CrimeStat III
Susan C. Smith
Christopher W. Bruce
About CrimeStat
About CrimeStat
• Spatial Statistics Program
• Analyzes Crime Incident Locations
• Developed by Ned Levine & Associates
– Grant 1997-U-CX-0040
– Grant 1999-U-CX-0044
– Grant 2002-U-CX-0007
– Grant 2005-U-CX-K037
• Provides supplemental statistical tools for
crime mapping
About CrimeStat
• Newest version is CrimeStat III (3.0)
• Program inputs incident locations (e.g.
robbery locations) in .dbf, .shp, ASCII or
ODBC-compliant formats using either
spherical or projected coordinates
• Program calculate various spatial statistics
and writes graphical objects to several GIS
programs (ArcMap for the purpose of this
workbook)
About CrimeStat
• The workbook provides copyright
information
• The workbook provides information on
how to correctly cite the program in
publications/reports
• The workbook provides a link to obtain
more information on CrimeStat, including
the complete manual
• Dr. Ned Levine’s contact information is
provided in the workbook
Chapter One
Introduction and Overview
In Chapter One….
•
•
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•
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Purpose of CrimeStat III
Uses of spatial statistics in crime analysis
CrimeStat III as a tool for analysts
Statistical Routines
Hardware and Software requirements
Downloading sample data
Chapter Layout and Design
Introduction
• Nearly all crimes have a location that can
be analyzed
• In crime analysis, we can identify patterns
by looking at the geography of the
incidents
• Analyzing crime location is a major part of
policing – from determining police districts
to response times to determining a tactical
deployment to an active crime series
Geographic Information Systems
• “GIS” is often synonymous with ‘crime
mapping’
• Crime mapping
– Geocoding incidents or other police-related
data and displaying them on a paper or
computerized map
• Geocoding
– The process of assigning geographic
coordinates to data records, usually based on
the street address
Geographic Information Systems
• When incidents are geocoded, a list or
database of crimes is turned into a map of
those crimes
• This map can now tell a story about the
police data
• Thematic maps are created
– Point Symbol maps
– Choropleth maps
– Graduated Symbol maps
Geographic Information Systems
• Why map crime?
–
–
–
–
–
–
–
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Identify patterns and problems
Identify hot spots
Use as a visual aid
Shows relationship between geography & other
factors
Look at direction of movement
Query data
Track changes in crime
Make maps for police deployment
…And many other reasons
Geographic Information Systems
• After you create the map, then analyze
• Why?
– To answer questions about data
• Historically, analysts relied heavily on
visual interpretation of the map to answer
the questions
– To identify hot spots
– To draw conclusions
– To recommend responses
Geographic Information Systems
• Why is visual interpretation not always possible?
– Can’t easily pick out hot spots among 1000s of data
points
– Can’t detect subtle shifts in the geography of a crime
pattern over time
– Can’t calculate correlations between two (or more)
geographic variables
– Can’t analyze travel times among complex road
networks
– Can’t apply complicated journey-to-crime calculations
across tens of 1000s of grid cells
• Spatial Statistics…a need filled by CrimeStat
CrimeStat III
• First released in August, 1999
• Current version, 3.1, released March 2007
• Not a GIS & does not create or display
maps
• It reads the files geocoded by a GIS and
then exports the results into formats the
GIS can read
• Effective use of CrimeStat requires a GIS
and knowledge of its use
CrimeStat III
• With geocoded crime data, CrimeStat can
perform calculations and output map
layers including (but not limited to):
– Mean/center of minimum distance of a group
of incidents
– An area representing the standard deviation
of a group of incidents or the entire
geographical extent of a group of incidents
– Statistics measuring the spatial relationship
between points
(con’t next slide)
CrimeStat III
• (con’t)
– Statistics that measure the level of clustering
or dispersion within a group of incidents
– Distance measurements between points
– Identification of hot spots based on spatial
proximity
– Estimation of density across a geographic
area through “kernel smoothing”
– Statistics that analyze the relationship
between space and time
(con’t next slide)
CrimeStat III
• (con’t)
– Statistics that analyzed the movement of a
serial offender
– Routines that estimate the likelihood that a
serial offender lives at any location in the
region, based on journey-to-crime research
– …And much, much more….
