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Substance Use & Misuse, 43:179­201 Copyright © 2008 Informa Healthcare USA, Inc. ISSN: 1082-6084 (print); 1532-2491 (online) DOI: 10.1080/10826080701690573

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The Geography of Drug Activity and Violence: Analyzing Spatial Relationships of Non-Homogenous Crime Event Types

CYNTHIA LUM

George Mason University, Administration of Justice Department, Manassas, Virginia, USA

The pervasiveness of interest regarding the theme of a relationship between street-level drug activity and violence has been reflected throughout criminal justice research, policy, and practice as well as in public opinion. Most research has focused on the connection between the two at the individual level. This study extends previous research by examining the place-based relationship between drugs and violence. To do so, this project employs three spatial statistical approaches--measures of spatial intensity/density, measures of spatial dependence for drugs and violence separately, and a modified spatial dependence approach for non-homogenous populations to explore the relationship between drug activity and violence. The findings indicate that while drugs and violence often exhibit overlapping spatial patterns, important variations exist in the spatial relationship between the two. Keywords drugs; violence; spatial analysis; geography; place-based; drug markets

Drugs and Violence at Places

Street-level drug activity and violence are two of the most pervasive crime-related social problems that plague large urban cities in the United States today. This unfortunate reality is not only reflected throughout criminal justice policy and practice but has also captured the interests of social scientists studying place-based criminal behavior and justice agency responses at these places (see, e.g., Anderson, 1990; Graham and Clarke, 1996; Rengert and Pelfrey, 1997; Roncek, 1981; Sherman and Rogan, 1995; Weisburd and Green-Mazerolle, 2000; Wilson, 1997). Additionally, a popular view exists among both law enforcement and citizens that connects drug activity to violence as well as to general notions of danger (see, e.g., Berhie and Hailu, 2000; Drug Enforcement Agency, 2002; Los Angeles Police Department, 2001; Lum, 2006; New York City Police Department, 2002; Walsh, Vito, Tewksbury, and Wilson, 2000). Despite this widespread belief of a connection between drugs and violence, in a recent review of the state of drug-violence research, MacCoun, Kilmer, and Reuter (2002) suggested that the large body of literature discussing the interaction between drugs and violence (especially at places) leaves many questions unanswered. The majority of this research has focused on the drug-crime nexus at the level of the individual--how drug activity (use or sales) affects, causes, or exacerbates a person's criminality (Chaiken

Address correspondence to Cynthia Lum, George Mason University, Administration of Justice Department, 10900 University Blvd., MS 4F4, Manassas, VA 20110-2203. E-mail: [email protected]

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and Chaiken, 1990; Chaiken, 1986). This individual-level research remains controversial, especially in terms of psychopharmacological explanations that connect the ingestion of drugs with violent behavior. Despite this seemingly common-sense interaction, evidence that drug use is a root cause of violent behavior is not consistently convincing (see Barker, Geraghty, and Webb, 1993; Farabee, Joshi, and Anglin, 2001; Goldstein, 1985; Inciardi, 1990; Miczek et al., 1994; Parker and Auerhahn, 1998; Tonry and Wilson, 1990; also, see White and Gorman, 2000, for a comprehensive review of the drug-crime literature). However, at other levels of analyses (over time, across places, within situations), scholars have asserted that there might be a more complex connection between drugs and violence. For example, a growing body of research has explored a link between crime trends and the expansion and contraction of illicit drug and firearm markets over time (Blumstein, 1995, 2000; Blumstein, Cohen, Cork, Engberg, and Tita, 1999; Blumstein and Wallman, 2000; Cork, 1999; Johnson, Golub, and Dunlap, 2000; Ousey and Lee, 2002). This work is more generally related to scholarship regarding "systemic" relationships between drugs and violence (see Goldstein, 1985). The systemic approach emphasizes the utility of violence in the multiple and varied interactions, routines, and structural mechanisms that take place within the drug market (Blumstein, 1995; Goldstein, 1985, 1998). For example, individuals involved in drug markets may be a part of subcultural systems that use violence to facilitate economic transactions as opposed to more legal business mechanisms such as laws, regulatory agencies, or other accepted business practices (Baumer, 1994; Baumer, Lauritsen, Rosenfeld, and Wright, 1998; Goldstein, 1998; Harrison and Backenheimer, 1998; Johnson et al., 2000; Ousey and Lee, 2002; Steffensmeier and Harer, 1999). Open-air drug markets can also bring together people with weapons, vulnerable victims, hard cash, and opportunities to rob and assault. Also relevant to a systemic approach is the idea that increased law enforcement in drug areas may exacerbate already existing violent subcultures of drug markets by affecting supply, demand, risks, and profits (Resignato, 2000). The systemic approach has been seen as a fruitful perspective in establishing links between drug activity and violent behavior (Blumstein, 1995; Goldstein, 1985, 1998; Johnson et al., 2000). Systemic explanations extend beyond psychopharmacological explanations and imply temporal, spatial, behavioral, or situational contexts by which drugs and violence might be related. In particular, the systemic approach is especially informative for a geographic understanding of the drug-violence relationship. If routines of individuals involved in the drug market (either as users or sellers) are geographically bound, then patterns of violence resulting from drug market interactions may also display overlapping geographic patterns with drug activity. For example, a recent work by Tita and Griffiths (2005) has indicated an individual-level spatial connection between homicide and drug activity through the use of mobility triangles (see Rand, 1986) and routine activities theory (see Cohen and Felson, 1979). At the same time, the systemic links between drug markets and violence do not necessarily suggest that drug activity and violence will occur at the same places. The locations of packaging, distribution, and use may extend over large geographic areas if modes of transportation are regularly involved in these routines. Or, violence may be discouraged in some areas where drug markets thrive because it scares away customers or may not be a functional aspect of a particular drug market's culture or organization. More stable drug markets may have less violence as competition wanes. It is unclear how individual routines aggregate into crime patterns and subsequently how drug-violence routines and interactions result in coinciding spatial patterns. Furthermore, the existence of drugs and violence at

