1. Point-pattern analysis of Nashville, TN robberies: It’s all about that kernel
Ingrid Luffman and Andrew Joyner, Department of Geosciences, East Tennessee State University
Joseph Harris, Department of Geography & Anthropology, Louisiana State University
Abstract
Spatial analytical techniques are important tools for crime pattern analysis. This research focuses on identification of spatial clustering and development of a risk surface map using a dataset of 282 robberies occurring in Nashville, TN from April through August Spatial point pattern analysis is a preferred approach because all of the available information is retained during analysis rather than lost during rate calculations for arbitrary geographic areas like census blocks or neighborhoods.
Nearest Neighbor Hierarchical Clustering identified five first order clusters around the downtown interstate loop and surrounding areas. All clusters are located in high population areas, but not all high population areas contain crime clusters. Kernel density maps generated using a quartic kernel with a 10 points per cluster (ppc) threshold identified two hot spots directly south and southeast of the downtown core and several other lower density hot spots nearby that correspond well to the first order cluster locations. Kernel density maps generated with other thresholds (30 ppc) and a triangular kernel yield many irregular and serrated high density hot spots throughout the metro Nashville area making it difficult to discern true areas of comparatively high crime. Nashville robbery data used for this study are better-suited to smoother kernel functions such as the quartic method, which is known to be realistic for most crime data.
3. Kernel Density Estimation (KDE)
Overview
The Kernel Density Estimate (KDE) is a summation of individual kernels at point locations. The smaller the distance between points, the greater the overlap and the higher the estimate (Figure 3).
This poster presents a hot spot analysis of 282 robberies occurring in Nashville, TN from April through August 2014 (Figure 1). Each robbery event was geocoded and analyzed in Crimestat using Nearest Neighbor Hierarchical Clustering and Kernel Density Estimation.
Research questions:
Is there spatial clustering, and if so, what are the locations of hot spots?
What is the robbery risk for the metro area given known robbery occurrence?
How do parameters such as kernel shape and points per cluster impact the risk surface?
Figure 3. Development of kernel density estimate from five normal kernels
Kernel density
estimate
Individual
kernels
Triangular kernel is best for isolated events.
Quartic kernel is best for events that transfer risk to nearby areas.
4. Hot Spot Analysis
2. Nearest Neighbor Hierarchical Clustering (NNHC)
The number of points per cluster (PPC) will impact the number and size of hot spots. During kernel density map development, the risk surface must be interpreted carefully to consider where suitable targets actually exist. KDE is a hot spot technique that produces an interpolated surface, and incidents do not necessarily occur at all locations within the “hottest” color (red in maps below).
Nearest Neighbor Hierarchical Clustering (NNHC) was used to pinpoint the location of robbery hot spots and clusters of hot spots (second order clusters) by identifying groups of paired points that are unusually proximal.
The clusters were, unsurprisingly, in highly populated areas, but not all highly populated areas contained crime clusters. Many areas of Nashville, specifically to the south and southwest, are densely populated, but did not have statistically significant clusters of crime. To assess risk, background factors such as a secondary population file can be included in analysis. Additionally, shape, boundary effects, and distances are also important when examining NNHC.
Figure 1. Nashville robberies, April – August 2014.
1. Nearest Neighbor Index (NNI)
10 ppc
30 ppc
The Nearest Neighbor Index (Rn) is the ratio of the average distance between points and their nearest neighbors, and the expected distance if the points were randomly distributed. Rn identifies spatial clustering in event data at the global level.
Rn = indicates a tendency toward clustering in the Nashville robberies dataset.
Where
D(Obs) = mean observed nearest neighbor distance
A = area under study
N = number of points
10 ppc
30 ppc
In addressing each of the three research questions, increasingly complex spatial analysis methods allowed us to examine crime patterns in Nashville from a more holistic perspective. We can conclude that most crime types show clustering and geostatistical analysis of inherently spatial issues revealed new information that may be useful to various groups including municipal government officials, police departments, businesses and chambers of commerce, and residents.
Figure 3. The Nashville robbery data are clustered in five first order clusters (small yellow ellipses) and one second order cluster (large orange ellipse).
Source: C. Brown, Geo Factsheet n°168