CrimeStat III
• Using CrimeStat statistical routines, an analyst is
able to
– Identify crime patterns & series
– Identify the ‘target area’ in which a serial offender is
most likely to strike next
– Identify and triage hot spots
– Conduct a risk analysis across a jurisdiction based on
known crime locations
– Create a ‘geographic profile’ to assist in investigating
suspected offenders
– Optimize patrol routes and response times
CrimeStat III
• CrimeStat is valuable for
– Tactical Crime Analysis
• Crime Patterns, Crime Series, Forecasting
– Strategic Crime Analysis
• Hot Spots, Problem Solving, Geographic Profiling
– Operations Analysis
• Patrol Routes, Patrol Districts, Response Times
Spatial Statistics in Crime
Analysis
• Some maps are simplistic and require only
a simple scanning and a limited amount of
human perception
– Hot Spot Identification, Spatial Forecasting
Spatial Statistics in Crime
Analysis
• Some map interpretation are impossible
without spatial statistics
– Geographic Profiling, Density Mapping
Spatial Statistics in Crime
Analysis
• It would be difficult to see subtle shifts in
crime incidents (within a series or pattern
or over years of changes in geography
within a jurisdiction)
These incidents are actually
moving northwestward over
time…..
Spatial Statistics in Crime
Analysis
• Other spatial statistics tools available to crime
analysts
– Those that come with ArcView & MapInfo
• ArcView’s SpatialAnalyst
• ArcView’s Animal Movements extension
– Geographic Profiling software
• Rigel byECRI
• Dragnet from Center for Investigative Psychology
– SPSS
– Microsoft Excel
• CrimeStat puts all of the methods into one
application…and it’s free!
Hardware and Software
• Windows operating system
– Windows 2000, Windows XP and Vista
• Must have 256 MB of RAM
• Must have 800MHz processor speed
– Best is 1GB of Ram / 1.6MHz processor
• Need a GIS to display the CrimeStat
outputs (ArcMap used in workbook)
Notes About the Book & Course
• Introductory course only
• Certain routines/techniques most
applicable to crime analysts
• So much more to learn…
– Correlated Walk Analysis
– Journey-to-Crime
– Crime Travel Demand
• Basic GIS background required
Exploring Lincoln, NE
• Lessons & screen shots use data from
Lincoln
• Some data has been manipulated or even
created/invented for lessons
• Outputs / maps should not be taken as an
accurate representation of crime in Lincoln
• Before starting the CrimeStat lessons,
explore the Lincoln data in the GIS
Exploring Lincoln, NE
• Open your GIS
• Add the following data layers
– Streets
– Citylimit
– Cityext
– Streams
– Waterways
• Display in a logical order
• Apply styles and labels as you please
Exploring CrimeStat
• There are five tab across the “top” of the
CrimeStat screen
• Under each tab, additional tabs appear
• They are color coordinated (in case you
lose your place)
• The five main tabs are:
– Data Setup
- Spatial Description
– Spatial modeling - Crime travel demand
– Options
Data Setup
• In CrimeStat
• Screen you specify the files on which you
want CrimeStat to perform
– The calculations
– The various parameters
• Note: CrimeStat does not query data
– You must already have the data queried out
– CrimeStat will perform spatial calculations on
the entire file
Data Setup
• CrimeStat requires at least one primary file
which will likely contain your crime data
• Allows for a secondary file for comparisons in
some types of spatial statistics
– Like comparing homicides (primary file) to poverty
rates (secondary file)
• A reference file is either imported or created in
CrimeStat
• A measurement parameters tab is provided to
input geographic information on your jurisdiction,
the length of the street network and the methods
for calculating distance.
Spatial Description
• Like descriptive statistics-analyze the data “as is”
• The Spatial Distribution tab includes functions
that tell us the central tendency and variance in
our data
– Includes the mean center, standard deviation ellipses
and convex hulls
• The Distance Analysis I screen has functions to
measure distances between points
– Nearest Neighbor Analysis & Ripley’s K help determine
the significant of the clustering or dispersion of the
incidents
– Assign primary points to secondary points takes the
points from one file and connect them to their nearest
neighbor in another file
Spatial Description
• Distance Analysis II has functions that create
matrices of distances between points
• Hot Spot Analysis I and II contains a series of
routines that help us identify, flag, and triage
clusters in our incident data
Spatial Modeling
• Helps create interpolations & predictions based
on our data
• The Interpolation tab contains the options to
create a kernel density estimation resulting in a
density map.
