A Spatial Statistics Program for the Analysis of Crime Incident Locations

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*CrimeStat* is a spatial statistics program for the analysis of crime incident locations, developed by Ned Levine & Associates, which was funded by grants from the National Institute of Justice (grants 1997-IJ-CX-0040, 1999-IJ-CX-0044, 2002-IJ-CX-0007, and 2005-IJ-CX-K037). The program is Windows-based and interfaces with most desktop GIS programs. The purpose is to provide supplemental statistical tools to aid law enforcement agencies and criminal justice researchers in their crime mapping efforts. *CrimeStat* is being used by many police departments around the world as well as by criminal justice and other researchers. The latest version is 3.3 (*CrimeStat III*).

The program inputs incident locations (e.g., robbery locations) in 'dbf', 'shp', ASCII or ODBC-compliant formats using either spherical or projected coordinates. It calculates various spatial statistics and writes graphical objects to ArcView/ArcGIS, MapInfo, Atlas*GIS, Surfer for Windows, and Spatial Analyst.

*CrimeStat* is organized into five sections:

Primary file - this is a file of incident or point locations with X and Y coordinates. The coordinate system can be either spherical (lat/lon) or projected. Intensity and weight values are allowed. Each incident can have an associated time value.

Secondary file - this is an associated file of incident or point locations with X and Y coordinates. The coordinate system has to be the same as the primary file. Intensity and weight values are allowed. The secondary file is used for comparison with the primary file in the risk-adjusted nearest neighbor clustering routine and the duel kernel interpolation.

Reference file - this is a grid file that overlays the study area. Normally, it is a regular grid though irregular ones can be imported.

*CrimeStat*can generate the grid if given the X and Y coordinates for the lower-left and upper-right corners.Measurement parameters - This page identifies the type of distance measurement (direct, indirect or network) to be used and specifies parameters for the area of the study region and the length of the street network. New in

*CrimeStat III*is the ability to utilize a network for linking points. Each segment can be weighted by travel time, travel speed, travel cost or simple distance. This allows the interaction between points to be estimated more realistically.

Spatial distribution - statistics for describing the spatial distribution of incidents, such as the mean center, center of minimum distance, standard deviational ellipse, directional mean, convex hull, Moran's I spatial autocorrelation index, Geary's C spatial autocorrelation index, Getis-Ord G spatial autocorrelation index, Moran correlogram, Geary correlogram, and Getis-Ord correlogram routines.

Distance analysis I - statistics for describing properties of distances between incidents including nearest neighbor analysis, linear nearest neighbor analysis, and Ripley's K statistic. New in

*CrimeStat III*is a routine that assigns the primary points to the secondary points, either on the basis of nearest neighbor or point-in-polygon, and then sums the results by the secondary point values.Distance analysis II - calculates matrices representing the distance between points for the primary file, for the distance between the primary and secondary points, and for the distance between either the primary or secondary file and the grid.

'Hot spot' analysis I - routines for conducting 'hot spot' analysis including the mode, the fuzzy mode, hierarchical nearest neighbor clustering, and risk-adjusted nearest neighbor hierarchical clustering. The hierarchical nearest neighbor hot spots can be output as ellipses or convex hulls.

'Hot spot' analysis II - more routines for conducting hot spot analysis including the Spatial and Temporal Analysis of Crime (STAC), K-means clustering, Anselin's local Moran, and the Getis-Ord local G statistics. The STAC and K-means hot spots can be output as ellipses or convex hulls.

Interpolation - a single-variable kernel density estimation routine for producing a surface or contour estimate of the density of incidents (e.g., burglaries) and a dual-variable kernel density estimation routine for comparing the density of incidents to the density of an underlying baseline (e.g., burglaries relative to the number of households).

Head Bang smoothing - the Head Bang statistic smooths zonal data to ensure reliable estimates. There is a standard Head Bang and an interpolated Head Bang for further smoothing over a study region.

Space-time analysis - a set of tools for analyzing clustering in time and in space. These include the Knox and Mantel indices, which look for the relationship between time and space, and the Correlated Walk Analysis module, which analyzes and predicts the behavior of a serial offender. New in

*CrimeStat III*is a spatial-temporal moving average.Journey-to-crime analysis - a criminal justice method for estimating the likely location of a serial offender given the distribution of incidents and a model of travel distance. The routine allows the user to estimate a travel model with a calibration file and apply it to the serial events. It can be used to identify an optimal central location given the distribution of 'points' and assumptions about travel behavior. New in

