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Identifying spatio-temporal patterns of articulated criminal offending: an application using phenomenologically meaningful police jurisdictional geographies.

INTRODUCTION

Understanding, identifying, and tracking the spatio-temporal mobility of criminal offending can have important implications for social scientists concerning both the development of applied policy as well as more general criminological theory. (1) However, there is currently a disjuncture between available data, geographic units of analysis, and the operationalization of analyses in such research. Pertinent to the current examination, we are interested in the ability to link publicly available crime data and tracking the 'mobility' of this data over a given period of time. Here we introduce a novel approach to aggregating, and delineating, reported crime data that is jurisdictionally relevant while making optimum usage of agency level aggregation at which the data are available to the public. By keeping the data at the agency level and creating a new jurisdictionally relevant geography, we have maintained the integrity of the data at the lowest level and linked it directly to the communities that the law enforcement serves.

The correct conceptualization, and subsequent operationalization, communities potentially has the ability to influence our understanding of the effects of the associated ecological context on a variety of social phenomena. Over time, a number of attempts have been made at improving the 'state of the art' in terms of defining what represents a community. Many aggregate level social research projects make use of Office of Management and Budget's (OMB) defined Metropolitan Areas (MA), which rely on social and economic integration across county level data as the primary unit of analysis (GARM, 1994). However, recent research has shown that not only are MA's extremely heterogeneous, in terms of population, economic and social indicators, but the counties within those metro areas suffer from similar measurement problems (for example and review see Porter and Howell, 2009).

One area, among many recently, that has taken an interest in the conceptualization and operationalization of 'communities' as urban and rural is the field of criminology. This increased attention within the field has been largely directed at the social and environmental context in which crimes occur as a way of testing existing ecological theories of crime (Wells and Weisheit, 2004). While a number of researchers have examined both between- and within-county variations in crime rates, still little has been done to account for the point of argument in the literature that claims that the county as a geographic unit is much to large to understand neighbourhood effects and areas like and Census Tracts focus too narrowly on an isolated urban-centric issues to truly understand the phenomena in its entirety (Messner et al., 1999, 2005; Cohen and Tita, 1999; Bailer et al., 2001; Messner and Anselin, 2004; Hipp, 2007).

Due to this disjuncture, most of the attention given to the ecological context of crime has focused primarily on minute portions of the available geographical units of analysis. Furthermore, the extreme heterogeneity, which exists in many of the geographies used in these examinations of crime, such as counties (Land et al. 1991; Messner et al., 1999; Messner and Anselin 2004), makes it evident that a better understanding of all ecologically distinct units is important in order to further our understanding of reported crime in general. It is important to note here, that in response to this issue there have been a number of sub-county approaches to the examination of reported criminal offending; however, often these tend to focus only on urban settings while neglecting areas of a more rural or of less-developed urban character (Clinard, 1942; Wells and Weisheit, 2004).

This oversight has, therefore, neglected to understand crime in the vast majority of place settlements in the U.S. as 77 per cent of all Census places are outside of urban areas and 60 per cent are in places with a population of less than 2500 people, the common Census definition of rural locality (Wells and Weisheit, 2004). That is not to say that these studies do not account for a good deal of the population, as most of the population in the U.S. resides in these MA's, but it is a significant proportion, which when coupled with those that do not reside in Census Places, creates an even more unequal treatment. In relation, it is hypothesized that Census Designated Places (CDP), as with most sub-county level geographies, vary qualitatively based on the context in which they are contained, including regionally and by metropolitan status.

Through the creation of a jurisdictionally relevant geography, this study extends the creative and resourceful work on tracking spatial mobility of crime by Cohen and Tita (1999) by implementing a spatially-centred multivariate approach in comparison to one introduced by the researchers through the multiple implementation of a similar statistic in univariate form (involving dynamic LISA results; see Anselin, 1995). While there are a number of recently developed, and extremely sophisticated, spatial methods aimed at understanding spatio-temporal relationships, the Local Indicator of Spatial Association (explained in greater detail below) has proven to be a consistent and accepted measure of spatial relationships.

This project is interested in modelling the mobility of crime associated with the fluidity of criminal behaviours across areas, between 1990 and 2000, based on their place-level classification; places or non-place territories. (2) Furthermore, within this analysis the mobility of criminal offending is examined via the implementation of analytic techniques situated within the framework of diffusion. Of the two primary types of spatial diffusion, contagion and hierarchical (Cohen and Tita, 1999), the process of interest here involves the contagious type due to the contiguous nature of the units of analysis and the core-periphery relationship associated with the inherent 'downward' transmission of behaviours, and social processes between core places and the periphery non-place territory (Agnew, 1993; Lightfoot and Martinez 2005). It is expected that the results of this analysis, which are aimed at improving the 'real-time' tracking of criminal offending, can lend themselves to future studies involving the use of spatial patterns in the prediction of spatial patterns through simulation models.

