First- and Second-Order Properties of Spatial Point Patterns: The Application of Crime Data from Baton Rouge, LA

LEITNER, Michael (mleitne@unix1.sncc.lsu.edu), Louisiana State University, E108 Howe-Russell Geoscience Complex, Baton Rouge, LA 70803

Key Words: crime analysis systems, spatial point pattern, Baton Rouge, LA

In recent years the United States (U.S.) has seen rapid development in the areas of crime analysis and mapping using geographic information systems (GIS) technology. Such development was in response to increasing crime rates especially in urban areas of the U.S. Instrumental in this development was the establishment of the Crime Mapping Research Center (CMRC) by the U.S. National Institute of Justice (NIJ) in 1996. The mandate of the CMRC is to promote research, evaluation, development, and dissemination of GIS for use in the field of criminal justice. The goal of this center and other law enforcement organizations has been to develop fully functional crime analysis systems (CAS) with standardized data collection and reporting mechanisms, tools for spatial and temporal analysis, visualization of data, and much more. The major problem of current CAS's are their lack of tools for spatial analysis, spatial modeling, and forecasting capabilities.

The purpose of this paper is to derive the first- and second-order properties of three different crime data sets and to investigate if these properties can be used to differentiate the spatial distribution between the data sets. This paper will further address if first- and second-order properties provide new insights into the spatial distribution of criminal activities previously not known. The first-order properties describe the way in which the expected value (mean or average) of the spatial point pattern varies across space (i.e., the intensity of the spatial point pattern). Such properties are usually measured with the so-called kernel estimation. Second-order properties describe the covariance (or correlation) between values of the spatial point pattern at different regions in space and are usually measured with the K function. Applied to crime data, both properties could be used to explore the spatial variation in the risk of being victimized by a crime, spatial and space-time clustering of criminal activities, and the raised incidence of criminal activities around point sources, such as robberies around ATM machines, subway entrances and exits, etc.

The three crime data sets used in this study were collected from police reports made available by the Homicide/Armed Robbery Division, Baton Rouge Police Department (BRPD). These data sets include the location of the homicide, the location of the victim's residence, and the location of the offender's residence. Altogether 497 homicide cases from the City of Baton Rouge, Louisiana, spanning1991-1997, are included in the analyses.

This paper will address the following conference topics: exploratory spatial data analysis and data mining; advances in geographical information systems, particularly in the area of spatial analysis; and geostatistics.