The document examines the relationship between criminal networks and violent victimization, focusing on Albuquerque, New Mexico, over three years of crime-related data. It explores how connections among offenders and the presence of victim ties inform the understanding of violence, highlighting the potential for identifying patterns and risks in criminal behavior. The findings suggest a sparse but significant presence of offender networks, indicating clustering of violence and raising questions about selection versus spread of violence within these networks.

1. Arrest Networks
and the
Spread of Violent Victimization
DANIEL T. RAGAN
UNIVERSITY OF NEW MEXICO

2. Other Team Members
Lisa Broidy
University of New Mexico
Brian Soller
University of Maryland, Baltimore County

3. Background
Violent victimization:
‣ As a health outcome
‣ Not randomly distributed
‣ Importance of social ties

4. Prior Research
Violent victimization: Predicted by arrest with other victims
‣ Exposure to similar risk factors
Gunshot and homicide victimization
‣ Generalizability to more common types of violence?
Chicago, IL; Boston, MA; Newark, NJ
‣ Generalizability to different geographic locations?

5. Our Goal: Network Approach to Violent Victimization
Primary data
‣ Law enforcement
Supplementary data
‣ Criminal courts
‣ State criminal history databases
‣ Emergency room visits
‣ U.S. Census

6. Pilot Project
Violent victimization in criminal networks
‣ Approximately three years of crime-related data
‣ Information on both offenders and victims
‣ Albuquerque, New Mexico

7. Current Goals
1) What can we learn about violence in criminal networks?
‣ Do offending networks link violent offenders and victims?
2) Assess feasibility of a larger project
‣ Do these data support a network approach?

8. Data: Overview
‣ Criminal event data
‣ Case numbers
‣ Suspects, arrestees, and victims: Unique identifiers
‣ Approximately three years of coverage
‣ 2011 into 2014
‣ Albuquerque, New Mexico

9. Albuquerque
‣ Population size
‣ Mobility
‣ City borders & Law enforcement jurisdiction

12. Data at a Glance: Cases
Records (case/person combination): 155,906
‣ Cases: 120,675
‣ Single offender: 45,348
‣ Multiple offenders: 4,150

13. Data at a Glance: People
Unique person identifiers: 120,345
‣ Offenders (suspects/arrestees): 40,858
‣ Multiple cases: 8,441
‣ Victims: 86,677
‣ Both offender and victim: 7,190

14. Violent Offenses: Examples
Battery/Aggravated battery/Aggravated assault
‣ 8,946 cases
Robbery/Commercial armed robbery/Auto car jacking
‣ 552 cases
Forcible rape/Attempted rape/Sexual assault with an object
‣ 490 cases
Murder and nonnegligent manslaughter/Justifiable homicide
‣ 83 cases

15. Building the Network
Offenders: Linked through crimes
‣ One-mode projection from two-mode data
‣ Assumption: Co-offending signifies social connection
‣ Case removal: > 10 offenders
‣ Case removal: Individual is both offender and victim
‣ Time dimension collapsed: Cross-sectional

16. Offender Network: Offenders
Offenders: 40,499
‣ Isolates: 32,637
‣ Connected offenders: 7,862

17. Offender Network: Ties
Ties: 5,990
‣ Average ties: 0.30
‣ Average ties, excluding isolates: 1.52
‣ Degree distribution:
1 2 3 4 5 6 7 8 - 18
5,476 1,444 534 219 81 67 27 14

18. Offender Network: Groups
Components, excluding isolates: 3,151
• Average component size, excluding isolates: 2.50
• Component distribution:
2 3 4 5 6 7 8 9 - 53
2,364 488 151 54 34 22 18 20

20. How are different offender-types connected?
Do victims of violence have ties to violent offenders?
‣ Do links within offending network suggest “spread”?

21. How are different offender-types connected?
Non-victim Victim
Non-violent
offender
Non-violent offender,
non-victim1
Non-violent offender,
victim3
Violent offender Violent offender,
non-victim2
Violent offender,
victim4

22. Non-violent offender,
non-victim1
Violent offender,
non-victim2
Non-violent offender,
victim3
Violent offender,
victim4
Non-violent offender,
non-victim1
001001 001102 001013 001114
Violent offender,
non-victim2
102001 102102 102013 102114
Non-violent offender,
victim3
013001 013102 013013 013114
Violent offender,
victim4
114001 114102 114013 114114

23. Non-violent offender,
non-victim1
Violent offender,
non-victim2
Non-violent offender,
victim3
Violent offender,
victim4
Non-violent offender,
non-victim1
0
Violent offender,
non-victim2
0 0
Non-violent offender,
victim3
0 013102 0
Violent offender,
victim4
0 114102 114013 114114

26. Exponential Random Graph Models
Y: Random variable for state of network
g(y): Vector of network statistics for model
𝜃: Vector of parameters
k: Normalizing constant
Conditional log-odds of a single tie between two actors:
𝑝 𝑌 = 𝑦 =
𝑒𝑥𝑝(𝜃′
𝑔 𝑦 )
𝑘 𝜃
𝑙𝑜𝑔𝑖𝑡(𝑌𝑖𝑗 = 1|𝑦𝑖𝑗
𝑐
) = 𝜃′𝛿(𝑦𝑖𝑗)

27. Exponential Random Graph Models
Parameter Estimate Std. Error
Edges -9.891*** 0.032
Isolates 1.695*** 0.027
Actor covariate: Number offenses 0.159*** 0.004
Attributes mixes: Offender type
Non-violent offender, victim3
x Violent offender, victim4 0.205 0.147
Violent offender, non-victim2
x Non-violent offender, victim3 -0.626*** 0.111
Violent offender, non-victim2
x Violent offender, victim4 0.617*** 0.070
Violent offender, victim4
x Violent offender, victim4 1.138*** 0.146

28. Non-violent offender,
non-victim1
Violent offender,
non-victim2
Non-violent offender,
victim3
Violent offender,
victim4
Non-violent offender,
non-victim1
0
Violent offender,
non-victim2
0 0
Non-violent offender,
victim3
0 — 0
Violent offender,
victim4
0 + n.s. +

29. Conclusions
1) Presence of offender network
‣ Ties: Sparse but not insignificant
2) Clustering of violence within network
‣ Violent offenders and victim ties: Victims are violent
‣ “Selection” vs. “Spread”

30. Next Steps
1) Continuing work: ERGMs
‣ Model specification & Goodness of fit
2) Pilot project: Future directions
‣ Projection of crime network
3) Larger project feasibility
‣ Current mood: “Cautiously optimistic”