Robustness of Kernel Density Crime Hotspot Maps
Robustness of Kernel Density Crime Hotspot Maps Michael Camponovo Dr. Paul Zandbergen Department of Geography University of New Mexico
Outline • • • • •
Crime Mapping Experimental Design Kernel Density Predictive Crime Mapping Results and Discussion
Crime Mapping • Why map crimes? – Where are crime events located? • Who is the audience and what is the purpose? –Media –Public –Law Enforcement
http://bigcitycrimescope.files.wordpress.com/2011/02/chicago_violent_crime_map.png
Crime Mapping for Law Enforcement • Where to allocate limited resources? – Predict Future Crime Events Using Hotspots
Research Question How Reliable is predictive hotspot mapping? • Which factors influence this reliability?
Research Design • Crime Types: – Assault, Auto Burglary, Auto Theft, Burglary, Drugs, Homicide, Robbery
• Jurisdictions – – – – – –
Albuquerque, NM Arlington, TX Charlotte, NC Las Vegas, NV San Diego, CA Tampa, Fl
• Total of 6 Different Hotspot Methods – Point Patterns (Kernel Density, Nearest Neighbor Hierarchical Clustering, Spatial and Temporal Analysis of Crime) – Aggregated Data (Grid‐Based Thematic, Local Moran’s I, Gi*)
• Use 2007 Data to Predict 2008
Research Design • Crime Types: – Assault, Auto Burglary, Auto Theft, Burglary, Drugs, Homicide, Robbery
• Jurisdictions – – – – – –
Albuquerque, NM Arlington, TX Charlotte, NC Las Vegas, NV San Diego, CA Tampa, Fl
• Total of 6 Different Hotspot Methods – Point Patterns (Kernel Density, Nearest Neighbor Hierarchical Clustering, Spatial and Temporal Analysis of Crime) – Aggregated Data (Grid‐Based Thematic, Local Moran’s I, Gi*)
• Use 2007 Data to Predict 2008
Why Focus on Kernel Density? • Popular • Relatively Robust
http://www.statcan.gc.ca/pub/85‐561‐m/2008010/maps/map3‐3‐en.gif
Kernel Density Benefits • Easy to produce • Only need crime events • Aesthetically pleasing output • Easy to understand
Limitations • Because it is a surface it places crime events where there might not be any records • Because it is a surface it places crime events where it is highly unlikely crime would occur, in a lake for instance
How Does the Kernel Density Tool Work?
http://jratcliffe.net/ware/spam1.htm
Kernel Density Interface
Kernel Density Output
Default Symbology
Kernel Density Symbology • Use ModelBuilder: – Remove all cells with value = 0 – Calculate the mean density of the remaining cells – Select cells that are: • • • • •
1 x Mean 2 x Mean 3 x Mean 4 x Mean 5 x Mean
Output Cell Size Default
Search Radius (Bandwidth) Default
Burglary, All Thresholds, 100 meter Bandwidth
Burglary, > 3 x Mean, Multiple Bandwidths
Predictive Hotspot Values • Hit Rate (%) – Percentage of crimes in period 2 that falls in hotspot derived from period 1 – Higher values are better
• Predictive Accuracy Index (PAI) – Ratio of hit rate to the area percentage – Higher values are better
Example Calculation Total Crimes 2007 Study Hotspot Total Crimes in 2007 Area Area in 2008
2008 Crimes That Fall Within the Hotspot
Collect the following Variables:
8975
1413 km2
37 km2
8562
3860
Hit Rate
=
Predictive Accuracy Index
= 17.1
= 45%
Burglary Hit Rate (%) 50 meters
100 meters
150 meters
200 meters
250 meters
300 meters
350 meters
400 meters
450 meters
500 meters
> 5 x Mean
11.4
12.5
12.0
12.4
12.4
12.5
12.4
12.6
12.8
12.7
> 4 x Mean
14.1
17.2
17.1
17.4
18.0
19.1
19.7
20.2
20.6
20.7
> 3 x Mean
21.1
21.4
24.6
25.5
27.8
29.7
31.1
32.3
32.5
32.9
> 2 x Mean
25.1
32.1
36.4
38.5
42.1
44.0
46.2