• Space-time analysis is about analyzing
progression in a series of crimes, including the
moving average (covered) and correlated walk
analysis (not covered)
• Journey-to-Crime and Bayesian Journey-toCrime Estimation helps determine the likelihood
of a serial offender living in a certain area based
on the locations of his offenses (not covered)
Crime Travel Demand
• Helps analyze travel patterns of offenders over
large metropolitan areas
• Emerging and potentially valuable analysis
• Very complex
• Not included in this workbook
Summary of CrimeStat Functions
• Refer to Table 1-1, pages 12-13
• Note the functions included in the workbook
Chapter 3
Mean Center, Standard Deviation
Ellipse, Median Center, Center of
Minimum Distance, Convex Hull
Chapter 4
Nearest Neighbor Analysis, Assign
primary points to secondary points
Chapter 5
Mode (Hot Spot), Fuzzy Mode, Nearest
Neighbor Hierarchical Spatial
Clustering, Spatial and Temporal
Analysis of Crime
Chapter 6
Kernel Density Estimate
Chapter 7
Spatial-Temporal Moving Average
Chapter Two
Getting Data into (and out
of) CrimeStat
In Chapter Two...
• File formats understood by CrimeStat
• Projection and coordinate system
considerations
• Associating your data with values needed
by CrimeStat
• Accounting for missing values
• Creating a reference grid
• Measurement parameters
• Getting data out of CrimeStat
Introduction
• Data must already be created, queried and
geocoded
• If your RMS or CAD automatically assigns
geographic coordinates, you can import
the data without going thru a GIS first
• CrimeStat can read many formats,
including .txt., .dat, .dbf, .shp, .mdb and
ODBC data sources
Introduction
• No matter the format, for CrimeStat to analyze
the data, the attribute table must contain X and
Y coordinates
– X and Y coordinates: X coordinate value denotes a
location that is relative to a point of reference to the
east or west and the Y coordinate to the north or
south
• Exception: ArcGIS ‘shapefiles’ which CrimeStat
will interpret automatically and add the X and Y
coordinates as the first columns in the table
Introduction
• Coordinate Systems
– Longitude (X) and Latitude (Y) data (spherical
coordinates)
• Can be determined easily because the X coordinate will be a
negative number (well, in North and South America)
• If data is in this format, CrimeStat doesn’t need anything else
• CrimeStat only reads long/lat data in decimal degrees (used
by most systems)
– U.S. State Plane Coordinates, North American Datum
of 1983 (projected coordinates)
• Specific to each state; based on an arbitrary reference point
to the south and west of the state’ boundaries.
• CrimeStat needs to know measurement units (feet/meters)
Entering Your First Primary File
•
•
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•
•
•
•
Open basemap in ArcView
Add burglary series shapefile
Check projection and coordinate system
Launch CrimeStat
Add shapefile to CrimeStat
Direct CrimeStat to X and Y coordinates
Select coordinate system and data units
Other Settings and Options
• These are not required
• Intensity – tells CrimeStat how many times to
‘count’ each point.