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the same places may not be due to an interaction between the two, but both may occur as a result of other factors. While many of these questions are beyond the scope of this study, the research here empirically explores the place-based indications of the systemic approach. Specifically, is there an overlap between the locations of drug activity and violent crime, and how can we detect this overlap? There have been a few studies that have informed our knowledge about the spatial relationship of drugs and violence across numerous places. Braga et al. (1999), in an experiment evaluating problem-oriented policing, found that violent crime hot spots in Jersey City also had evidence of active drug markets. In some of these places, their analysis revealed that violence was directly drug market related. Also examining Jersey City, Weisburd and Green-Mazerolle (2000) aggregated drug crimes in specific street segments and intersections and found that in selected areas with high amounts of drugrelated calls for service there were also abnormally high violent crime counts. Additionally, they discovered that drug hot spots were characterized by high volumes of disorder or nuisance calls. Gainey and Payne (2003) examined crimes in Norfolk, Virginia, and found a strong, positive correlation between rates of drug and violent crimes across census block groups. While none of these studies examined the spatial relationship between individual locations of drug and violent crime events, their work provides an important empirical starting point in thinking about the spatial overlap of drugs and violence. This study adds to these works by utilizing spatial statistical techniques to conduct a comprehensive study of the spatial relationship between drugs and violent crime at all places across an entire city. Similar to Weisburd and Green-Mazerolle and Gainey and Paine's works, this study begins with comparing the intensity of drugs and violence at census tracts and block groups. Measures of intensity are similar to aggregating rates of crime in places without concern about the specific relationship between the locations of individual drug and violent crime incidents. This research then extends previous work by examining whether clusters (or "hot spots") of drug activity and clusters of violent crime occur at the same locations using spatial dependence statistical methods. Finally, this study modifies spatial dependence analyses to accommodate the comparison of non-homogenous also called inhomogenous crime categorizations, comparing individual locations of drug activity to individual locations of violent crime to ascertain their spatial dependence upon each other.

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The Data

To explore the spatial relationship between locations of street-level drug activity and violent crime, official crime data and digital maps were obtained from the Seattle Police Department and the City of Seattle. Deciphering the behavior of drugs and violence across geography depends on both the quality of the data and the viability of the method used for analysis. With regards to the data, the choice of the source of information to study this relationship could influence the outcome of the analysis. In particular, the validity of data used to measure drug activity is often challenged because of the nature of the offense (often considered consensual and underreported) as well as its enforcement (reporting may be systematically biased by police choices as to what and where to enforce). Because of this, four different types of data were initially collected, compared, and analyzed for this study: 911 calls for service as first recorded by the dispatcher, officer-modified 911 calls for service database where incidents were modified upon the initial response of an officer, computerized records

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of written reports, and reports of arrest. Additionally, only crimes that occurred in the years 1999, 2000, 2001, and 2002 were used since these were the years for which data existed from all four sources. Throughout the cleaning and analysis of the data, differences emerged regarding the validity of each data source and their meaningfulness in analysis, common concerns that have been well documented (Decker, 1978; Klinger and Bridges, 1997; Sherman, Gartin, and Buerger, 1989). These differences presented problems at all stages of this research, including selecting, cleaning, and analyzing spatially referenced data (see Lum, 2003, for a detailed discussion of this problem in Seattle). In short, it became clear that written report data underreported drug activity, arrest data underreported violent crime, and dispatchercoded 911 calls systematically miscoded call types and their locations for a variety of reasons (for example, there were no records of homicide in the dispatcher database and addresses were often not specified). Thus, for the purposes of this exercise, an officer-modified version of the calls for service database was chosen to explore the drug-violence spatial connection. Unlike the dispatcher calls for service database, entries in the officer-modified database were further specified after an initial police officer response, correcting for errors in the recording of the location or type of offense by dispatchers. Although such modifications by officers have other problems (for example, systemic biases influenced by officer culture, personality, or departmental practices), this database was a good compromise given the variety of issues with all four databases. Only violence (homicide, all assaults including sex crimes, robberies, shootings and other weapon offenses) and drug crimes (possession, use, distribution or manufacturing of illegal drugs) were retained. In total, 105,447 records were analyzed. To explore the spatial relationship between drug activity and violent crime as measured by the officer-modified database, latitude and longitude coordinates were assigned to each crime event based on the recorded location using an interactive approach involving a geographic information1 and database manipulation software.2 The coordinates were then subsequently transferred into a spatial statistical program3 for analysis.

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Traditional and Modified Exploratory Spatial Data Analysis (ESDA) for Non-Homogenous Populations

Because of the complexities involved in spatially analyzing the relationship between two or more categories of crimes, three types of exploratory spatial data analyses were employed. The first was intensity/density analysis, which standardizes the number of crimes to the size of a geographic area. Secondly, spatial dependence analyses of drugs and violence were separately conducted and then compared to the other. I labeled this analysis as withinclassification spatial dependence, indicating that spatial clustering of drug activity and violent crime were calculated within their own classification. Finally, a modified dependence analysis was conducted to determine the dependence between individual locations of drug activity and violent crimes (as opposed to comparing clustering of each). This was labeled between-classification spatial dependence and is similar to strategies suggested in spatial epidemiology for inhomogenous populations (see Cuzick and Edwards, 1990; Diggle and Chetwynd, 1991; Waller and Gotway, 2004). As theories about the behavior of crime over geography develop, these types of spatial statistical approaches have become helpful in understanding crime patterns and provide a geographic context to crime causation (Anselin, Cohen, Cook, Gorr, and Tita, 2000; Harries, 2001; Mencken and Barnett, 1999; Messner et al., 1999).

