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CrimeStat IV

Susan C. Smith

Christopher W. Bruce

Revised by: Thomas Mueller

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About CrimeStat PowerPoint

This PowerPoint was revised from the Susan C. Smith and Christopher Bruce’s work. The Original can be found at:
http://www.icpsr.umich.edu/CrimeStat/workbook.html

Their PowerPoint and Manual was developed for CrimeStat 3.0. This PowerPoints was revised for CrimeStat 4.0
The GeoTech Center wants to thank both of them for allowing us to use this tremendous resource.

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Chapter Six��Kernel Density Estimation

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In Chapter Six...

How kernel density estimation works
Understanding different interpolation methods
Guidelines for kernel size and bandwidth
Creating and mapping a kernel density estimation
Uses and misuses of kernel density

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Introduction

Crime Analysts most often create

Pin maps
Kernel density maps

AKA surface density maps
AKA continuous surface maps
AKA density maps
AKA isopleth maps
AKA grid maps
AKA hot spot maps

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Introduction

From the last chapter we examined Hot Spots. There is a difference:
Chapter 5: “Actual volumes of incidents at specific locations” (Smith and Bruce p.62)
The next slide explains KDE

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Introduction

Kernel Density Estimation (KDE)

Generalizes data over larger regions

As opposed to volumes of incidents at specific locations

Good image to show estimation
Comparative to weather maps
“What is going on here is probably going on there”
Question on accuracy in crime analysis
Provides a “risk surface” more than an actual picture of what “is” occurring

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How KDE Works

Every point on the map has a density estimate based on its proximity to crime incidents
Done by overlaying a grid on top of the map

Calculates the density estimate for the centerpoint of each grid cell

Number of cells in the grid is defined by the user

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How KDE Works

CrimeStat measures the distance between each grid cell centerpoint and each incident data point and determines the cell weight for that point
Sums the weights received from all points into the density estimate
But the weight of each cell depends on three things….

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How KDE Works

Weight of each cell depends on

Distance from the grid cell centerpoint to the incident data point
Size of the radius around each incident data point
Method of interpolation

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How KDE Works

Method of Interpolation

KDE places a symmetrical surface called a kernel over each point (size specified by user, shape specified by method of interpolation)
the value is then smoothed throughout the kernel
finally, overlay a grid

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How KDE Works

In a map, the grid cells are color-coded based on the density

Often reds for hottest area and blues for coolest

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KDE Parameters

Many parameters involved
Analyst must use experience & judgment
Single versus dual kernel density estimates

Single is usually used in crime analysis
Dual can help normalize data for population or other risk factors or calculate change from one time to the next

Bandwidth

Refers to the size of the cone; specified by user

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KDE Parameters

Methods of interpolation (shape of bandwidth)

Normal (bell curve)

peaks & declines rapidly
No defined radius; continues across entire grid

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KDE Parameters

Methods of interpolation (shape of bandwidth)

Uniform (flat) distribution

Represented by cylinder; all points in radius equal

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KDE Parameters

Methods of interpolation (shape of bandwidth)

Quartic (spherical) distribution

Gradual curve; density highest over point; falls to limit of radius

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KDE Parameters

Methods of interpolation (con’t)

Triangular (conical) distribution

Peaks above the point; falls off in a linear manner to edges of radius

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KDE Parameters

Methods of interpolation (con’t)

Negative exponential distribution

Curve that falls off rapidly from the peak to a specified radius

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KDE Parameters

Each method will produce different results

Triangular & negative exponential produce many small hot and cold spots
Quartile, uniform and normal distribution functions smooth data more

Negative exponential Normal Distribution

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KDE Parameters

Parameter to specify size of bandwidth

Choice of Bandwidth
Minimum Sample Size
Interval

With “adaptive”, CrimeStat will adjust the size of the kernal until it’s large enough to contain the minimum sample size
With “fixed interval” bandwidth, you specify the size

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KDE Parameters

Output units (any will work fine)

Absolute densities

Sum of all the weights received by each cell, but re-scaled so the sum of the densities equal the total number of incidents (default)

Relative densities

Divides the absolute densities by the area of the grid

“Red represents “X” points per square mile, not per grid cell”

Probabilities

Divides the density by the total number of incident

“Chance” that any incident occurred in that cell

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KDE Parameters

Deciding which parameters to use for a particular dataset

Across how great an area is this incident likely to have an effect

Adjust interval distance (bandwidth size)

How much of this effect should remain at the original location; how much dispersed?

Adjust method of interpolation

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Incident Type	Interval	Interpolation Method	Reasoning
Residential burglaries	1 mile	Moderately dispersed: quartic or uniform	Some burglars choose particular houses, but most cruise neighborhoods looking for likely targets. A housebreak in any part of a neighborhood transfers risk to the rest of the neighborhood.
Domestic violence	0.1 mile	Tightly focused: negative exponential	Domestic violence occurs among specific individuals and families. Incidents at one location do not have much chance of being contagious in the surrounding area.
Commercial robberies	2 miles	Focused: triangular or negative exponential	A commercial robber probably chooses to strike in a commercial area, and then looks for preferred targets (banks, convenience stores) within that area. The wide area may thus be at some risk, but the brunt of the weight should remain with the particular target that has already been struck.
Thefts from vehicles	0.25 mile	Dispersed: uniform	If a parking lot experiences a lot of thefts from vehicles, your GIS will probably geocode them at the center of the parcel. This method ensures that the risk disperses evenly across the parcel and part of the surrounding area (which probably makes sense)—but not too far, since we know that parking lots tend to be hot spots for specific reasons.

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Creating a KDE

Data setup; add ArcGIS Pro SHP file theftfromautos;

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Creating a KDE

Create or Load (Ch.2) reference grid on Reference File tab

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Creating a KDE

Create or Load (Ch.2) reference grid on Reference File tab

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Creating a KDE

On Spatial modeling tab, Interpolation sub-tab, chose Single KDE;
Method: Uniform
Bandwidth: Fixed Interval
Interval: 0.25
Interval Units: Miles
Area Units: points per: Square Miles
Output Units: Absolute Densities

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Creating a KDE

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Creating a KDE

Save result to:
Save it as a SHP and call the file LFA (CrimeStat will add a K to the front of the file name) Click Compute

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Creating a KDE

Add the KLFA Shapefile to ArcGIS Pro and add the projection (similar to previous labs)

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Open KLFA shapefile in ArcView and create a choropleth map

Highlight KLFA
Click Appearance then click Symbology
Under Advacned Symbology Options – Sample Size – Maximum Sample Size – Set it to 1000000

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Open KLFA shapefile in ArcView and create a choropleth map

Primary Symbology – Graduated Colors
Field = Z
Method = Natural Breaks
Classes = 5

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Create a choropleth map

Click Dropdown menu on Color Scheme
Put Checks in Show Names and Show all
Choose Prediction

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Create a choropleth map

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Open KLFA shapefile in ArcView and create a choropleth map

You can have your students complete the lab using different intervals, etc.