– Default is to count each point once
• Weight allows us to apply different statistical
calculations to different points
– Rarely used; but will see in a future chapter
• Time is used in several CrimeStat space-time
calculations
– Must be input as integers or decimal numbers; will
see in a future chapter
Other Settings and Options
• The missing value column allows us to
account for bad data
– Tell CrimeStat which records to ignore when
performing calculations
– Default is ‘blank’ which excludes blank fields
and those with nonnumeric values
– Users often choose “0”
– Enter each missing value (-1, 99, 999)
– Cannot enter ranges
Other Settings and Options
• Directional and distance fields are used
if your data uses polar coordinate systems
– This is rare
• The secondary file screen allows us to
enter a second file to relate to the first
– Must use the same coordinate system and
data units as the primary files
– Cannot include a time variable
Creating a Reference Grid
• CrimeStat needs to know the extent of the
jurisdiction
• The reference file is a grid that sits over
the entire study area
– Can be imported or created by CrimeStat
• To have CrimeStat create the grid
– Specify coordinates of lower left and upper right
extremities of the jurisdiction
» Coordinates must be in the same system as the
primary file
Creating a Reference Grid
• Select the Reference File tab; create grid
• Enter values for Lower Left & Upper Right
• Specify grid parameters
– Either distance for each cell, or
– Number of columns desired
• Save ‘LincolnGrid’
Measurement Parameters
• Final bits of data for certain routines
• Total area of jurisdiction (88.19 square miles in
Lincoln)
• Length of street network is the sum of all of
the individual lengths of the streets (1283.61
miles in Lincoln)
• The distance measurement tells CrimeStat
how we want to see the distances calculated
– Direct (as the crow flies), Indirect or Manhattan (along
a grid) or Network (uses actual road network)
Entering Measurement
Parameters
• Select the Measurement Parameters tab
• Enter values for Area & Length of street
Network
• Choose “Indirect (Manhattan)” for type of
distance measurement
Getting Data Out of CrimeStat
• If the routine results in calculations for a
number of records, it exports as a .dbf
• If the routine results in one or more sets of
coordinates, exports as
– a .shp for ArcView
– a .mif for MapInfo
– a .bna for Atlas GIS boundary file
Chapter Three
Spatial Distribution
In Chapter Three...
•
•
•
•
•
Spatial Forecasting
Mean and median centerpoints
Measures of variance
Analyzing a cluster
Limitations of spatial distributions
Introduction
• Introducing Spatial Distribution
– Forecasting
• Part Art / Part Science
– Probability
• Of being right
• Of being wrong
• Forecasting is inherent in any spatial or
temporal analysis
AGGRAVATED BURGLARY / SEXUAL ASSAULT SERIES
Recently three reports have been taken that share many similarities. These incidents involve a male
suspect targeting young females, who live alone (most likely in apartment complexes), specifically in
the northern part of Overland Park. Two of the crimes occurred at Blue Jay Apartments. The suspect
description has varied in all reported incidents; however it is believed to be the same person.
DEPLOYMENT IS RECOMMENDED IN THE AREA OF BLUE JAY APARTMENTS.
Also, officers are highly encouraged to conduct unoccupied vehicle checks northbound and
southbound on Metcalf from I-35 Hwy to 58th Street, between 2200 and 0200 hours.
Please document all contacts in this immediate area.
Investigators have followed up on Registered Sex Offenders residing in the area, Newly Released
Offenders from Probation/Parole, and tenants who have moved in or out of Blue Jay Apartments within
the past 60 days, but have found no leads. This information is also being disseminated metro-wide to
determine if this series is specific to Overland Park.
Spatial Forecasting
• Two Step Process
– Identify the target area for the next
incident
– Identify potential targets in the target area
Spatial Forecasting
Targets
– Consider availability of targets in any
given area
• Banks, restaurants, convenience stores (vs.)
• Pedestrians, parked cars, houses
Spatial Forecasting
• Three types of spatial patterns in tactical
crime analysis
– Those that cluster
• Concentrated in an area, but randomly
dispersed
– Those that walk
• Offender moving in a predictable manner in
distance & direction
– Hybrids
• Multiple clusters with predictable walks, or
• Cluster in which the average points “walks”
Types of Spatial
Patterns in Tactical
Analysis
Spatial Distribution
• How are the crimes distributed?
– Average location?
– Greatest volume / concentration?
– Boundaries?
• Questions can be answered by looking
at (points):
– Mean Center
- Geometric Mean
– Harmonic Mean - Median Center
– Center of Minimum Distance
Spatial Distribution
• Questions can be answered by looking
at (areas):
– Standard Deviation of X & Y Coordinates
– Standard Distance Deviation
– Standard Deviation Ellipse
– Two Standard Deviation Ellipse
Measures of Spatial
Distribution
• Mean Center
– Intersection of the mean of the X coordinates and
the mean of the Y coordinates
• Mean Center of Minimum Distance
– The points at which the sum of the distance to all
the other points is the smallest
• Median Center
– Intersection between the median of the X
coordinates and the median of the Y coordinates
• Great if you have outliers!
