Estimating the Active Offender Population

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Estimating the Active Offender Population

• Martin Kelly

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Introduction

• Todays presentation looks at a Home Office
  methodology for determining 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  are unpublished and awaiting peer review.
• The estimates that will be presented today should
  therefore be viewed as unofficial and are subject
  to change.

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Background

• Evidence Based Policy
• Increasingly there is a focus on evidence based
  policy.
• There are numerous policies regarding crime
  reduction.
• Crime Trajectory Model
• The Crime Trajectory Model was built to produce
  crime projections based on anticipated crime
  reduction interventions and policies.
• This model requires a detailed understanding of
  the offending population.

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What is the Active Offender Population?

• Total estimated number of offenders and offences
  in 02/03
• Those we know about (Convicted)
• Those we dont know about (Non-Convicted)
• Final Population split into segments based on
• Serious or non-serious offences?
• Prolific or non-prolific offenders
• Prolific is defined as 6 or more offences in a
  year
• Drug Related Offender
• Offender has used crack / heroin in past 12
  months
• Ages 10 65, Male and Female

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Not all Offences are Covered
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Not all Offences are Covered
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Key Sources of Information

• PNC Police National Computer
• Contains information on 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 people arrested aimed at measuring
  drug-use and self-reported offending

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CONVICTED OFFENDERS
CONVICTED OFFENCES
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CONVICTED OFFENDERS
CONVICTED OFFENCES
???
TOTAL ESTIMATED OFFENCES
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CONVICTED OFFENDERS
CONVICTED OFFENCES
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
???
TOTAL ESTIMATED OFFENCES
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CONVICTED OFFENDERS
CONVICTED OFFENCES
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
TOTAL ESTIMATED OFFENCES
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Non-Convicted Offences by Convicted Offenders
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS

• Bayes Theorem Used
• An offender with y convictions will actually have
  x offences (xy)
• 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
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS

• P (x offences) distribution of offences
• Based on OCJS and AS
• Exponential distributions fitted to data
• P(y convictions) distribution of convictions
• Directly from PNC

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Non-Convicted Offences by Convicted Offenders
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS

• P(y convictions x offences)
• Assumed to follow a Binomial Distribution
• Are convictions independent?
• pi probability of being convicted for offence
  type i
• P(y convictions x offences)

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Non-Convicted Offences by Convicted Offenders
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS

• These 3 sets of probabilities allow us to
  calculate P(x offences y convictions)
• From this we can calculate the average expected
  amount of extra offences for offenders

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CONVICTED OFFENDERS
CONVICTED OFFENCES
NON-CONVICTED OFFENCES BY CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENDERS
ADDITIONAL NON-CONVICTED OFFENCES
TOTAL ESTIMATED OFFENCES
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Non-convicted Offences by Non-convicted Offenders
ADDITIONAL NON-CONVICTED OFFENCES

• Non-Convicted Offences
• Difference between total estimated offences and
  current estimate of offences
• 14 different offence types, 14 different values
• Need to spread these non-convicted offences
  over the population (by age / gender / segment)
• This is done proportionally by the OCJS and age
  distribution of existing offenders

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Non-Convicted Offenders
ADDITIONAL NON-CONVICTED OFFENDERS

• Already know the population of non-convicted
  offences (N)
• Now need to estimate how many non-convicted
  offenders (P) are committing these offences
• From OCJS we can estimate qi the proportion of
  offenders who commit i offences
• N 1.q1P 2.q2P 3.q3P
• P N / (q1 2.q2 3.q3 )

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Non-Convicted Offenders
ADDITIONAL NON-CONVICTED OFFENDERS

• Already know the population of non-convicted
  offences (N)
• Now need to estimate how many non-convicted
  offenders (P) are committing these offences
• From OCJS we can estimate qi the proportion of
  offenders who commit i offences
• N 1.q1P 2.q2P 3.q3P
• P N / (q1 2.q2 3.q3 )

Number of non-convicted offenders with 1 offence
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Results Offences Offenders
Note all figures are unpublished and subject to
revision
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Next Steps

• Updated Calculations
• More fluent calculation process
• Sensitivity analysis
• Frequently and easily updated
• Updated with latest convictions and crime survey
  data
• Update Methodology?
• Want to use this occasion as an opportunity to
  listen to suggested alternative approaches

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Alternative Approaches?

• Capture / Recapture Methods
• A method for estimating the size of partly hidden
  populations.
• This has been used to estimate drug use
  prevalence in the UK by the Home Office.
• Survey Methods
• The Offending Crime and Justice Survey (OCJS)
  describes active offending in detail for each of
  its respondent and in principle could be used for
  estimating active offender numbers.

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Summary

• We used a statistical model based on Bayes
  theorem to estimate a population of total
  offences and offenders. We have essentially used
  our knowledge of known convicted offenders and
  offences as well as survey data to extrapolate
  this population.
• This produced a total estimated population of
  offences and offenders.

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Questions / Feedback???
Martin Kelly Martin.Kelly_at_homeoffice.gsi.gov.uk
020 7035 3392