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Before explaining and providing the results for each method used, it should be noted that to conduct these three types of analyses, individual locations of all drug and violent crime events within every area of Seattle were analyzed as opposed to only "hot spots" of these classifications. As already alluded to, while hot-spot analysis has proven useful in identifying small areas for targeted police deployment, it may not provide a complete picture of variations in the drug-violence relationship across all places or an understanding of the spatial relationship between the individual locations of multiple categories of events. Thus, Seattle was divided into multiple geographic units and exploratory spatial data analysis was conducted separately for each of these data sets. Specifically, for intensity analysis, 124 U.S. census tracts and 579 block groups were analyzed. For both types of dependence analyses, only tracts were used, for reasons shortly given. This means that 124 separate data sets were developed and separate analysis conducted for each. Separate analyses for multiple regions is utilized because exploratory spatial data analysis cannot be conducted once (e.g., on the entire city of Seattle) as this would violate a number of spatial statistical assumptions necessary for spatial analysis. The appropriate applications of these statistical assumptions of spatial analysis are influenced by the size, shape, and location of the study region (see Bailey and Gatrell, 1995, for a detailed explication of these assumptions). Spatial processes can be stochastic and therefore modeled mathematically through probability distribution functions, which in turn depend on the location of those processes. For example, the intensity (or count) of crime at one place may be related to the intensity of crime at an area nearby but unrelated to the intensity of crime at the other end of the city (even though the intensities may be very similar). Thus, to represent the distribution across a geographic area, Bailey and Gatrell (1995) argue that one may need a "set of possibly non-independent random variables" (p. 28), which they view as a particular spatial stochastic process. As they point out, this could be a daunting task; thus, assumptions are made about the data within the geographic region of interest to deal with this issue. The two main assumptions that are made in spatial analysis are stationarity (or homogeneity) and isotropy (see Bailey and Gatrell, 1995, for an elaboration of these issues). Stationarity implies that the mean and variance of values within a geographic region are independent of absolute location. The spatial process of crime across Seattle, if stationary, would suggest the mean crime rate does not vary due to the location or the area studied. A descriptive map of the spatial point patterns of drugs and violence reveals that this is not the case; across the city of Seattle, crime patterns vary dramatically depending on their locations. The second assumption of isotropy (given the assumption of homogeneity) suggests that the dependence between points relies only on the distance between points, rather than on distance and direction. Again, crime maps also suggests that across Seattle as a whole, the assumption of isotropy may not hold, given that greater concentrations of crime occur at the central part of Seattle. There also appears to be a global southeast to northwesterly trend of crime in the city. To decrease the potential of violating these assumptions, one can decrease the size of the geographic unit of analysis, which reduces large variations that exist across jurisdictions such as cities, counties, or states. However, other problems may arise with smaller geographical units, in particular, smaller sample sizes, which may lead to less meaningful results as well as the magnification of the modifiable areal unit problem (where clusters are divided by artificial boundaries). The balance between the geographic size of the region to maintain these assumptions and sample sizes and reduce the modified aerial unit problem for meaningful analysis is often what leads to the exploratory nature of spatial analysis;

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the researcher may run multiple analyses on different geographic units in a trial-and-error fashion. While not perfect, this study employed both United States Census tracts and block groups to create the separate subregions for different types of analysis to accommodate these concerns. When comparing rates of crime in an area (intensity analysis), both block groups and tracts are examined. However, because small sample sizes and the modified areal unit problem are more problematic the smaller the geographic unit, only tracts are used when examining the dependence between drugs and violence. Additionally, in a related study (see Lum, 2006), the author needed a geographic unit that recorded social and demographic information. Overall, while it is acknowledged that other geographic units may reveal different findings (as is the case with any spatial analysis), tracts best served these multiple study goals. As will be explained, this does not mean that drug and violent crimes are only aggregated across an entire census tract and then compared with each other. The spatial relationship analyses conducted in this study compare both general rates of crime and the individual locations of drug and violent crime events within tracts. The units of analysis, therefore, are the individual events, not the census tract.

Analysis I: The Spatial Intensity of Drugs and Violence

As aforementioned, spatial patterns and processes in this study are measured in two ways: by intensity and by dependence. Intensity or density analysis measures the rate of events per unit area, whereas spatial dependence analysis measures the relationship of points (or attributes of points in the case of spatial autocorrelation) to each other. The estimation of spatial intensity is often the starting point of analyzing any spatial pattern (Bailey and Gatrell, 1995; Upton and Fingleton, 1985) but should not be confused with spatial clustering, which is a measure of both intensity and distance (dependence) between points. Although there are numerous ways to measure intensity, two methods--averaging or counting events in an area as well as kernel density estimations--are commonly used. In the calculation of intensity, the specific location of each event (the exact point location, such as the address) is not compared to the location of other event locations. Rather, an average, aggregate measure, such as the rate of events per geographic unit, is calculated. Thus, while comparing the intensities of drugs and violence for many geographic units may provide a general understanding as to their spatial connection (for example, as done by Gainey and Payne, 2003), this method does not necessarily indicate that the locations of drug and violent crime events are spatially dependent upon (or overlap with) each other. An example of the spatial generality of measures of intensity is illustrated in Figure 1. This figure shows a simple example of drug (D) and violence (V) patterns within a hypothetical small spatial region of area = 1 square unit. The intensities of drugs and violence in both Figure 1(a) and 1(b) are equal to 10 events per square unit, even though it is clear that their geographic dependence upon and location with one another is different. Compared to Figure 1(b), Figure 1(a) does not show drug and violent crimes to geographically overlap. Figure 1 illustrates how using intensities to make statements about spatial relationships may be misleading. Thus, measures of intensity between drugs and violence in Seattle should be viewed as only a general indication of a spatial relationship between the two. When deriving intensities for drugs and violence in this study, the correlations between drug and violent crime intensities in Seattle are strong and positive across tracts (Pearson's correlation = .808, p < .001) as well as block groups (Pearson's correlation = .720, p < .01). These

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Figure 1. An illustration of two areas with equal spatial intensity but different spatial dependence.

