Estimating the Total Active Offender Population

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Estimating the Total Active Offender Population

• Martin Kelly
• GSS Methodology Conference, June 07

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Presentation

• Introduction background
• What is the active offender population?
• How do we calculate this population?
• Results / outputs
• Questions

3
Introduction

• Home Office methodology for estimating the size
  and profile of the active offender population
• Developed in conjunction with Red Scientific Ltd.
• The methodology and the estimates derived from it
  are unpublished and awaiting peer review
• Results should therefore be viewed as unofficial
  and are subject to change

4
Background

• Evidence-based policy making
• Crime Trajectory Model
• Model used to evaluate impact of crime reduction
  policies on total number of offenders and
  offences
• This model requires a detailed understanding of
  the total offending population
• Model starts in 02/03

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Active Offender Population?

• Population snapshot. Total estimated number of
  offenders and offences in 02/03
• Total?
• Those we know about (Convicted)
• Those we dont know about (Non-Convicted)
• Convicted covers the following
• Reprimands
• Warnings
• Cautions
• Court Convictions

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What do we produce?

• Total estimated number of offenders and offences
  broken down by
• 14 offence types
• Offender age (10-65)
• Gender
• Also broken down by segment
• NPNS, NPS, PNS, PS, DRO
• Serious or non-serious offences / offenders
• Prolific or non-prolific offenders
• Drug-related offenders

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14 Offence Types?
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14 Offence Types?
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Data Sources

• PNC Police National Computer
• Police disposals and convictions
• OCJS Offending Crime and Justice Survey
• National longitudinal survey examining extent of
  offending (amongst other things)
• AS Arrestee Survey
• Survey of arrestees aimed at measuring
  self-reported offending and drug-use
• BCS British Crime Survey
• Survey of households in England and Wales aimed
  at measuring crime levels

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Total Estimated Offences Offenders

• We already have total estimated offences for the
  14 offence types
• Only headline figures no detailed populations
• Come from surveys (mainly BCS)

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Total Population of Offences
Total Population of Offenders
OFFENDERS
OFFENCES
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Total Population of Offences
Total Population of Offenders
OFFENDERS
OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
27M Offences
??? Offenders
15
Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Convicted Offences Convicted Offenders

• PNC extract
• PNC is used by police for operational purposes
• Also used by Home Office for research
• From this we extract information on all convicted
  offences and convicted offenders for 14 offence
  types in 02/03

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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Non-Convicted Offences by Convicted Offenders

• Bayes Theorem
• A convicted offender with y convictions will
  actually have committed x offences. x y
• P(x offences y convictions)
• P(y convictions x offences) P(x offences)
• P(y convictions)

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Non-Convicted Offences by Convicted Offenders

• P(x offences)
• Distributions of offences from AS and OCJS
• Proportion of offenders who have committed 1
  domestic burglary, 2 domestic burglaries

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Non-Convicted Offences by Convicted Offenders

• P(y convictions)
• Distributions of convictions from PNC
• Proportion of offenders with 1 conviction for
  domestic burglary, 2 convictions
• P(y convictions x offences)
• Calculated using Binomial Distribution

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Non-Convicted Offences by Convicted Offenders

• Pi probability of being convicted for offence
  type i
• PDB Total Domestic Burglary Convictions /
  Total Estimated Domestic Burglaries
• Does Pi remain constant?
• For each offence type, 3 values combined to
  calculate P(x offences y convictions)
• Expected extra offences for offenders with y
  convictions calculated

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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES N
27M Offences
??? Offenders
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Additional Non-Convicted Offences

• N Additional Non-Convicted Offences
• 27M estimated offences
• - convicted offences
• - non-convicted offences by convicted offenders
• In fact, 14 different values
• N1, N2,, N14 (S N)
• Take these 14 values and spread them over
  existing offences
• Assign to segment using OCJS
• Assign to age gender using existing offence
  distributions

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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS P
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Additional Non-Convicted Offenders

• How many offenders are responsible for these N
  offences?
• P, total number of non-convicted offenders
• From OCJS we can estimate the proportion of
  non-convicted offenders who have committed i
  non-convicted offences, q1, q2,
• Number of non-convicted offenders with 1
  non-convicted offence q1P
• Number of non-convicted offenders with 2
  non-convicted offences q2P

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Additional Non-Convicted Offenders

• Therefore,
• N 1.q1P 2.q2P 3.q3P
• P N / (1.q1 2.q2 3.q3 )
• This value P is spread proportionally over the
  existing known offenders using OCJS and age
  distribution

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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
??? Offenders
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Total Population of Offences
Total Population of Offenders
CONVICTED OFFENCES
CONVICTED OFFENDERS
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
27M Offences
4.2M Offenders
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Drug-Related Offenders

• Population only currently broken down by 4
  segments (NPNS, NPS, PNS, PS)
• No drug-related offenders (DRO) segment
• Arrestee Survey (AS) is used to estimate
  proportion of offenders (and corresponding
  offences) who are drug users
• These offenders (and corresponding offences) are
  then moved to a new DRO segment

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Results
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Results
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What next?

• Updated Calculation Tool
• Initial calculations carried out over 13
  spreadsheets and 68 worksheets
• New tool uses 1 key spreadsheet
• Easier to update with new data
• Sensitivity analysis
• Now facing further data issues
• OCJS was restricted to 10-25 year olds
• OCJS now suspended
• Future of AS uncertain

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Alternative Methodology?

• Capture / Recapture Methods
• Method for estimating the size of partly hidden
  populations
• This has already been used to estimate drug use
  prevalence in the UK by the Home Office
• Any other suggestions?

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Summary

• We have developed a statistical model to estimate
  a population of total offences and offenders
• We have essentially used our knowledge of known
  convicted offenders and known convicted offences
  combined with survey data to extrapolate this
  population
• This estimated population is the basis of
  modelling that we do to estimate the impact of
  potential crime reduction policies and
  initiatives

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Finally
"Reports that say that something hasn't happened
are always interesting to me, because as we know,
there are known knowns there are things we know
we know. We also know there are known unknowns
that is to say we know there are some things we
do not know. But there are also unknown unknowns
-- the ones we don't know we don't know."
Donald Rumsfeld
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Questions
Martin Kelly martin.kelly_at_homeoffice.gsi.gov.uk
020 7035 3392