www.sccjr.ac. uk Something Fishy? Uncovering heterogeneity in the distribution of crime victimisation in general populations Tim Hope and Paul Norris SCCJR (CJ-QUEST) University of Edinburgh December 2008
Mar 28, 2015
www.sccjr.ac.uk
Something Fishy? Uncovering heterogeneity in the
distribution of crime victimisation in general populations
Tim Hope and Paul NorrisSCCJR (CJ-QUEST)
University of EdinburghDecember 2008
www.sccjr.ac.uk
The Distribution of Property Crime in the BCS
Maximum count present in BCS is 27. Based on six crimes capped at 6 incidents per crime.
Unweighted BCS Sample: 1992 - 11713, 1996 - 16348, 2001 - 8927, 2003/04 -37931, 2006/07 - 47027, Total - 121946
www.sccjr.ac.uk
Understanding and Modelling the Distribution of
Crime• The distribution shown on the
previous slide poses two questions :-
- Substantive question: What is the data generation process that underpins the distribution?
- Statistical question: What kind of dependent variable is best employed to model victimisation?
www.sccjr.ac.uk
Theoretical Models of Victimisation
• Simple Exposure (pure heterogeneity)
• Mixture Model
• Simple RV (pure state-dependency)
T. Hope and A. Trickett (2004). ‘La distribution de la victimation dans la population’, Déviance et Société, 28 (3), 385-404.
- Large proportion of the population experience no victimisation
- Small proportion of the population experience chronic victimisation
- One or more groups for low-level victimisation
www.sccjr.ac.uk
Dependent Variable for Victimisation Research
• Type of crime victimisation– Type of incident– One type verses more generalist victim
• Frequency of crime victimisation– Nominal (0,1), Ordinal (0, 1, 2+), Count
(0-n)– Distribution of count variables – Poisson verses Negative Binomial
www.sccjr.ac.uk
Data• British Crime Survey - England and Wales
(BCS)– 1992, 1996, 2001, 2003/04, 2006/07
• Scottish Crime Victimisation Survey (SCVS)– 1993, 1996, 2000, 2003, 2006
• Crime types– Household Property Crime (6 questions)– Count data (victim screeners, capped at 6)
www.sccjr.ac.uk
Latent Class Models• Latent Class Analysis (LCA) is analogous to cluster Latent Class Analysis (LCA) is analogous to cluster
analysis but: analysis but:
-Can handle missing data-Can handle missing data--Can handle non-normal dataCan handle non-normal data
-Can be used with longitudinal -Can be used with longitudinal datadata
www.sccjr.ac.uk
A Simple LCA Model
Victim Type
Household Theft Victimisation Vandalism Victimisation Forced Entry Victimisation+ + = Total Victimisation
Age Household Income Neighbourhood Type
LCA indicator considers both level of victimisation and type of crime
www.sccjr.ac.uk
Accuracy Verses Parsimony
• How many groups are required?-range of statistical indicators
-substantive interpretation is crucial
• Within group variation?
www.sccjr.ac.uk
Distribution of Victimisation Indicators
• Count data often modelled using Poisson distribution
• Victimisation appears to follow Negative Binomial distribution
BCS Combined Sample
Variable Mean Std. Dev Variance Ratio of Variance to Mean
Defaced Property (Outside) 0.09 0.50 0.25 2.72
Stolen Property (Outside) 0.08 0.40 0.16 1.97
Property Stolen from Home 0.01 0.14 0.02 2.30
Tried to Gain Entry to Commit Theft/Damage 0.04 0.26 0.07 1.86
Entered Property and Caused Damage 0.00 0.09 0.01 2.16
Entered Property and Commited Theft 0.03 0.23 0.05 1.49
Unweighted BCS Sample: 1992 - 11713, 1996 - 16348, 2001 - 8927, 2003/04 -37931, 2006/07 - 47027, Total - 121946
• What about zero-inflation?
www.sccjr.ac.uk
ABIC for BCS Data• Lower ABIC figures represent better
fit between model and data
• ABIC suggests six groups should be used
208000
209000
210000
211000
212000
213000
214000
1 2 3 4 5 6 7
Number of Groups
AB
IC S
tati
sti
c
Results based on Negative Binomial Distribution. Results using zero-inflated Negative Binomial reveal an identical pattern but exhibit a slightly worse fit to the data
www.sccjr.ac.uk
BCS Six Class Solution
00.20.40.60.8
11.21.41.61.8
Type of Crime
Nu
mb
er
of
Ev
en
ts Non-victims (79.8%)
Outside Victims (13.4%)
Moderate Victims (2.4%)
One-off Victims (3.8%)
Moderate Victims 2 (0.2%)
Chronic Victims (0.3%)
00.20.40.60.8
11.21.41.61.8
Defac
ed p
rope
rty (o
u tside
)
Stolen
pro
perty
out
side
Prope
rty st
olen
from
hom
e
Tried
to g
ain e
n ty to
com
mit
thef
t/dam
age
Enter
ed p
rope
rty a
nd ca
used
dam
age
Enter
ed p
rope
rty a
nd co
mm
itted
thef
t
Type of Crime
Nu
mb
er
of
Ev
en
ts
Non-victims (79.8%)
Chronic Victims (0.3%)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Type of Crime
Nu
mb
er o
f E
ven
ts
Outside Victims (13.4%)
Moderate Victims (2.4%)
One-off Victims (3.8%)
Moderate Victims 2 (0.2%)
www.sccjr.ac.uk
Results for Scottish Data• Distribution of property crime in
Scottish data is very similar to BCS
• ABIC statistic suggests 4 class solution is optimal
Results based on Negative Binomial Distribution. Results using zero-inflated Negative Binomial reveal an identical pattern but exhibit a slightly worse fit to the data
39000
39100
39200
39300
39400
39500
39600
39700
39800
39900
1 2 3 4 5 6 7
Number of Groups
AB
IC
S
ta
tis
tic
www.sccjr.ac.uk
Scottish 4 Class Solution
0
0.2
0.4
0.6
0.8
1
1.2
Defac
ed p
rope
rty (o
u tside
)
Stolen
pro
perty
out
side
Prope
rty st
olen
from
hom
e
Tried
to g
ain e
n ty to
com
mit
thef
t/dam
age
Enter
ed p
rope
rty a
nd ca
used
dam
age
Enter
ed p
rope
rty a
nd co
mm
itted
thef
t
Type of Crime
Me
an
Nu
mb
er
of
Ev
en
ts
One-off Victims (2.6%)
Non-victims (85.2%)
Chronic Victims (0.4%)
Outside Victims (11.8%)
www.sccjr.ac.uk
Summary• Overall distribution obscures
heterogeneity• Heterogeneity of both substantive and statistical interest
• Most “uncertainty” occurs around the middle of the distribution
• Key issues around how solution is affected by sample design, prevalence of incidents and how useful apparent classes are for analysis