findings suggest that generally places with higher intensities of drug activity also have higher intensities of violent crime and is supportive of Weisburd and Green-Mazerolle (2000) and Gainey and Paine (2003). A second type of intensity measure--kernel density analysis--provides a more visual illustration of drugs and violent crime. Kernel density estimations are ascertained by creating a moving circular window or "kernel" around the region that measures the intensity of event locations from the center of the window outward at a specified distance called the bandwidth (Anselin et al., 2000; Bailey and Gatrell, 1995).4 Kernel density estimation, although still a general spatial measure, has the advantage over average measures of intensity in that rates are estimated at every point within a region, allowing for a visual display of a smoother, more continuous illustration of intensity. To compare the kernel densities of drug activity and violent crimes, equal numbers of drug and violent events were examined across Seattle using equal distant bandwidths for these moving windows. Although the counts of drugs and violence were not initially equal in each region, a random sample of the more numerous category was drawn to match the smaller category's count. This process was justified not only because neither the drug nor violent crime recorded data were believed to contain the entire universe of drug or violent crime events, but also because this was necessary to not confound dependence effects (as will be shortly explained) with intensity effects when comparing the two. As the use of kernel estimation was for visualization purposes only (and also due to space limitations), six of the many maps developed for this project are shown in Figure 2.5 One immediate observation across these maps was that kernel estimations of violence evidenced darker and more numerous "hot spots" than those estimated for drugs, even when comparing equal number of events of each using equal-distant bandwidths. This preliminarily suggests that drug and violent crime patterns are not spatially similar, and that violence tends to be more spatially concentrated than drug activity. This initial visual inspection of kernel density maps indicates that there may be both variability in the locations of drug activity and violent crime as well as the dispersion of drug and violent crime patterns.

Spatial Dependence of Drugs and Violence: A General Discussion

As both Figures 1 and 2 illustrate, measures of intensity may not provide a complete picture of the spatial relationship between two non-homogenous crime categories such as drugs

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Figure 2. Kernel density estimations for three areas in Seattle.

and violence. Although measures of global intensity and kernel estimations illustrate how the intensity of these crimes vary over geography, intensity and density effects do not tell us about the relationship or dependence of the location of events to each other (Bailey and Gatrell, 1995). Spatial dependence analysis measures the intensity of crime and the spatial relationship of events to each other and measures what is commonly referred to as clustering. This is done by measuring distances between points and then developing probability distributions of these distances. By doing so, dependence analysis helps determine whether events that are closer in geographic proximity are more spatially (and perhaps, although not necessarily, causally) related than events further away (Bailey and Gatrell, 1995; Boots and Getis, 1988; Fotheringham, Brunsdon, and Charlton, 2000; Waller and Gotway, 2004).

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Two types of point pattern dependence analyses can be used to test for spatial dependence of the locations of violent and drug crimes: nearest neighbor distances methods and estimates of reduced second moment measures. Nearest neighbor methods help examine whether spatial dependence exists within point pattern data by comparing two types of distances: those between actual events (and their nearest neighbor) and those between events and randomly chosen points across a study region. If event-to-event distances exist at higher frequencies than event-to­random point distances, then clustering or spatial dependence is suggested (see Bailey and Gatrell, 1995, or Waller and Gotway, 2004, for detailed explanations of nearest neighbor analyses). Reduced second moment measures of dependence, also known as the Ripley's K functions (again, for detailed explanation, see Bailey and Gatrell, 1995, and Waller and Gotway, 2004) is another measure of spatial dependence and is sometimes seen as more powerful than nearest neighbor methods as it can be used for larger geographic areas.6 The K function (and a derived cousin, labeled "LHAT" here) is a measure of the average number of events within a specified distance of an arbitrary event and displays the likelihood of finding another event next to a point. The K function also allows for tests of statistical significance of clustering against a null hypothesis of complete spatial randomness (CSR) by comparing distributions to "simulation envelopes" or multiple simulations of random allocations of data points.7 In this analysis, both nearest neighbor methods and Ripley's K functions were used to ascertain spatial dependence across all tracts in Seattle. As already emphasized, while tracts are used as the region of analysis, spatial dependence does not examine a rate of crime in a tract but uses the tract as a region in which to examine the distances between specific points in that region. Additionally, spatial dependence analysis is used twice here--first to determine within-classification spatial clustering (of drugs and violence separately), and then between-classification spatial dependence (distances between drug and violent crime events). Normally, spatial dependence analysis is conducted on one event category, such as drugs, homicides, crime, or offender residences, and not between two or more categories (for example, "drugs and violence," "homicides and offender residences," "crime and location of bars"). The term dependence is commonly used, therefore, to describe the spatial relationship of individual events within its own category (such as drugs) to themselves to ascertain clustering. However, in this study, I also employed a modified nearest neighbor approach used for non-homogenous populations. In other words, I modified the nearest neighbor approach to allow for the spatial statistical testing of the dependence of two separate crime classifications upon each other.

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Analysis II: Within-Classification Spatial Dependence of Drugs and Violence

First, to examine the spatial dependence of drugs and of violence within their own classifications and then to compare them, the K function was utilized. Again, space limitations do not permit showing all K function results.8 However, Figures 3 and 4 illustrate a sample of 16 (of 124) drug and 16 (of 124) violent crime LHAT function analyses (recall, as noted in note 6 and 7, the LHAT is a derivation of the K function and is used here), respectively, including the simulation envelopes which test for statistically significant clustering of each classification against a hypothesis of complete spatial randomness. For example, in Figure 3 Tract 42, the light, dashed lines represent the simulation envelopes used to test the hypothesis of complete spatial randomness and the bolder LHAT line represents the distribution of distances for the specific type of event in each tract. Lines outside and above the envelopes would suggest statistically significant spatial clustering at the specified distance

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Figure 3. Within-classification spatial dependence of drug activity for a sample of tracts (solid lines represent K functions for drugs, dashed lines represent simulation envelopes).

