Point Pattern Analysis

Steve Henderson


 


Standard Deviational Ellipses

 

This first graphic shows the first and second standard deviation ellipses for attempted street robbery in St. Louis.  These ellipses show that attempted street robbery is centered loosely downtown near the river.

 

Att Str Rob

 

The second graphic shows that Gun Homicides are centered farther north and more in the center of th City.  The ellipses do not provide much information on the pattern of the events, but may help show trends in the changes of crime locations over time.

 

Random with Empty Spaces

 

 





Nearest Neighbor Distance Statisitics

 

Nearest neighbor distance statistics calculate the tendency of the data to cluster and measure the likelihood that the patterns are random or not..

 

Inhmg Pos

 

Calculations for this tendency to cluster for both attemped street robbery and gun homicides showed a very strong tendency to cluster using Elucidian or straight line distances between  events.  However, both showed no real tendency toward clustering when measured using the Manhattan distances, or the distance assuming that the real distance would be the distance if you had to travel two legs of a triangle as you would in a City block rather than the straight line distance.  The change in the distance is ~423 observed vs ~547 expected for Elucidian and ~529 observed vs ~547 expected for Manhattan.  I would not expect the change in clustering tendency to be that strong for the two different measures..

 

Inhmg Pos w/Clustering

 




Quadrat Analysis

 
A quadrat analysis is shown benlow for attempted street robbery.  The Census method was used because we are interested in the locations of the clusters in addition to the likelihood that the pattern is random.

 

Interaction

 

A similar quadrat count of gun homicide.

 

XY-diff=4

 




Kernel Density Estimation

 

Kernel density estimation shows the size, shape, and relative strength of the clusters.  The graphic below is of the central portions of the attempted street robberies.  A bandwith of 1500 meters was selected because it showed the clustering best.

 

Att Str Rob

 

The same KDE analysis of gun homicides, also using a 1500 meter bandwidth..

 

Random with Empty Spaces