Measures of Spatial
Distribution
• Geometric Mean & Harmonic Mean
– Alternate measures of the mean center
– Just rely on the mean
Measures of Concentration
• Standard Deviation of the X and Y
coordinates
– A rectangle encloses the area in which four
lines intersect: one s/d above the mean of the
X axis, one s/d below the mean on the X axis,
one s/d above the mean on the Y axis and
one s/d below the mean on the Y axis
• Standard Distance Deviation
– Calculates the linear distance from each point
to the mean center point, then draws a circle
around one s/d from the center point.
Measures of Concentration
• Standard Deviational Ellipse
– Similar to the standard distance deviation but
accounts for skewed distributions, minimizing
any “extra space” that might appear in a circle
• Convex Hull Polygon
– Encloses the outer reaches of the series.
– No points fall outside of the polygon
• Outliers may greatly increase the size of the
polygon
Analyzing a Cluster
• Open burglary series in ArcView
• Click on Spatial Description tab in
CrimeStat
• Select appropriate checkboxes
• Save results for “burglaryseries”
• Compute
• Ten (10) ArcView shapefiles will be
created
• Open each, format and compare
Exercises – Page 33 & 34
Cautions & Caveats
• You generally can’t do this by hand
– Wouldn’t account for multiple incidents at a
single location
– Larger series or large volumes of crime would
be nearly impossible to interpret on your own
– CrimeStat can be precise; you cannot
(usually)
• Nothing should replace your experience,
intuition and the obvious (see Figure 3-7)
Figure 3-7: An unhelpful spatial distribution. The mean center, standard deviation ellipse,
and standard distance deviation circle are technically correct, but they miss the point of
the pattern, which is that it appears in two clusters. The analyst in this case would
probably want to create a separate dataset for each cluster and calculate the spatial
distribution on them separately.
Chapter Four
Distance Analysis
In Chapter Four...
• Nearest neighbor analysis
• Comparing relative clustering and
dispersion for multiple offense types
• Assigning points from one dataset to their
nearest neighbor in another dataset
Introduction
• Distance Analysis – statistics for
describing properties of distances between
incidents including nearest neighbor
analysis, linear nearest neighbor analysis
and Ripley’s K statistic
– Answers questions about the dispersion of
incidents
– Answers questions to help us identify where
crimes concentrate
Nearest Neighbor Analysis
• With random crimes scattered in a
jurisdiction, it’s normal to have small cluster
and wide gaps, but you’d still have an
average distance
• CrimeStat compares the actual average
distance between points and their nearest
neighbors with what would be “expected” in a
random distribution
• Now you can identify if your incidents are
significantly clustered or dispersed.
Measures for Distance
Analysis
• Two primary measures for distance
analysis in CrimeStat
– Nearest neighbor analysis
– Ripley’s K statistic
• (not covered in this workbook)
Nearest Neighbor Analysis
• Nearest Neighbor Analysis
– Measures the distance of each points to its
nearest neighbor, determines the mean
distances between neighbors and compared
the mean distance to what would have been
expected in a random distribution
• Can run routine to nearest, second nearest, third, etc.