LITERATURE REVIEW

Geography, Crime and the Modifiable Ariel Unit Problem

The spatial demography of crime as a subdiscipline has adopted a number of demographic approaches to the study of the patterns, motivations, and spatial spread of crime. A county-level study on the structural covariates of crime by Land et al. (1991) has led to the growing devotion of criminologists, demographers, and other social scientists to the spatial distribution of criminal violence (Baller et al., 2001, Anselin, 2003). Land et al. (1991) pointed out that the general trend in most of the existing literature of the time used states as the primary unit of analysis, due to the fact that state-level data were readily available and often required less data management. However, other studies have argued that a more appropriate measure is the Metropolitan Area (MA) level, based upon the argument that MA's more readily represent community boundaries (Messner et al., 1999). On the other hand, this is further debated as the use of metro areas neglects substantial within-unit variability, often concerning both the structural covariates as well as the dependent variable of interest (crime in this case) (Messner et al., 1999).

More recently, a number of researchers have reduced scale and examined between-county variations in crime rates (Messner et al., 1999, 2005; Baller et al., 2001; Messner and Anselin, 2004). However, there still exists a certain level of within-county variation and a lack of agreement on the community or neighbourhood associated with a particular sub-county boundary (Cohen and Tita, 1999; Messner et al., 1999; Bailer et al., 2001; Anselin, 2003; Hipp 2007). In regard to these works, there is the increasing use of GIS combined with spatial statistics, which is a documented pattern throughout the social sciences (Goodchild and Janelle, 2004). Figuring prominently among these issues is the specification of the optimal unit of analysis (Cohen and Tita, 1999; Messner et al., 1999; Baller et al., 2001; Anselin, 2003; Goodchild and Janelle, 2004; Hipp, 2007). Thus, it is important to add to what is known about more optimal geographies, which will add to our understanding of the spatial demography of reported crime and its patterns of change.

The reoccurring theme in this study is the importance of location in the determinacy and conceptualization of crime and covariates used to examine the phenomena. Currently, in the field of demography, theories of location are becoming of greater importance because of the changing population dynamics associated with new technological advancements and the ever-developing global society (Anselin, 1995; Goodchild and Janelle, 2004). Such advancements make it possible to transcend historical geographic boundaries and spatial limits. In fact, these advancements, in a sense, devalue the once 'priceless' commodity of geographical closeness, making it possible to maintain communication and carryout regular business operations without traditional concerns of proximity. Furthermore, these advancements seem to go in opposition to the classic statement concerning space: 'location, location, location'.

Crime comes in many forms and varies based on a number of factors and one major, but understudied, factor is place. However, as the previous section has suggested, the current examination of crime has been modified to accompany changes in the way in which processes are affected, spread and reorganized through space. In fact, now there is a great deal of concern on the actual unit of analysis appropriate for the examination of type-specific criminal offending in relation to the determinants of ecologically related criminal offending and the diffusion processes through which crime mobilizes in geographic space.

This argument follows a much larger issue, which has received a large amount of attention in the field of geography. That is issue is the ability to select the correct unit of analysis or geography based on what has been called the Modifiable Aerial Unit Problem (MAUP) (Bolstad, 2006). MAUP is interested in the idea that smaller units of analysis do not necessarily constitute the communities they are designed to and in the same vein larger units of analysis tend to dilute variation between units. (3) In essence, MAUP makes the point that relationships between aggregate variables can vary widely, including changes in sign, but the choice of unit for the analysis must be distinguished by theory and empirical analysis.

In all cases, the unit of analysis, as represented by the level of geography, plays an important role in being able to understand crime, where it happens and why it might be happening in those places. However, the 'proper' unit of analysis for this examination has been extensively debated. Messner et al. (1999) found that there are a number of geographies that could possibly be used for both the statistical and spatial analysis of crime, including metro areas, states, counties, cities, tract and blocks. The authors went on to emphasis that the selection of geography ultimately should rely on proper investigation of the phenomenon or process of investigation. Therefore, an uncritical acceptance of existing, yet flawed, units of analysis may yield results that are not reliable in relation to others gained from more theoretically driven units of analysis.

Previous research on the geography of crime has identified a number of spatial relationships across geographic communities (Weisburd and Green, 1995; Eck, 1998; Rengert et al., 2000, 2005). In this analysis, we are interested in these linkages, via the relationship of 'core' population centres (places) and 'peripheral' hinterlands within a larger unit. In this case a hierarchical system within the county. The ability to track the mobility of crime within this system may further contribute to a growing research concerned with the simulation of criminal offending given what we understand as identified patterns and applying those to the prediction of further offending patterns (Dray et al., 2008). Increasingly, this agent-based modelling simulation method is being used to better understand these relationships (Epstein and Axtell, 1996; Ferber, 1999; Janssen, 2002; Perez and Batten, 2006). These simulation models build upon the mathematical modelling of explanatory approaches, such as the modelling undertaken here, in order to understand future trends given the complex interplay of identified explanatory covariates and spatial relationships (Dray et al., 2008).