48.2
49.6
50.6
> Mean
42.7
50.9
55.6
57.0
62.3
65.8
68.2
70.3
72.0
73.2
Burglary Predictive Accuracy Index (PAI) 50 meters
100 meters
150 meters
200 meters
250 meters
300 meters
350 meters
400 meters
450 meters
500 meters
> 5 x Mean
152.8
51.4
28.3
20.8
16.8
14.6
13.1
12.3
11.7
11.1
> 4 x Mean
112.3
40.8
22.7
16.1
13.1
11.9
10.8
10.0
9.4
9.0
> 3 x Mean
83.4
27.8
17.2
12.4
10.6
9.4
8.6
8.1
7.6
7.2
> 2 x Mean
53.1
19.1
12.1
9.1
7.9
7.0
6.5
6.1
5.8
5.6
> Mean
28.9
11.2
7.7
5.9
5.2
4.7
4.4
4.2
4.0
3.8
Hit Rate vs PAI Hit Rate
80 > 5 * mean > 4 * mean > 3 * mean > 2 * mean > mean
70 60
Predictive Accuracy Index
180 160
> 5 * mean
140
> 4 * mean
120 50
> 3 * mean > 2 * mean
PAI
Hit Rate
100 40
> mean
80 30 60 20
40
10
20
0
0 0
100
200
300
Kernel Bandwidth (m)
400
500
0
100
200
300
Kernel Bandwidth (m)
400
500
Conclusions • No matter what tool you are using, understand your parameters before accepting the defaults • Search radius plays a major factor in Predictive Crime Mapping using Kernel Density • There is no “perfect” set of parameters – must have tradeoffs between kernel bandwidth and hotspot threshold
Contact • Michael Camponovo – [email protected]
• Dr. Paul Zandbergen – [email protected] – www.paulzandbergen.com – Check Publications and Presentations
Thank You • New Mexico Geographic Information Council • National Institute of Justice – Project #: 2010‐696J‐00 – Principle Paul Zandbergen, UNM Investigators: Timothy Hart, UNLV – Start Date: February 2010 – End Date: June 2012
Outline • • • • •
Crime Mapping Experimental Design Kernel Density Predictive Crime Mapping Results and Discussion
Crime Mapping • Why map crimes? – Where are crime events located? • Who is the audience and what is the purpose? –Media –Public –Law Enforcement
http://bigcitycrimescope.files.wordpress.com/2011/02/chicago_violent_crime_map.png
Crime Mapping for Law Enforcement • Where to allocate limited resources? – Predict Future Crime Events Using Hotspots
Research Question How Reliable is predictive hotspot mapping? • Which factors influence this reliability?
Research Design • Crime Types: – Assault, Auto Burglary, Auto Theft, Burglary, Drugs, Homicide, Robbery
• Jurisdictions – – – – – –
Albuquerque, NM Arlington, TX Charlotte, NC Las Vegas, NV San Diego, CA Tampa, Fl
• Total of 6 Different Hotspot Methods – Point Patterns (Kernel Density, Nearest Neighbor Hierarchical Clustering, Spatial and Temporal Analysis of Crime) – Aggregated Data (Grid‐Based Thematic, Local Moran’s I, Gi*)
• Use 2007 Data to Predict 2008
Research Design • Crime Types: – Assault, Auto Burglary, Auto Theft, Burglary, Drugs, Homicide, Robbery
• Jurisdictions – – – – – –
Albuquerque, NM Arlington, TX Charlotte, NC Las Vegas, NV San Diego, CA Tampa, Fl
• Total of 6 Different Hotspot Methods – Point Patterns (Kernel Density, Nearest Neighbor Hierarchical Clustering, Spatial and Temporal Analysis of Crime) – Aggregated Data (Grid‐Based Thematic, Local Moran’s I, Gi*)
• Use 2007 Data to Predict 2008
Why Focus on Kernel Density? • Popular • Relatively Robust
http://www.statcan.gc.ca/pub/85‐561‐m/2008010/maps/map3‐3‐en.gif
Kernel Density Benefits • Easy to produce • Only need crime events • Aesthetically pleasing output • Easy to understand
Limitations • Because it is a surface it places crime events where there might not be any records • Because it is a surface it places crime events where it is highly unlikely crime would occur, in a lake for instance
How Does the Kernel Density Tool Work?