• User define whether distance is
– Direct (standard)
– Indirect (linear)
– Based on a Network
Nearest Neighbor Analysis
• NNA produces the Nearest Neighbor
Index (NNI)
– Score of 1 = no discrepancy between
expected distance and measured distance
– Score lower than 1 = incidents are more
clustered than would be expected
– Scores higher than 2 = incidents are more
dispersed than would be expected
Nearest Neighbor Analysis
• Most crime types show clustering
– Geography plays a significant role
• No business burglaries in places without businesses
• No residential burglaries in places without residences
• No bank robberies in cities with no banks
• Primary value for analysts
– Conduct distance analysis for several crimes and
compare the results to each other
– You can then determine which offenses are most
clustered into “hot spot” and which are more
disperse
Comparing Distances for Three
Offenses
• Set up data in new CrimeStat session
• On Measurement Parameters, enter
jurisdiction information and type of distance
measurement
• Check Nearest Neighbor Analysis box on
Spatial description/Distance Analysis I tab
• Compute and examine results
• Repeat for other files
• Examine findings
Crime
Actual
Expected
NNI
Robberies
1066.8578
1874.1078
0.56926
Residential
Burglaries
348.7187
636.7427
0.54766
Thefts from Autos
236.2937
447.2314
0.52835
Cautions, Caveats and Notes
• We are computing single nearest neighbor
– You can change to another value, but not
higher than 100
– Significance is only calculated on single
nearest
– Limited utility for doing this
• Nearest Neighbors may occur on borders
– NNA overestimates in this case,
compensating for the “edge effect” if “Border
correction” option is chosen
Assigning Primary Points to
Secondary Points
• Two ways to conduct
– Nearest Neighbor Assignment
• Assigns each point in the primary file to the
nearest point in the secondary file
– Point-in-polygon Assignment
• CrimeStat interprets the geography of a polygon
rile (like police beats) and calculates how many
points fall within each file, regardless of anything a
point is technically closest to
• ArcGIS & MapInfo can perform this easily
Assigning Primary Points to
Secondary Points
• Set up CrimeStat for
“afternoonhousebreaks”
• Add schools on the Secondary File tab
• On Spatial Description / Distance Analysis
I tab, check Assign Primary Points to
Secondary Points box
• Save results
• Compute and examine results
Chapter Five
Hot Spot Analysis
In Chapter Five...
• Summary of different hot spot routines
• Mode and fuzzy mode
• Nearest neighbor hierarchical spatial
clustering
• Spatial and Temporal Analysis of Crime
Introduction
• Identifying hot spots
– A spatial concentration of crime, or
– A geographic area representing a small
percentage of the study area which contains a
high percentage of the studied phenomenon
– Can be on a variety of scales
•
•
•
•
A hot address
A hot office building
A hot block
A hot area
Hot Spot Routines
• Mode
– Identifies the geographic coordinates with the
highest number of incidents
• Fuzzy Mode
– Identifies the geographic coordinates, plus a
user-specified surrounding radius, with the
highest number of incidents
• Nearest-Neighbor Hierarchical Spatial
Clustering
– Builds on NNA by identifying clusters of incidents
Hot Spot Routines
• Spatial & Temporal Analysis of Crime
(STAC)
– Alternate means of identifying clusters by
“scanning” the point and overlaying circles on
the map until the density concentrations are
identified
• K-Means Clustering
– User specifies the number of clusters and
CrimeStat positions them based on the
density of incidents
Hot Spot Routines
• Aneslin’s Local Moran statistic
– Compares geographic zones to their larger
neighborhoods and identifies those that are
unusually high or low
• Kernel Density Interpolation
– A spatial modeling technique
Mode
• Just counts the number of incidents at one
spot
– Note: same address vs. X & Y coordinates
• Which is your records management or CAD
system receiving?
• How would this effect the mode?
Mode
• Set up a new CrimeStat session
• Check Mode on Spatial description / Hot
Spot Analysis I tab
• Click compute
• Top 45 locations, ordered by frequency
• Save result to (.dbf)
• (You could then import to GIS)
Fuzzy Mode
• User can specify a search radius around
each point
– Hence, it will include all of the points within
that radius in the count
• For agencies with GPS data, may be only
way to find hot spots
– Unlikely two incidents will have identical X & Y
coordinates
Figures 5-3 and 5-4: Accidents at several intersections. The agency has been ultraaccurate in its geocoding, assigning the accidents to the specific points at the
intersections where they occur. The mode method (left) would therefore count each
point only once, whereas the fuzzy mode method (right) aggregates them based on
user-specified radiuses