(measured along the "dist" axis in map units).9 Lines within the envelopes suggest that no statistically significant clustering occurred in that tract and lines below the envelopes suggest statistically significant regularity (equally spaced events). In the case of Tract 42, there is no statistically significant clustering of drugs activity in that tract. Table 1 summarizes all of the K functions derived for drugs and violent crime separately by displaying the percentage of census tracts for each classification (violence and drugs) where dependence, some dependence at limited and small distances, and no dependence was evident. Figures 3 and 4 and Table 1 illustrate that the locations of drug and violent crimes do not pattern randomly or regularly across all census tracts. Spatial dependence is not always evident within each crime classification and for every tract. Although 40% of all tracts displayed violent crime clustering, at least 36% of the tracts did not have any evidence of violent crime hot spots. Similarly, while 52% of tracts showed drug activity clustering, 29% did not, and 19% of tracts only at limited distances. While Table 1 shows the general occurrence of drug or violent crime clustering in tracts, Table 2 summarizes the different combinations of drug and violent crime withinclassification spatial dependence across tracts. Here, six different combinations are given, based on the existence of within-classification dependence for drugs and violent crime

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Figure 4. Within-classification spatial dependence of violent crime activity for a sample of tracts (solid lines represent K functions for violence, dashed lines represent simulation envelopes).

separately and the distances by which dependence was detected. Forty-two percent of tracts had clear evidence of both drug and violent crime clustering within their own classifications and across similar distances. While 42% may seem high, it should be noted that the size of census tracts is inversely related to the population density of a tract. Nineteen percent of the 124 census tracts were found to have varying distances at which clustering of violence and drugs within their own classifications were detected. This suggests, as the kernel density maps hinted to, that patterns of drug activity and violent crime may be dispersed differently.10 Perhaps even more interesting was that 15% of the tracts evidence only drug or violent crime clustering but no evidence of clustering of the other classification. And a quarter of the entire Table 1 Within-classification spatial dependence for drugs and violence separately across tracts Violence Dependence evident (%) Some dependence evident (%) No dependence evident (%) 40.3 24.2 35.5 Drugs 52.4 18.5 29.0

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Table 2 Combinations of within-classification dependence for drugs and violence across all tracts

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Percentage of total Clustering evident for both at similar maximum distances Clustering evident for both but across more distances for drugs Clustering evident for both but across more distances for violence Drug but not violence clustering Violence but not drug clustering Neither drug nor violent crime within-classification dependence 42 14 5 11 4 25

city showed no evidence of violent or drug-crime clustering whatsoever. It is clear that spatial dependence analysis provides a more detailed picture than the correlations found between drug and violent crime intensities, which seemed to indicate a much stronger relationship and did not provide a spatial context to that relationship.

Analysis III: Between-Classification Spatial Dependence of Drugs and Violence

Yet the primary interest of this study is not only whether violent and drug crimes are spatially dependent within their own classifications or even if both exhibit spatial dependence within the same area. The main concern is the spatial dependence between non-homogenous populations; that is, drugs to violence. In other words, do the locations of drug and violent crimes not only cluster among themselves, but are individual locations of drugs and violence spatially related to each other? As already mentioned, exploratory spatial data analysis is usually conducted testing the locations of one type of phenomenon to itself (as shown in Figures 3 and 4). However, analyzing the spatial dependence of multiple categories of crime of non-homogenous populations requires manipulation of spatial statistical techniques. Here, as opposed to comparing a pattern of events against complete spatial randomness, multiple crime patterns are compared to see if they are spatially independent from each other. The analysis of the spatial clustering of non-homogenous populations is theoretically possible (see Bailey and Gatrell, 1995), although the statistical software available to accomplish this has been limited. However, scholars, especially in the field of spatial epidemiology, have explored approaches to deal with analyzing clusters of two or more non-homogenous populations. In particular, Cuzick and Edwards (1990) outline a spatial statistical strategy to examine non-homogenous disease populations by randomly select control cases from one population in which to find nearest neighbors of another population. Others, such as Diggle and Chetwynd (1991) have built on this approach to examining clustering of two or more categories of phenomena using what they term a random labeling process, where a random sample is chosen from one population to compare with a qualitatively different population. Similar to these approaches, I used S-PLUS to test the between-classification spatial relationship of drugs and violence by modifying the process of estimating nearest neighbor distances to accommodate two non-homogenous events (drug activity and violence). Instead of comparing drug event­to­drug event with drug event­to­random point distances to see if the nearest neighbor drug-to-drug distributions are more frequent than drug-to­random point distributions, random points are exchanged with a random equal sample of another category

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Figure 5. Between-classification spatial dependence of drug activity to violent crime. Betweenclassification dependence (circles), within-classification dependence for drugs (dashes), withinclassification dependence for violence (solid lines).

of events--violent crimes. Then, the probability distributions of three nearest neighbor distances are compared: drug-to-drug distances, drug-to-violence distances, and violenceto-violence distances. This process was repeated 124 times for each of the census tracts. Figure 5 illustrates the same sample of 16 (of 124) tracts shown in Figures 3 and 4 for which this modified analysis was conducted. The circles represent the between-classification dependence and the dashed and solid lines represent the within-classification drug and violent crime dependence, respectively. When the between-classification circles are above the separate drug and violence dependence distributions, there are more drug-to­violent crime nearest neighbor distances than drug-to-drug or violent crime­to­violent crime distances at the corresponding distance. This would suggest dependence was occurring between drug and violent crime events more so than within their own classifications. For example, in Tract 44, there is stronger spatial dependence between drug activity and violence than of drugs or violence separately. To summarize, for the 124 between-classification dependence analyses conducted, 47.6% of tracts evidenced strong spatial dependence between drugs and violent crimes, suggesting that in these tracts, the locations of drug activity and violent crime were more spatially dependent upon each other than among themselves. Another 23.4% of

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Table 3 Within-classification categorical combinations according to evidence of betweenclassification dependence Between-classification dependence Within-Classification Dependence Clustering evident for both at similar max distances Clustering evident for both but more widespread for drugs Clustering evident for both but more widespread for violence Drug but not violent clustering Violent but not drug clustering Neither drug nor violent crime dependence within own class Total Strongly evident Not evident Total 52 (41.9%) 17 (13.7%) 6 (4.8%)

