crimestat iii susan c. smith christopher w. bruce

CrimeStat III

Susan C. SmithChristopher 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….

• 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


• 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


• Why map crime?– 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


• 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


• 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


• Some map interpretation are impossible without spatial statistics– Geographic Profiling, Density Mapping


• 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…..


• 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-to-Crime 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 workbookChapter 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

• 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


• 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


• 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


• 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


• 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– 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


• 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


• 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 ultra-accurate 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


• 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


• 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


• 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

• 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


bandwidth)– Uniform (flat) distribution

• Represented by cylinder; all points in radius equal


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 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.

Creating a KDE

• Data setup; add ArcView SHP file theftfromautos;

• Create reference grid on Reference File tab• On Spatial modeling tab, Interpolation sub-

tab, 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

crimestat iii susan c. smith christopher w. bruce

Documents

slide slide

crimestat slide

crime mapping slide

crime analysis crimestat

map crime

workbook slide

use slide

design slide