Mapping Crime for Analytic Purposes: Location Quotients, Counts, and Rates

Crime can be analyzed and mapped in a number of different ways. This article compares maps of violent crime across the cities of British Columbia utilizing three crime measures: counts, rates and crime location quotients (LQCs). The LQC, adapted from regional planning, provides views of crime patterns not obtained with the two more traditional measures of crime. When used in conjunction with crime counts and rates, the LQC offers a way of understanding how one area is different from another for purposes of research and deployment of prevention and control resources. Crime and its contextual backcloth exist at many spatial and temporal levels of resolution, from the international scene to the individual crime site, from the trends of centuries to the patterns of seconds (Brantingham and Brantingham, 1993, 1984; Brantingham et al., Address correspondence to: Patricia L. Brantingham, School of Criminology, Simon Fraser University, Room WMC-1630, Burnaby, BC V5A 1S6, CAN (e-mail: pbrantin@sfu .ca). 264 — Patricia L. Brantingham and Paul J. Brantingham 1976). That is, crime can be studied, analyzed and dealt with at many different levels of aggregation in time and space. Meaningful crime analysis can be done, for instance, at international levels, at national levels, across smaller areas that range from regions to states to counties to cities, and at detailed levels within a particular city — even down to the street block or individual address level. Temporal analyses can sweep across centuries, can examine a set of years, months, days, hours, minutes or seconds. Over the past decade, mapping has become a key tool for crime analysts seeking to understand the patterns of crime (see, e.g., Block et al., 1995), enabling them to see or visualize differences and similarities across time and space. Analyses of individual criminal events and of individual person, building or street victimization studies are currently of great interest (Clarke, 1980, 1992), but for practical purposes individual criminal events must be aggregated in order to assess patterns and devise methods for addressing them (e.g., Kohfeld and Sprague, 1990; Kennedy and Forde, 1990; Normandeau, 1987; Brantingham et al., 1991; Cusson, 1983, 1993). The variety of questions open to the crime analyst and the level in the cone of resolution used in analysis will always vary with the type of problem being considered. In addition, the type of crime measure used in analysis will vary with the problem under consideration. This article explores how questions about crime, measures of crime and levels of resolution are linked conceptually, and how crime analysis can be improved by mapping different measures of crime and comparing the results. The article illustrates this by mapping three different crime measures — the crime count, the crime rate, and the crime location quotient (LQC) — at the interurban level of resolution, utilizing 1994 crime data from the 68 separate municipal policing jurisdictions in British Columbia, CAN. A particular emphasis is placed on crime location quotients because this is a relatively new technique for criminologists. The LQC will be described in more detail later in this article, but it is basically a method of measuring the relative mix of different types of crimes for a particular area compared to the mix in surrounding areas. For example, a city such as Tucson or Virginia Beach can have a relatively low robbery rate but still have neighborhoods in which robbery makes up a relatively high proportion of all crimes compared to the city as a whole. Robbery is a problem in such neighborhoods even when it is not a problem citywide. Conversely, robbery can make up a very high proportion of offenses in a city such as San Francisco or Mapping Crime for Analytic Purposes — 265 Newark, but within such "robbery* cities there will be subareas in which robbery represents a low proportion of crimes. Such proportional mixes are independent of total crimes in an area, and really represent a local crime "specialization." As will be shown in this article, when used in conjunction with crime counts and crime rates, LQCs offer a way of understanding how one area is different from another for purposes of research and deployment of prevention and control resources. This article focuses on city-level data, but the LQC can be used for comparison of states or nations on the one hand or for comparison of regions, cities or neighborhoods on the other. The LQC can be used for comparison of the crime mix in different decades within centuries in historical research, or for comparison of the crime mix within the different hours of the day in thinking about deployment of police during different shifts. It is a tool that can be used at different levels of spatial and temporal resolution. STATISTICAL CRIME ANALYSIS There is a need for constant improvement and innovation in methods of analysis, no matter what questions are being asked or what levels of resolution are being studied. Methods are constantly changing. The methods used by criminologists frequently originate from other disciplines such as sociology, psychology, geography, statistics or mathematics. These are not static disciplines. Interestingly, many currently used techniques had their origins in studies of criminal events. For instance, in statistics both Quetelet (1842) and Poisson (1837) focused on the study of crime. Galton, Pearson and Yule were all concerned, among other things, with developing statistical techniques that could be used to understand crime, as both hereditary and social problems (Stigler, 1986). This article describes and maps the LQC, a new type of crime measure borrowed from the related disciplines of regional economics and regional planning. The location quotient (LQ) is used in regional planning and regional economics to look at relative local economic activity. LQs will be described in some detail after a brief review of crime counts and crime rates. Crime analysis in the tradition of Guerry (1831) and Quetelet (1842), and as conducted by most criminologists, looks at crime as an aggregate measure for some summary unit. The most common summary measures are crime counts and crime rates based on po266 — Patricia L Brantingham and Paul J. Brantinqham lice-recorded offenses, victimization rates based on survey estimates, and offender rates based on surveys and judicial convictions data. Crime counts are used to assess the locations of "hot spots," assess police work loads and estimate future resource needs. Police, after all, must respond to discrete events, not estimates or ratios. In Canada, crime counts take the form of "actual crimes." These represent events recorded as crimes following a preliminary investigation that has established that a "reported crime" has in fact occurred. Crime rates, in contrast, are used to assess the risk of crimes occurring to particular types of people in particular locations or at particular times, and to assess trends discounted for changing conditions (such as population growth). Crime rates are particularly useful in planning prevention campaigns and in assessing the impact of changing social conditions of the risk of crime. Crime rates use some measure of crime occurrence as a numerator and units at risk as a denominator. The numbers in the numerator and denominator vary. Ideally the numerator is some measure of events or occurrences, and the denominator is the most direct measure of units at risk. When the numerator is a personal crime, the denominator frequently is the number of people residing in the aggregation area. When the numerator is residential breaking and entering, the denominator frequently is the number of dwelling units. There are always problems with such crime measures. The count of events, based on official data, is usually an undercount both because some crimes are not reported to police and because counting and recording rules typically record only the most serious offense in any complex criminal transaction. Such counts do, however, appear to be good measures of serious offenses and of offenses involving lost property covered by insurance (Litton and Pease, 1984; Brantingham and Brantingham, 1984; Gove et al., 1985). There are difficulties obtaining reasonable estimates for denominators when the potential "victims" move or are moveable. Boggs' (1960) work began the exploration of how patterns change as the denominator in the ratio changes. For example, an auto theft rate based on a residential population ratio produces a very different picture of highand lowcrime areas in a city from that produced by a rate calculated using the number of automobiles present in the different areas. Boggs' (1960) work has been carried many steps further by Harries (1991); both show the interesting variability in what is "seen" as denominators change. Mapping Crime for Analytic Purposes — 267