Fuzzy Mode
•
•
•
•
•
•
•
Return to CrimeStat screen
Uncheck Mode / Check Fuzzy Mode
Search radius of 500 feet
Save result to
Compute
Note different results from Mode
Create proportional symbol map based on
frequency in ArcView
Nearest Neighbor Hierarchical
Spatial Clustering
• Builds on NNA (NNA determines if a particular
crime was more clustered than might be expected
by random chance)
• NNH takes the analysis to the next level by
actually identifying those clusters
• CrimeStat clusters groups of pairs that are
unusually close together
• It creates “first order”, “second order” etc. clusters
• Continues until it cannot locate any more clusters
• Creates both s/d ellipses & convex hulls
Nearest Neighbor Hierarchical
Spatial Clustering
• Options that can be used when running
NNH
– Fixed distance vs. threshold distance
• Becomes a subjective measure vs. probability
– Minimum points per cluster
• Default is 10
• Alter depending on volume & type of crime
– Search Radius Bar
• Adjust threshold distance and associated
probability
– Left – smallest distance, but 99.999% confidence
– Right – greatest distances, but only .1% confidence
Nearest Neighbor Hierarchical
Spatial Clustering
• Options (con’t)
– Number of standard deviations for the ellipses
• Single s/d is the default/norm
– Can make small ellipses that are hard to view at a small
scale
• Another option is two s/d’s
– May exaggerate the size of the hot spot
– Convex hull vs. ellipse
• Convex hull has greater accuracy
• Convex hull has a higher density than an ellipse
• Convex hulls are defined by the data
Nearest Neighbor Hierarchical
Spatial Clustering
• Data Setup; Measurement parameters
• Spatial description, Hot Spot Analysis I,
uncheck Fuzzy Mode, check NNH
– Adjust minimum number points & size of ellipses
•
•
•
•
•
Save ellipses to….
Save convex hulls to….
Compute
Add to ArcView project; evaluate
Experiment with other NNH settings
Spatial and Temporal Analysis
of Crime (STAC)
• Originally a separate program; integrated
into CrimeStat in Version 2
• Produces ellipses and convex hulls
• STAC’s algorithm scans the data by
overlaying a grid on the study area and
applying a search circle to each node of
the grid
• Size is specified by user
• Routine counts the number of points in
each circle to identify the densest clusters
Spatial and Temporal Analysis
of Crime (STAC)
• Un-check NNH option; check STAC option
• Set STAC Parameters
– Note reference file “From data set” option
•
•
•
•
•
•
Save ellipses to….
Save convex hulls to….
Compute
Open in ArcView
Examine results
Run with other parameters
Final Notes on Hot Spot
Identification
• Clusters are identified based on volume, not
risk
– Two areas of town
• 3 burglaries in rural area vs. 20 burglaries in midtown
• Technique to normalize hot spots available
– Risk-Adjusted Nearest Neighbor Hierarchical
Spatial Clustering (RNNH)
• Relies on a secondary file with a denominator
– Number of houses, parking spots, etc
• In all of these routines, subjectivity plays a
role
Chapter Six
Kernel Density Estimation
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
Introduction
• Crime Analysts most often create
– Pin maps
– Kernel density maps
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AKA surface density maps
AKA continuous surface maps
AKA density maps
AKA isopleth maps
AKA grid maps
AKA hot spot maps
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
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
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….
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
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
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
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
KDE Parameters
• Methods of interpolation (shape of
bandwidth)
– Normal (bell curve)
• peaks & declines rapidly
• No defined radius; continues across entire grid
KDE Parameters
• Methods of interpolation (shape of
bandwidth)
– Uniform (flat) distribution
• Represented by cylinder; all points in radius equal
KDE Parameters
• Methods of interpolation (shape of
bandwidth)
– Quartic (spherical) distribution
• Gradual curve; density highest over point; falls to
limit of radius
KDE Parameters
• Methods of interpolation (con’t)
– Triangular (conical) distribution
• Peaks above the point; falls off in a linear manner
to edges of radius
KDE Parameters
• Methods of interpolation (con’t)
– Negative exponential distribution
• Curve that falls off rapidly from the peak to a
specified radius
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
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
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
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
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
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.
