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Something Fishy? Uncovering heterogeneity in the

distribution of crime victimisation in general populations

Tim Hope and Paul NorrisSCCJR (CJ-QUEST)

University of EdinburghDecember 2008

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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

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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?

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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

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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

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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)

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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

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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

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Accuracy Verses Parsimony

• How many groups are required?-range of statistical indicators

-substantive interpretation is crucial

• Within group variation?

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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?

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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

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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%)

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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

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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%)

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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