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CrimeStat III Susan C. Smith Christopher W. Bruce

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About CrimeStat

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•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

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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)

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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

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Chapter One Introduction and Overview

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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

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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

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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

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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

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Geographic Information Systems •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

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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

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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

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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

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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)

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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)

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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….

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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

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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

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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

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Spatial Statistics in Crime Analysis •Some map interpretation are impossible without spatial statistics –Geographic Profiling, Density Mapping

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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…..

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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!

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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)

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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

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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

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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

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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

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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

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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.

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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

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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

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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)

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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

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Summary of CrimeStat Functions •Refer to Table 1-1, pages •Note the functions included in the workbook Chapter 3Mean Center, Standard Deviation Ellipse, Median Center, Center of Minimum Distance, Convex Hull Chapter 4Nearest Neighbor Analysis, Assign primary points to secondary points Chapter 5Mode (Hot Spot), Fuzzy Mode, Nearest Neighbor Hierarchical Spatial Clustering, Spatial and Temporal Analysis of Crime Chapter 6Kernel Density Estimate Chapter 7Spatial-Temporal Moving Average

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Chapter Two Getting Data into (and out of) CrimeStat

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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

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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

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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

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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)

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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

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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

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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

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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

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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

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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’

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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 ( 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)

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Entering Measurement Parameters •Select the Measurement Parameters tab •Enter values for Area & Length of street Network •Choose “Indirect (Manhattan)” for type of distance measurement

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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

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Chapter Three Spatial Distribution

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In Chapter Three... •Spatial Forecasting •Mean and median centerpoints •Measures of variance •Analyzing a cluster •Limitations of spatial distributions

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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

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Spatial Forecasting •Two Step Process –Identify the target area for the next incident –Identify potential targets in the target area

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Spatial Forecasting Targets –Consider availability of targets in any given area •Banks, restaurants, convenience stores (vs.) •Pedestrians, parked cars, houses

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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”

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Types of Spatial Patterns in Tactical Analysis

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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

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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

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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!

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Measures of Spatial Distribution •Geometric Mean & Harmonic Mean –Alternate measures of the mean center –Just rely on the mean

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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.

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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

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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

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Exercises – Page 33 & 34

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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)

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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.

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Chapter Four Distance Analysis

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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

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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

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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.

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Measures for Distance Analysis •Two primary measures for distance analysis in CrimeStat –Nearest neighbor analysis –Ripley’s K statistic •(not covered in this workbook)

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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

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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

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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

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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

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CrimeActualExpectedNNI Robberies Residential Burglaries Thefts from Autos

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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

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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

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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

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Chapter Five Hot Spot Analysis

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In Chapter Five... •Summary of different hot spot routines •Mode and fuzzy mode •Nearest neighbor hierarchical spatial clustering •Spatial and Temporal Analysis of Crime

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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

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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

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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

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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

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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?

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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)

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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

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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

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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

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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

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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 % confidence –Right – greatest distances, but only.1% confidence

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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

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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

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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

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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

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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

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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 •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 TypeIntervalInterpolation MethodReasoning Residential burglaries 1 mileModerately dispersed: quartic or uniformSome 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 mileTightly focused: negative exponentialDomestic 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 milesFocused: 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 mileDispersed: uniformIf 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 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

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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)

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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

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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

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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

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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

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Chapter Seven Spatial Temporal Moving Average

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In Chapter Seven... •Understanding the Spatial Temporal Moving Average •Using a time variable in CrimeStat

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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

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Introduction This one walks

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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

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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

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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.

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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 •We have already used Excel to figure the Microsoft date from the actual date, and the field is labeled “MSDate”

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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

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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

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CrimeStat III

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