Predicting Next Event
Locations in a Crime Series
using Advanced Spatial
Prediction Methods
Presented by
Dr. Derek J. Paulsen
Director, Institute for the Spatial Analysis of Crime
Assistant Professor
Eastern Kentucky University
2005 UK Crime Mapping Conference
Spatial Forecasting and Crime
Analysis
Evolution of Crime Analysis in the U.S.
Increasing focus on Tactical Analysis and
assistance in major crime investigations.
Increasing use of advanced technology
Geographic profiling
Crime Series Identification software
Forecasting/Prediction
Great potential to assist in investigations,
but research has been limited.
Main Research Questions
How accurate are traditional and emerging
strategies at predicting the location of a
future crime event in an active crime series?
Practically, are these technologies providing
any real benefits to police agencies in
investigations?
While anecdotally there is much discussion
of these strategies, research has been
virtually non-existent in terms of measuring
accuracy and effectiveness.
Forecasting Strategies Studied
Traditional Methods
Standard Deviation Rectangles: “Gottleib Rectangles”
Jennrich/Turner Ellipse
Minimum-Convex-Hull Polygon
New Methods
Modified Correlated Walk Analysis
Time-Weighted Kernel Density Interpolation
Control Method
Modified Center of Minimum Distance
Standard Deviation Rectangle
2 Standard Deviation rectangle around the mean center of the
incident locations in the series
Jennrich-Turner Ellipse
2 Standard Deviation ellipse based around the mean center of the incident locations in the
series and drawn around a least squares trend line
Minimum Convex-Hull Polygon
Creates a minimum bounding polygon around all of the incident locations in the series
Modified Correlated Walk Analysis
Uses the CWA as a seed point and creates a search area by drawing a circle with a radius of
the average distance between crime events in the series.
Time-Weighted Kernel Density
Interpolation
Kernel Density Interpolation of crime incident locations using time as a weighting variable
Modified Center of Minimum
Distance
Uses the CMD as a seed point and creates a search area by drawing a circle with a
radius of the average distance between crime events in the series.
Data Used in Study
247 serial crime events that occurred in Baltimore County, MD
between 1994-1997.
Random sample of 45 cases in which there were 6 or more incidents.
Series ranged from 6-14 events
Burglary, Robbery, Arson, Auto theft, Rape, Theft
Last Crime was removed from series and remaining crimes were
used to predict the final event.
Analysis was conducted using:
Arcview 3.3 and 9.0
Crimestat 2.0
Animal Movement Extension/CASE Program
Measuring Accuracy of Predictions
How do you measure accuracy in predicting next events in a crime
series?
Accuracy in prediction needs to encompass both correctness and
the precision of the prediction in order to maintain practical utility.
A prediction may be accurate, but the predicted area may so
large as to provide little practical benefit.
Methods
1. Correct: Was the final event location within predicted area.
2. Search Area: Average size of the predicted area.
3. Search Cost: Percent of base search area covered by the final
predicted area.
4. Accuracy Precision: % of correct forecasts divided by the
average predicted area.
Search Area, Search Cost, and
Accuracy Precision
Method
% Correct
Avg. Search
Area
Avg. Search
Cost
Accuracy
Precision
SDR
80%
151.68
170%
.5274
JTE
73%
122.10
134%
.5978
MCP
42%
23.21
26%
1.8095
CWA
24%
59.82
85%
.4012
TWKDI
52%
19.35
21%
2.6873
CMD
80%
59.82
85%
1.3373
Average base search area was 92 sq. miles
Factors Influencing Success of
Prediction
Factors
Time-Weighted
Kernel Density
Convex-Hull
Polygon
Modified Center of
Minimum Distance
Number of
Offenses
.456*
1.527
.423
Dispersion
1.150
.819
.461
Avg. distance
between crimes
.440*
.284
1.428
Avg. Base
Search Area
1.020
1.013
1.054
NNA Score
.732
408.60
109.02
Repeat Victim
Location
43.942*
9.780
.597
Constant
298.360
.032
355.91
* Significant at .05 level
Factors Influencing Search Cost
Factors
Time-Weighted
Kernel Density
Convex-Hull
Polygon
Modified Center of
Minimum Distance
Number of
Offenses
-.254
1.023**
-.210
Dispersion
-.504
-1.924**
-.883*
Avg. distance
between crimes
-.340
.636
1.223**
Avg. Base
Search Area
-.458
-.378
-.570
NNA Score
1.298*
1.726*
-.072
-2.42
-.214
.088
.424
.579
.343
Repeat Victim
Location
Adjusted RSquare
* Significant at .05 level
** Significant at .01 level
Factors Influencing Search Area
Factors
Time-Weighted
Kernel Density
Convex-Hull
Polygon
Modified Center of
Minimum Distance
Number of
Offenses
.099
.431**
-.017
Dispersion
-.756**
-.983**
-.527**
Avg. distance
between crimes
.144
.303
1.074**
Avg. Base
Search Area
.637**
2.822**
.356**
NNA Score
.843**
2.245*
.047
-.003
-.578
.005
.914
.857
.948
Repeat Victim
Location
Adjusted RSquare
* Significant at .05 level
** Significant at .01 level
Overall Findings
Time-Weighted is the best at reducing the
search area while remaining accurate.
Success most influenced by repeat location
victimizations, avg. distance between crimes and
number of incidents in series.
Convex-Hull Polygon and modified CMD
also produced good results, whereas other
traditional strategies were poor performers.
While average predicted areas are rather
large, practical use could reduce them to
smaller area.
Future Issues
More research, more data.
Determine impact of other factors such as
crime type, city type, and road network.
Determine case variables that may indicate
predictive success.
Develop and analyze other new strategies.
Temporal as well as spatial forecasting/prediction
More research on serial offender spatial
and temporal behavior.
Data or Suggestions?
Contact Information:
Dr. Derek J. Paulsen
Assistant Professor
Director, Institute for the Spatial Analysis of Crime
Eastern Kentucky University
Richmond, KY USA 40507-3102
Derek.Paulsen@eku.edu
859-622-2906