4th National Crime Mapping Conference
Crime Forecasting for Police Deployment:
Results from a Large-Scale
Research Programme
by
Wil Gorr
1
Objective
• Assess time series forecasting methods for
use by police
– Using over 10 years of offense reports and computer
aided dispatch calls from Pittsburgh, Pennsylvania,
and Rochester, New York (crimeforecasting.org)
• Forecast Methods
– Univariate extrapolative
– Leading indicator
– Tracking signal
2
Crime Early Warning System
(CEWS)
3
Scenario
• It’s the first day of July in Rochester, New York
• You have made time series forecasts for July:
– For part 1 property crimes (P1P)
– By patrol district
• You are about to view the forecasts in CEWS
4
Crime Level: July Forecast
P1P July Forecast
5
Crime Change: July Forecast
6
Crime Analysis: June’s Crimes
7
Crime Time Series Forecasting
8
Crimes Analyzed
P1V (Part 1 Violent Crimes)
= Aggravated Assault + Murder + Rape +
Robbery
P1P (Part 1 Property Crimes)
= Burglary + Larceny + Motor Vehicle Theft +
Robbery
9
Pittsburgh, PA
Rochester, NY
City
Area
(sq.
miles)
2000
Population Density
Population (persons/sq. mile)
Pittsburgh
56
335,000
6,000
Rochester
36
220,000
6,100
10
Geographies
Pittsburgh
Rochester
42 Patrol Districts
38 Patrol Districts
178 Census Tracts
90 Census Tracts
11
Monthly Time Series Data:
Rochester, NY
3500
3000
2500
2000
1500
1000
P1P
P1V x 10
500
200012
199912
199812
199712
199612
199512
199412
199312
199212
199112
0
12
Crime Count
Extrapolative Forecast
Month
Now
13
Crime Count
Leading Indicator Model
Leading Indicator
P1V
Now
Months
14
Leading Indicator Crimes
for P1P and P1V
•
•
•
•
•
•
•
•
Arson
CAD Drugs
CAD Shots Fired
Criminal Mischief
Disorderly Conduct
Drug Offenses
Family Violence
Gambling
•
•
•
•
•
•
•
Liquor Law Violations
Prostitution
Public Drunkeness
Simple Assault
Tresspass
Vandalism
Weapons
15
Crime Forecast Accuracy
16
Crime Changes
Forecasted Change(t) =
Forecasted Crime(t+1) - Actual Crime(t)
Actual Change(t) =
Actual Crime(t+1) - Actual Crime(t)
17
Sample Decision Rule and
Performance Measures
• If Forecasted Change
>= 4 then issue an Exception Report
• Actual Change for Exception Reports
>= 4 is a Positive (10%)
= 2, 3 is a “Medium Positive” (15%)
<= 1 is a False Alarm (75%)
• Positive Rate
= 100*Positives/Actual Positives
18
Forecast Methods
• Chance
– Randomly choose 10% of areas each month
– Strawman
• Extrapolative method: simple smoothing
– Deseasonalized with multiplicative classical decomposition
• Leading indicator: regression model
– Time and space lags of leading indicators
– Monthly seasonal indicators
– Neighborhood factors
• Leading indicator: neural network model
– Same variables as in linear regression
– www.neuralware.com
19
Forecast Experiments
• Design
– One-month-ahead forecasts
– Rolling, 5-Year estimation window
• Cities
– Rochester
• Forecasted January 1996−December 2001
– Pittsburgh
• Forecasted January 1995−December 2001
20
Crime Change Forecast Accuracy
Pittsburgh Tracts
Positive Monthly
Rate
Exception
Reports
Monthly
Positives
Monthly
Medium
Positives
Monthly
False
Positives
Crime
Method
P1V
Chance
11%
17.0
2.1
3.1
11.8
P1V
Smoothing
21%
17.3
5.4
4.1
7.8
P1V
Regression
25%
12.6
4.8
3.3
4.6
P1V
Neural Net
47%
31.8
8.9
8.5
14.6
P1P
Chance
10%
17.0
1.8
2.7
12.5
P1P
Smoothing
25%
12.7
4.4
3.2
5.1
P1P
Regression
29%
21.7
5.2
5.1
11.5
P1P
Neural Net
44%
40.4
7.7
9.1
23.6
178 tracts in Pittsburgh
21
Crime Change Forecast Accuracy
Pittsburgh Patrol Districts
Positive Monthly
Rate
Exception
Reports
Monthly
Positives
Monthly
Medium
Positives
Monthly
False
Positives
Crime
Method
P1V
Chance
11%
4.2
0.5
0.8
2.8
P1V
Smoothing
25%
3.3
1.2
0.9
1.3
P1V
Regression
25%
3.8
1.1
1.0
1.6
P1V
Neural Net
43%
7.8
2.0
2.0
3.9
P1P
Chance
10%
4.2
0.4
1.0
2.7
P1P
Smoothing
19%
2.5
0.8
0.8
0.9
P1P
Regression
28%
6.9
1.2
2.3
3.5
P1P
Neural Net
39%
11.0
1.6
3.3
6.1
42 patrol districts in Pittsburgh
22
Monitoring Crime Time Series Data
23
Crime Count
Counterfactual Forecast
Year ago
Month
Now
24
Crime Count
Counterfactual Forecast
Forecast
Error
Year ago
Month
Now
25
l-0
1
l-0
2
02
2
l-0
3
03
3
l-0
4
04
4
Ju
05
l-0
5
Ap
r-
5
26
Oc
t- 0
5
Step
Jump
Ja
n-0
Oc
t- 0
4
Ju
Ap
r-
Ja
n-0
Oc
t- 0
3
Ju
Ap
r-
Ja
n-0
Oc
t- 0
2
Ju
Ap
r-
Ja
n-0
Oc
t- 0
1
Ju
01
1
40
Ap
r-
Ja
n-0
911 Drug Calls
70
Spike
60
50
Step
Jump
30
20
10
Spike
0
Approach
• Had Pittsburgh Police crime analysts code a
sample of jumps and spikes of potential
importance
• Tuned monitoring techniques based on coded
sample
• Use cross validation to make performance
comparisons among alternative techniques
27
Tracking Signal Alternatives
• Comstat method
Change from last year
Critical value for crime count differences
• Standardized frequency
Z score for crime count with critical value
• Standardized forecast errors
Z score for forecast error with critical value
• Trigg tracking signal
Smoothed forecast errors divided by
smoothed absolute forecast error with critical value
28
Cross Validation of Tracking Signals
29
Recommendations
1. Build a crime early warning system
2. Use tracking signals to evaluate performance
and trigger crime analysis
3. Use a neural network leading indicator model to
trigger crime analysis for prevention
4. Drill down to leading indicators and recent P1
crimes and apply traditional crime analysis
methods
30