from
Creating a KDE
• Data setup; add ArcView SHP file
theftfromautos;
• Create reference grid on Reference File tab
• On Spatial modeling tab, Interpolation subtab, chose Single KDE; adjust bandwidth and
select interpolation method
• Save result to; compute
• Open KLFA shapefile in ArcView and create
a choropleth map
• Experiment with different settings
Dual KDE
• KDE based on two files
– Primary & Secondary
– Primary use is to normalize for risk
• In single KDE, hot spots are based on volume
• In dual KDE, hot spots are based on risk
– Four things to keep in mind
• Sometimes you just want volume
• Data for secondary file is hard to come by
• The point data in the secondary file is interpolated just
like the primary file
• You cannot use a different interpolation method for
numerator and denominator (but you can use an
adaptive bandwidth)
Dual KDE
• Set up Secondary File like Primary File
except
– Ratio of Densities
• Divides the density in the primary file with the density in
secondary file
– Log ratio of densities
• Helps control extreme highs and lows
– Valuable in strongly skewed distributions
– Absolute difference in densities
• Subtracts the secondary file densities from the primary
file densities
– Valuable in analyzing one time period to the next
Dual KDE
• Set up Secondary File like Primary File
except (con’t)
– Relative difference in densities
• Option divides primary and second files densities by
area of the cells before subtracting them (just like
absolute difference)
– Sum of densities
• Adds two densities together
– Useful to show combined effects of two types of crime
– Relative sum of densities
• Divides primary and second files by the area of the
cells before adding them
Dual KDE
• On Data Setup, remove larcey from autos
and add resburglaries.shp file
• On Secondary File, select
censusblocks.dbf, set variables, including
Z (Intensity)
• On Spatial Modeling, Interpolation tabs,
select “Dual” box (check weighting
variable option)
• Save Result to (.shp)
• Open ArcView, add layer, create
choropleth map
Dual KDE Uses and
Cautions
• KDE is a hot spot technique, but it is part
theoretical
• KDE maps are interpolations
– Meaning incidents did not occur at all of the
locations within the hottest color
• Creates a uniform risk surface (which is rare)
• You can only have bank robberies where there are
banks
– Hence, interpret a KDE in reference to where
suitable targets may exist within the risk
surface
Chapter Seven
Spatial Temporal Moving
Average
In Chapter Seven...
• Understanding the Spatial Temporal
Moving Average
• Using a time variable in CrimeStat
Introduction
• Spatial-Temporal Moving Average (STMA)
• Set of points in robbery series
– But mean, SD, SDE doesn’t represent the
series
– Something is “off”
• Recall two types of crime patterns (Chpt 3)
– Those that cluster
– Those that walk
Introduction
This one walks
Introduction
• STMA calculates the mean center at each
point in the series
– Tracks how it moves over time
– User specific how many point are included in
each calculation using the “span” parameter
• A span of “3” means it calculates the average for
that point and the two points on either side of it in
the sequence
– Final result is a series of moving average
points tied together to create a path
Introduction
• Span is the only parameter in the STMA
calculation
– Use an odd number for the center observation
to fall on an actual incident
– Default is five (5)
– Use caution when changing it
• Too high – won’t see much movement
• Too low – just viewing changes from one incident
to the next
Introduction
• All of the “Space-Time” analysis routines require a time
variable
• STMA needs it so it will know how the incidents are
sequenced.
• CrimeStat will not accurately calculate actual date/time
fields like “06/09/2008” or “15:10.”
– Instead, it requires actual numbers.
– It doesn’t matter where the numbers start as long as the intervals
are accurate, so if your data goes from June 1, 2008 to July 15,
2008, you could assign “1” for June 1, “2” for June 2, “31” for July
1,” and so on—or you could assign “3000” for June 1 and “3031”
for July 1.
• It’s really only the intervals that matter.
Introduction
• Microsoft makes date/time conversions easy
• It stores dates as the number of days elapsed
since January 1, 1900 and times as proportions
of a 24-hour day
• In either Access or Excel, we can convert date
values to these underlying numbers, so June 1,
2008 becomes 39600, and 15:10 becomes
0.6319
• We have already used Excel to figure the
Microsoft date from the actual date, and the field
is labeled “MSDate”
STMA
• New CrimeStat session using
CSRobSeries.shp file
• Add “Time” setting
– Note it needs a number, not an actual
date/time
– Already calculated in MSExcel; use MSDate
• Time Unit = Days
• Spatial Modeling, space-time analysis tab,
check STMA
STMA
• Save Output as .dbf
– CSRobSeries
• Save Graph as ArcView SHP
– CSRobSeries
• Compute
• Examine results
– Offender moving which way?
– What targets are available?
– Forecast next offense
CrimeStat III