http://jratcliffe.net/ware/spam1.htm
Kernel Density Interface
Kernel Density Output
Default Symbology
Kernel Density Symbology • Use ModelBuilder: – Remove all cells with value = 0 – Calculate the mean density of the remaining cells – Select cells that are: • • • • •
1 x Mean 2 x Mean 3 x Mean 4 x Mean 5 x Mean
Output Cell Size Default
Search Radius (Bandwidth) Default
Burglary, All Thresholds, 100 meter Bandwidth
Burglary, > 3 x Mean, Multiple Bandwidths
Predictive Hotspot Values • Hit Rate (%) – Percentage of crimes in period 2 that falls in hotspot derived from period 1 – Higher values are better
• Predictive Accuracy Index (PAI) – Ratio of hit rate to the area percentage – Higher values are better
Example Calculation Total Crimes 2007 Study Hotspot Total Crimes in 2007 Area Area in 2008
2008 Crimes That Fall Within the Hotspot
Collect the following Variables:
8975
1413 km2
37 km2
8562
3860
Hit Rate
=
Predictive Accuracy Index
= 17.1
= 45%
Burglary Hit Rate (%) 50 meters
100 meters
150 meters
200 meters
250 meters
300 meters
350 meters
400 meters
450 meters
500 meters
> 5 x Mean
11.4
12.5
12.0
12.4
12.4
12.5
12.4
12.6
12.8
12.7
> 4 x Mean
14.1
17.2
17.1
17.4
18.0
19.1
19.7
20.2
20.6
20.7
> 3 x Mean
21.1
21.4
24.6
25.5
27.8
29.7
31.1
32.3
32.5
32.9
> 2 x Mean
25.1
32.1
36.4
38.5
42.1
44.0
46.2
48.2
49.6
50.6
> Mean
42.7
50.9
55.6
57.0
62.3
65.8
68.2
70.3
72.0
73.2
Burglary Predictive Accuracy Index (PAI) 50 meters
100 meters
150 meters
200 meters
250 meters
300 meters
350 meters
400 meters
450 meters
500 meters
> 5 x Mean
152.8
51.4
28.3
20.8
16.8
14.6
13.1
12.3
11.7
11.1
> 4 x Mean
112.3
40.8
22.7
16.1
13.1
11.9
10.8
10.0
9.4
9.0
> 3 x Mean
83.4
27.8
17.2
12.4
10.6
9.4
8.6
8.1
7.6
7.2
> 2 x Mean
53.1
19.1
12.1
9.1
7.9
7.0
6.5
6.1
5.8
5.6
> Mean
28.9
11.2
7.7
5.9
5.2
4.7
4.4
4.2
4.0
3.8
Hit Rate vs PAI Hit Rate
80 > 5 * mean > 4 * mean > 3 * mean > 2 * mean > mean
70 60
Predictive Accuracy Index
180 160
> 5 * mean
140
> 4 * mean
120 50
> 3 * mean > 2 * mean
PAI
Hit Rate
100 40
> mean
80 30 60 20
40
10
20
0
0 0
100
200
300
Kernel Bandwidth (m)
400
500
0
100
200
300
Kernel Bandwidth (m)
400
500
Conclusions • No matter what tool you are using, understand your parameters before accepting the defaults • Search radius plays a major factor in Predictive Crime Mapping using Kernel Density • There is no “perfect” set of parameters – must have tradeoffs between kernel bandwidth and hotspot threshold
Contact • Michael Camponovo – [email protected]
• Dr. Paul Zandbergen – [email protected] – www.paulzandbergen.com – Check Publications and Presentations
Thank You • New Mexico Geographic Information Council • National Institute of Justice – Project #: 2010‐696J‐00 – Principle Paul Zandbergen, UNM Investigators: Timothy Hart, UNLV – Start Date: February 2010 – End Date: June 2012
