Estimation of Offending and Co-offending Using Available Data with Model Support

Abstract

Police data under-report the numbers of crimes and of offenders, the numbers of offenders participating in individual criminal incidents (incident sizes) and the numbers of incidents in which individual offenders participate (offender activity). Criminal participation in incidents is a concept that underlies and unifies all of these phenomena, so that the numbers of incidents and of offenders, and incident size distributions and offender activity distributions, can all be derived from the criminal participation matrix. Two related probability models are presented that permit the estimation of numbers of incidents and offenders, incident size distributions, offender activity distributions, and co-offending distributions, from police-reported crime data, and data on the reporting of crime to police. The models are estimated, using data from the Canadian Uniform Crime Reporting Survey and national victimization surveys for the period 1995–2001.

Keywords:

• co-offending
• criminal participation matrix
• estimation of incident size
• estimation of offender activity
• models of incident reporting
• models of offender identification
• Uniform Crime Reporting Survey

Preparation of this paper was supported by Social Sciences and Humanities Research of Council of Canada Research Grants 410-2000-0361 and 410-2004-2136. The authors gratefully acknowledge helpful comments on earlier drafts by Martin Bouchard, Pierre Tremblay, and the editor and an anonymous referee of JMS.

Notes

¹The definitions of technical terms and notation are summarized in the Appendix.

Sources:

Canadian Centre for Justice Statistics, Canadian Crime Statistics 1995; 1996; 1997; 1998; 1999; 2000; 2001. Catalogue No. 85–205. Ottawa: Statistics Canada, 1996–2002.

²It is purely a coincidence that this value of 0.42 for α is the same as the proportion (42%) of cleared incidents in Canada which are covered by the UCR2 Survey.

Notes:

^a Calculated using UCR empirical clearance rate = 0.261 (Table 1).

Notes:

^a The 882 thousand offenders in Table 3 were identified in the 1.46 million cleared incidents of Table 2. There are 1.75 million identified participations which are distributed according to identified size of the incident in Table 2 and according to identified activity of the offender in Table 3.

^b Numbers of offenders with high identified activity may be inflated, due to false positive matches of offender records.

³Zelterman' estimator has been used to estimate hidden populations such as drug users (Bouchard, 2006; Bouchard & Tremblay, 2005; Collins & Wilson, 1990; Hay & Smit, 2003).

Sources:

Canada 1999: Besserer & Trainor, 2000, table 7.

Canada 1993, 1988: Gartner & Doob, 1994, table 7.

USA 1996, 1999: Bureau of Justice Statistics, 2001.

ICVS (International Crime Victimization Survey): Mayhew & van Dijk, 1997, Table 9.

Notes:

“Theft motor vehicle or parts”: for Canada, this includes a small number of non-M.V. thefts of goods worth over $5,000

“Theft other”: for Canada, this is theft of goods worth $5,000 or less.

“Break & enter” = burglary; for Canada, this includes non-residential burglaries

“Vandalism”: this includes all types of “mischief”

Assault: for US data, this is limited to aggravated assault

Sexual assault: for US data, this is limited to rape

“All crime” includes all Criminal Code, including traffic, drug, and other federal statutes

Sources:

Canada: Canadian Centre for Justice Statistics, 1998 1999 2000 2001. table 3.3.

US: Bureau of Justice Statistics, 1995; 1998. table 4.19.

Submitted: September 2, 2003; Resubmitted: January 31, 2006.