38 (30.6%) 3 (2.4%) 7 (5.6%) 1 (0.8%) 4 (3.2%) 2 (1.6%)

3 (2.4%) 6 (4.8%) 14 (11.3%) 2 (1.6%) 2 (1.6%) 5 (4.0%) 5 (4.0%) 22 (17.7%) 30 (24.2%) 59 (48%) 65 (52%) 124 (100%)

Note. Percentages indicate the percentage of the cell value to all tracts in Seattle (N = 124).

tracts were shown to have between-classification dependence that did not occur at every distance, but rather only evidence more between-classification dependence at limited, smaller distances. A large minority of tracts (29%) generally did not show that betweenclassification dependence existed more often than within-classification dependence at most distances. It is important to note that lack of between-classification dependence does not suggest that spatial dependence of drugs or violence did not exist separately, but rather, when compared to within-classification nearest neighbor distances, between-classification dependence did not occur at higher levels. Sometimes, to the contrary, dependence of drugs and violence may exist separately even without between-classification dependence (illustrated by Figure 1a). To emphasize this point, Table 3 shows the counts and percentages of total tracts that fall under the nominal classifications given for combinations of within-classification dependence of drugs and violence separately (Table 2) and accordingly whether there was evidence of between-classification dependence. The most likely expectation would be where strong evidence of within-classification dependence for both drugs and violence existed (or lack thereof), then so would strong evidence of between-classification dependence (or lack thereof). Table 3 suggests that although a large percentage of tracts (48%) display this type of behavior, 52% of tracts show evidence that the behavior of drugs and violence separately do not always match their behavior together. Also interesting is that eight tracts in Seattle show results counter to expectations. There are areas with spatial clustering of violence or drugs separately but no evidence of spatial dependence between violence and drug activity (or vice versa). But generally, the log odds of having between-classification dependence increased when within-classification dependence for either drugs or violence was at all evident (drugs: = 2.767, exp() = 15.91, S.E. = .485, p < .001; violence: = 2.757, exp() = 15.75, S.E. = .487, p < .001). The overall message, however, was that while spatial dependence between violence and

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drug activity was clearly present for almost half of all places in Seattle, these tracts varied in terms of their individual drug and violent crime patterns. Other important questions of interest that are not addressed here primarily due to small sample sizes is the between and within spatial dependence relationship of subcategories of drugs (e.g., cocaine, marijuana, heroin), drug activity (use, sales, distribution, manufacturing), violence (homicide, robbery, assaults, sex crimes), or within smaller geographic units (block groups). Hypothetically, it should be possible to manipulate existing statistical approaches to accommodate more than two subcategories in smaller regions to explore the spatial relationship. However, limitations of homogeneity, isotropy, sample size, and geographic region are difficult to reconcile for small sample data. Yet this exploratory analysis suggests that important nuances with the spatial relationship between different categories of crime may be ascertained using this approach.

Discussion and Conclusion

The results of the exploratory spatial data analysis in this study confirm in part colloquial beliefs; a spatial relationship between drugs and violence was found in almost half of all census tracts in Seattle, confirmed by the between-classification spatial dependence analysis. Correlations of crime rates or intensities and comparisons of drug and violent crime clustering only provide general indications of a spatial relationship between drugs and violence. However, the between-classification analysis of non-homogenous categorizations of crimes also shows that nearest neighbor distances between drugs and violence occur at much higher frequencies than nearest neighbor distances among drugs or violent crime separately. This suggests, as Figure 1b illustrates, a spatial overlap between the two. However, important variations in this relationship were also found. From the kernel density illustrations, it appears that drug activity and violent crimes may not pattern similarly, even when examining the same number of events in each category. This could be due to a number of explanations. Drug activity, even as it is reported through calls for service (as opposed to officer-generated reports) may be less address-specific than violence. Violence is more accurately and frequently reported by the police and it is likely that recording the exact location of a violent crime is much more emphasized than the location of a drug crime, which may be labeled more generally. Additionally, enforcement activities by police officers,11 combined with evasion techniques of drug dealers, may also have the effect of dispersing drug activity more frequently than violent crime enforcement. The dynamic nature of drug activity (individuals constantly on the move) may also lead to different patterns. The spatial dependence analyses also show that there were places with strong drug clustering, for example, that did not show evidence of high intensities or clustering of violence (and vice versa). In other words, not all highly active drug areas are violent places, as often perceived. This confirmed the initial hypothesis upon which this project was based. The hypothesis was generated from a similar observation by the author when working as a police officer in an urban area with high levels of drug activity and violent crime. In some places, very high levels of drug activity were bereft of violence, while similarly comparable drug areas seemed infested with violence. The between-classification analyses revealed that there is not a consistent and strong relationship between the specific locations of drug activity and violent crime, but perhaps only in those areas in which drugs and violent crimes occur more frequently. Even in areas of less crime, a strong drug-violence relationship at the location level would still reveal a spatial link between the two. This hypothesis may not be supported with this analysis, as spatial clustering between drugs and violence was more