*CrimeStat III*is a routine for drawing lines between origins and destinations (crime trips).Bayesian Journey-to-crime analysis - a routine for adding information on where other offenders lived who committed crimes in the same locations to the Journey-to-crime estimate. This method improves accuracy and precision of the Journey-to-crime method and has been tested on sets of serial offenders in Baltimore County, Chicago, the Hague (Netherlands), and Manchester (England)

Regression modeling - CrimeStat III includes a regression module for modeling crime and other rare events as a function of one or more independent variables. Version 3.3 includes Ordinary Least Squares and Poisson models. The Poisson is generally a better method for modeling skewed distributions, such as crime. The current version includes "pure" Poisson, Poisson with linear correction, Poisson-Gamma, and Poisson-Gamma-CAR (a spatial regression) models. The Poisson-Gamma and Poisson-Gamma-CAR models are estimated by the Markov Chain Monte Carlo (MCMC) method. Additional models are currently being added.

Trip Generation - Separate models are produced that predict the number of crimes originating in each zone (origins) and the number of crimes ending in each zone (destinations).

*CrimeStat III*uses a multivariate Poisson regression model, with stepwise options, to create the prediction. Trips from outside the study area (external trips) can be added to the origin model to account for travel from outside the region. Once the models are created, a balancing procedure ensures that the number of origins equals the number of destinations.Trip Distribution - Using the predicted number of crime trips originating in each zone and the predicted number of trips occurring in each zone, the second stage distributes trips from each zone to every other zone using a gravity model. There are routines for calculating the actual (observed) distribution from individual data, for estimating the prediction coefficients, and for applying the predicted coefficients to the predicted origins and destinations. Another routine allows a comparison of the predicted trip distribution with the observed trip distribution.

Mode Split - The predicted number of trips for each zone-to-zone pair can be split into likely travel modes using an accessibility function that approximates the utility of one mode relative to the others.

Network Assignment - Finally, the predicted trips from each zone to every other zone by travel mode are assigned to a likely route based on the A* shortest path algorithm. The output includes the likely routes taken for each origin-destination zone pair and the total volume of trips on network links. This step requires a travel network, one for each travel mode. There are additional utilities for calcuating transit networks from station/stop locations and for testing for one-way streets.

Parameters can be saved and re-loaded.

Tab colors can be changed.

Monte Carlo simulation data can be output.

Crime travel demand modeling is an application of travel demand modeling, widely used in transportation planning, to crime analysis. The analysis is done by zones. First, crime 'trips' are defined as a link between an offender residence/origin location and a crime location. The number of crimes originating in each zone is counted as is the number of crimes ending in each zone. Second, the model is run sequentially in four separate stages with multiple routine in each stage:

*CrimeStat* is accompanied by sample datasets and a manual that gives the background behind the statistics and examples. The manual also discusses applications of *CrimeStat* developed by other analysts and researchers. The program and sample data sets are in Windows-based zipped files that can be downloaded. The manual is a set of individual chapters in PDF files which can be viewed online or downloaded.

Here are some maps from Baltimore County (MD) that illustrate statistical calculations made by CrimeStat.

The above map shows the distribution of vehicle thefts in Precinct 11 between June and July 1996.

The above map shows vehicle theft risk (vehicle thefts relative to population).

The above map shows robbery 'Hot Spots'.

Finally, the above map shows crime trips on the Baltimore road system.

- Ned Levine
**,***CrimeStat III: A Spatial Statistics Program for the Analysis of Crime Incident Locations*(version 3.3). 2010, Ned Levine & Associates: Houston, TX/ National Institute of Justice: Washington, DC.

- Ned Levine and Phil Canter. “Linking origins with destinations for DWI Motor Vehicle Crashes: An application of crime travel demand modeling”.
.2011, In press.*Crime Mapping* - Ned Levine and Richard Block. “Bayesian Journey to crime estimation: an improvement in geographic profiling methodology”.
. 2011, 63(2) 2011, 1–17.*The Professional Geographer* - Ned Levine. “Introduction to the special issue on Bayesian journey to crime modeling”.
. 2009, 6 (3), 167-185.*Journal of Investigative Psychology and Offender Profiling* - Ned Levine, "Crime mapping and the CrimeStat program".
. 2006, 38 (1), 41-55.*Geographical analysis* - Ned Levine, "Spatial statistics and GIS: Software tools to quantify
spatial patterns".
. 1996, 62 (3): 381-392.*Journal of the American Planning Association* - Ned Levine, Karl E. Kim, and Lawrence H. Nitz, "Spatial analysis of Honolulu motor vehicle
crashes: I. Spatial patterns".
. 1995, 27 (5): 663-674.*Accident Analysis & Prevention*

Last updated March 11, 2011