51
-349.5
Weibull Frailty Model
0
.2
.4
.6
Weibull regression
0
5
10
analysis time
15
20
High and Low Risk Offenders
0
.2
.4
.6
.8
1
Log-normal regression
0
5
10
analysis time
class=1
class=3
15
class=2
class=4
20
Conclusions



Glide path looks more realistic than strict
intermittency
People experience reduced risk as they
last longer on parole
But, don’t go to zero very quickly

Desistance takes time
Next Steps

Multi-Event Hazard

What happens after arrest?

For people who have not offended for 5
years?
Intermittency: should start offending again at a
regular rate
 Glide path: should continue to decrease in
offending rate

Policy Implications/Questions

Most people don’t desist “instantaneously”

Declining risk

Recidivate or not mentality may miss declining risk

Is it feasible to tolerate “less” offending?

Do current practices implicitly acknowledge reality?

Do changes in other behavior (work/housing/family)
serve as proxy for “declining hazard”