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likely in areas with drug and violent crime clustering. This conclusion, however, should be approached cautiously. Incorporated into measures of spatial dependence are measures of intensity that cannot be separated from dependence. Other limitations to this study should also be noted. First, the presence of a drugviolence spatial link does not imply that there is a sociological causal relationship between the two. As already mentioned, exploring a systemic causality between drug activity and crime requires examining the behavior of drug users and dealers, perhaps requiring researchers to physically follow these individuals to record their geographic routines, movements, and criminal activities. While officer-modified calls for service were the best data available for this study, there may be better sources of information that could further get at this systematic causality, including ethnographic observations of the involved populations, and perhaps public health violent crime and drug measures. Furthermore, although the geographic units for this study were chosen due to both statistical and informational practicality; block groups, for example, were not used for dependence analysis. It might be interesting to see whether such results remain if analyses could be done on smaller geographic units. Despite these limitations, these findings can provide a geographic context in thinking about the systemic or routine activities relationship between drugs and violence. Although much of the empirical testing of routine activities theory has focused on surveying individuals about their daily behavior and determining the risk of that behavior (see, e.g., Kennedy and Forde, 1990; Miethe, Stafford, and Long, 1987; Miethe, Stafford, and Sloane, 1990; Osgood, Wilson, O'Malley, Bachman, and Johnston, 1996; Sampson and Lauritsen, 1990; Wittebrood and Nieuwbeerta, 2000), a spatial interpretation of the routine activities theory has also become dominant in crime and place research (see, e.g., Braga, 2001; Brantingham and Brantingham, 1993; Eck, 1997; Eck and Weisburd, 1995; Ratcliffe, 2004, 2005; Sherman, 1995; Sherman et al., 1989; Sherman and Weisburd, 1995; Weisburd, 1997; Weisburd and Green-Mazerolle, 2000). Routine activities theory might suggest that certain places may be more vulnerable targets to the coincidence of drugs and violence because the routines of individuals involved in both overlap or because targets are similar. In this way, routine activities theory is partly implied by the systemic approach aforementioned, which suggests that drug routines, such as the prevalence of drug distribution, the type of drugs sold or used, the mechanisms by which transactions occur, or the daily activities of drug dealers and users, might involve violent activities. If these routines have spatial components, then we might also expect drug activity and violence to pattern similarly. In addition to these theoretical implications, these findings also suggest that methodology may matter when drawing conclusions about spatial patterns. The use of both withinand between-classification spatial dependence analyses can be helpful in analyzing whether the specific locations of drugs and violence cluster separately or together, relationships that were masked by analysis using first-order intensity analysis or general comparisons of crime rates. The development and use of a modified nearest neighbor approach for non-homogenous populations follows in the work of other fields, especially in disease epidemiology, and could be one fruitful statistical methodological strategy in moving away from only looking at spatial relationships for single crime categories. Understanding how different types of crime or combinations of crime phenomena might be spatially related is interesting; for example, understanding the relationship between the locations of offender residences to the places where they commit crime or the relationship between gang jurisdictions and locations of their crimes. Combining these types of statistical innovations with contextual understanding of street-level relationships can provide a more comprehensive understanding of crime events.

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Additionally, different methods give rise to more detailed policy implications. When police or criminologists determine hot spots of crime for crime prevention or deployment, areas may evidence different types of hot spots, which might lead to differences in choices for deployment. An area with high levels of drug activity but without violence may require significantly different types of enforcement than places with a strong spatial relationship between the two. Such areas may not be violent because they are highly stable drug markets with actors who have well-developed schemes of enforcement detection and evasion. Police may have to invest resources in developing confidential informants or in nuisance abatement, rather than, for example, open-air buy and bust techniques where dealers will be more able to detect strangers. Violent drug areas may be areas in which markets are less stable, more visible, and whose actors take more risk (for example, selling drugs in more public, visible areas). Areas with high levels of violence with the presence of open-air drug markets might be adjacent gang turf boundaries, or perhaps places where smaller dealers are interacting with out-of-town larger distributors. Or such areas may reflect the place component of drug market competition. In these areas, police deployment may be bolder and can include open-air undercover operations, drug crackdowns, or hot-spot policing. These hypotheses and others implied by the systemic approach no doubt warrant further investigation and are not addressed in this limited study. The establishment of spatial dependence is only a first step in examining whether nearness implies causality and what is the qualitative nature of that causal relationship. Further research calls for exploring the connections between the findings here and individual behavior to obtain a fuller understanding of the drug-violence relationship. Additionally, developing methods that can analyze the spatial relationship between specific types of drug and violent crimes a might also elucidate this relationship. However, this study challenges some beliefs not only about the relationship between drugs and violence but, more importantly, about how different crimes may pattern individually and together.

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Acknowledgments

This research was partially supported by a grant from the National Institute of Justice (No. 2001-IJ-CX-0022). The author thanks Ralph Dubayah, David Weisburd, Peter Reuter, Keith Harries, Sally Simpson, Gary LaFree, Al Blumstein, and anonymous reviewers for their invaluable insights in the development of this article.

RESUMEN La geograf´a de la actividad y de la violencia de la droga: Analizando i relaciones espaciales de poblaciones del crimen no-homog´ neas e

La imponencia del inter´ s entre la relaci´ n de la actividad de drogas en las calles y la e o violencia ha sido reflejada en todos los estudios de investigaci´ n, la pol´tica, y la pr´ ctica o i a de la justicia penal, como tambi´ n en la opini´ n p´ blica. La mayor´a de los estudios se han e o u i enfocado en esta relaci´ n a nivel de individuos. Este estudio amplia los estudios anteriores o entre individuos y en cambio examina la relaci´ n entre las drogas y la violencia en difero entes areas geogr´ ficas desde el a~ o 1999 hasta el 2002 en Seattle, Washington. Para ello, ´ a n este proyecto utiliza tres m´ todos de estad´stica espacial - medidas de intensidad/densidad e i

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espacial, medidas de la dependencia espacial separada de las drogas y la violencia, y un m´ todo modificado de dependencia espacial para poblaciones no-homog´ neas - para exe e plorar la relaci´ n geogr´ fica entre 105,447 incidentes criminales de drogas y violencia. o a Las conclusiones indican que aunque las drogas y la violencia a menudo se superponen, existen variaciones importantes en su relaci´ n espacial. Discutimos las implicaciones y o limitaciones de estas conclusiones para la pol´tica. i

RESUME

La g´ ographie des infractions li´ es aux drogues et des violences: une analyse e e des corr´ lations spatiales pour les populations d'incidents criminels e non-homog` nes e

L'existence d'un large int´ r^ t concernant la relation entre les comportements li´ s aux ee e stup´ fiants et les violences est visible dans la recherche en mati` re de justice criminelle, les e e politiques publiques, les pratiques professionnelles tout autant que dans l'opinion publique. La plupart des recherches se sont focalis´ es sur les liens entre les deux choses au niveau e individuel. Cette recherche etend la recherche existante au niveau individuel en examinant ´ la relation entre les drogues et la violence au plan g´ ographique sur une p´ riode qui s'´ tend e e e de 1999 a 2002 a Seattle, Washington. Dans ce but ce projet utilise trois approches statis` ` tiques pour explorer les corr´ lations g´ ographiques entre 105.447 incidents li´ s a la drogue e e e ` ou a la violence (des mesures de la densit´ /intensit´ spatiale, des mesures distinctes de la ` e e d´ pendance spatiale pour les drogues et les violence, une approche spatiale modifi´ e pour e e analyser les populations h´ t´ rog` nes). Les r´ sultats indiquent que bien que les drogues et les ee e e violences pr´ sentent souvent des formes spatiales se recouvrant, des variations importantes e existent entre ces formes. Les limites de ces r´ sultats et les implications pour les politiques e publiques sont discut´ es. e

RESUMEN

A Geografia da Droga e Viol^ ncia: Uma Analise das rela¸ oes espaciais entre e c~ duas popula¸ oes n~ o ­ homog´ neas c~ a e

´ E extenso o interesse na rela¸ ao entre a droga e a viol^ ncia, como indica a quantidade de c~ e pesquisa em criminologia, pol´tica e opini~ o publica. Uma larga maioria dos estudos t^ m i a e focado na liga¸ ao entre os dois com indiv´duos. Este estudo e importante pois visa aumenc~ i ´ tar o nosso conhecimento sobre a liga¸ ao entre a droga e a viol^ ncia, examinando blocos c~ e geogr´ ficos em Seattle, Washington entre os anos de 1999 e 2002. Tr^ s tipos de analise esa e tat´stica foram empregues- medidas de intensidade/densidade espacial, medidas individuais i de depend^ ncia espacial entre a droga e a viol^ ncia e uma medida de depend^ ncia espae e e cial para popula¸ oes n~ o homog´ neas - para explorar a rela¸ ao geogr´ fica entre 105,447 c~ a e c~ a incid^ ncias de crimes relacionados com droga e viol^ ncia. Os resultados indicam que ene e quanto a droga e a viol^ ncia exibem padr~ es espaciais sobrepostos, existem importantes e o varia¸ oes na sua rela¸ ao espacial. S~ o discutidas as limita¸ oes destes resultados assim como c~ c~ a c~ sugest~ es para a pol´tica publica. o i

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THE AUTHOR

Cynthia Lum, Ph.D., is an assistant professor at George Mason University in the Administration of Justice Department, located in the Commonwealth of Virginia. She holds a Ph.D. from the University of Maryland in Criminology and Criminal Justice. Her areas of interest are international and domestic policing reform and deployment strategies, criminal justice and counter-terrorism evaluation research, and place-based criminological theory.

Glossary

Hot Spots of Crime: generally, this term refers to the clustering of crime events within a geographical area. Isotropy: (given the assumption of homogeneity) suggests that the dependence between points relies only on the distance between points, rather than on distance and direction. Non-Homogenous Populations: normally, spatial analysis is conducted on a single category of crimes, such as "violence," "drugs," or "homicides." This term is used specifically in this study to emphasize that the analysis utilizes a special approach to examine two different categories of crimes simultaneously to determine their relationship. The non-homogenous populations in this study are drug activity and violent crime incidents. Place-Based Criminology: research in crime and justice that focuses on the relationship between geographic areas, spaces, places, and criminological events. This area of criminology covers a number of traditions from social disorganization theories of the Chicago School to hot-spot policing studies, environmental criminology, situational crime prevention, routine activities, and other geographic or place-oriented studies related to crime. Stationarity: one of two main assumptions that are made in spatial analysis. Stationarity (or homogeneity) implies that the mean and variance of values within a geographic region are independent of absolute location.

Notes

1. The geographic information system used was ARCGIS 8.2, which is a product of the Environmental Systems Research Institute (www.esri.com). 2. The database manipulation software used was Visual FOXPRO, which is a product of the Microsoft Corporation (www.microsoft.com).

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3. The spatial analytic software used were S-PLUS and S+ SpatialStats Extension, which are products of the Insightful Corporation (www.insightful.com). 4. Formally, the kernel density estimation function is represented by the following equation (see Bailey & Gatrell, 1995, p. 85): ^ (s) = 1 t (s)

n i=1

s - si 1 k 2

Here, the mean estimated intensity of a particular location is denoted by (s). k() is a probability density function, the radius of the kernel being the bandwidth, or and the center of the kernel, s. One common functional form of the kernel is a "quartic" function (used in this analysis), a hill-like, three-dimensional cap. Using a quartic function for k(), the measure of intensity (s) then becomes (see Bailey and Gatrell, 1995, p. 85): ^ (s) =

h i

h2 3 1 - i2 2

2

where hi is the distance between the point s and the observed event location s i . 5. Please contact the author for all illustrations alluded to in this study. 6. The K function is mathematically represented by the following equation (see Bailey & Gatrell, 1995, p. 92): 1 ^ K (h) = 2 R Ih (di j ) wi j

i= j

where 2 R is the intensity times the area of the region of interest and di j is the distance between events i and j. Ih (di j ) equals 1 if di j h and 0 otherwise; wi j is an edge correction factor. 7. To do this more easily, one plots the "LHAT" function, which is derivative of the K function. The LHAT function is denoted by (see Bailey and Gatrell, 1995, p. 104): ^ L(h) = ^ K (h) -h

8. Please contact the author for all illustrations alluded to in this study. 9. Map units are standardized measures used in S-Plus. For example, a block approximately measures between 200 and 400 map units in length. 10. The differences in the distance of which clustering was detected for drugs and violence, when tested against a null hypothesis of no difference was statistically significant (t = 8.944, df = 123, p < .001). 11. This was suggested by a previous anonymous reviewer of this article.

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