Scale and the Place-Level Spatial Mobility of Criminal Offending

The ecological dynamics of criminal offending and its spatio-temporal trends are directly impacted by the geographic scale of the area of interest (Agnew, 1993). Mobility processes that help disseminate, or are directly concerned with the spatial mobility of a social issue or innovation, occur at many different geographic scales and can be quite different based on the resolution used in the study (Abler et al., 1971). However, as the modern world has become more and more urbanized, and made up of aggregates of individuals, spatial mobility has taken on an 'oozing' dynamic associated with the contagious spread of processes from one area to another (Abler et al., 1971). The globalized patterns brought to light by Yearley (1996) and Wallerstein (1974, 1980, 1989), help to set the framework for place interactions at lower levels of geography. Furthermore, from this point of view, it is evident that places tend to perform some sort of function for one another, meaning that the relationship between them can be viewed as structural (Agnew, 1993).

Often studies of U.S. crime are often relegated to heterogeneous units of analysis, such as counties, or minute portions of the country, such as local examinations of tract and block data. This study introduces the examination of these spatio-temporal patterns at substantively meaningful sub-county geography at a national scale through the implementation of a place-level examination of reported crime. A half-century ago, Esselstyn (1953) called for the development of a 'geographically non-urban' criminology. Esselstyn was primarily focused on the development of a conceptualized space, resulting in the development of the term 'open country' used to describe any area not under some form of place-level police (and by inference, other city-based) jurisdiction. Since this early call for a better understanding of the geography of crime, which is included in the ecological analysis of crime, we must point out that there has been substantial discourse on the constitution of urban and rural, in relation to a number of demographically pertinent issues. Among these are how to include space into such analyses as well as the appropriate geography upon which to base these inquiries.

Here, it is made evident that the spatial mobility of criminal processes can be identified and examined at various spatial resolutions (Agnew, 1993). Furthermore, each of these resolutions tends to illicit a somewhat different understanding and potential analytic problem of the process at hand, whether it is from dilution of variation and activity on a large scale or a misidentification of the process on small scales (Abler et al., 1971). Also, it is evident that the 'mobility' of social processes tends to be downward in the sense that core areas tend to send information and ideas to periphery areas (1974, 1980, 1989; Agnew, 1993; Lightfoot and Martinez, 1995; Yearley, 1996). In the examination of crime, this downward/hierarchical 'spreading' process is most commonly concerned with the outward mobility of crime from a core central location to more periphery surrounding locations. Grounded in this framework, it is expected that criminological patterns spread between urban cities, along with innovation, ideas, etc., and the rural hinterlands.

Purpose

The purpose of the current paper is to introduce a newly constructed geographic coverage that is relevant to agency based reported criminal offending data. Furthermore, the use of this new geographic coverage allows for the comparative testing of the multivariate LISA statistic, which it is hoped can provide a more robust and reliable measure of diffusion than its univariate counterpart. Given the review of the literature provided above, it is hypothesized that the significant relationships concerning the mobility of crime between places and NPT's from 1990 to 2000 can be identified as a process of spatial mobility in a contiguous manner, via the implementation of the multivariate LISA statistic. This is supported by research which points out that in urban areas, there is an 'oozing' dynamic associated with the spread of social processes that accompanies the spread of population (Abler et al., 1971). In this sense, we would expect crime to 'ooze' from 'concentrations of population' (i.e. Census Designated Places) to the less inhabited balance of the county (i.e. Non-Places). Again, this 'oozing' is expected to be identified via the comparative implementation of the LISA statistic in univariate and multivariate form. With the newly introduced multivariate form expected to produce more reliable and robust results.

METHODOLOGY

Data

The data used in this study were obtained from multiple sources, all ultimately pertaining to sub-county geographic areas within the contiguous 48 states. Data concerning reported crimes were obtained from the agency-level UCR for both 1990 and 2000. Geographic data were obtained for the years of 1990 and 2000 from the U.S. Census Bureau's Cartographic Boundary website (http://www.census.gov/geo/www/cob/).

Construction of Sub-County Geography and Data

All original data, concerning both the dependent and independent variables of interest, has been aggregated from the block-group level to the place/non-place level, using the following equation as the bases for the relationship between the three geographic units:

County = [SIGMA] (Places) + NonPlaceTerritory (1)

From Equation 1, one can see that the identity of the county is made up of nothing more than the sum of all of the places of a county plus whatever is left over, the non-place. That being the case and since data can be obtained at both the county and place level, it is possible to compute the non-place territory as the difference between the counties and places. Each of the places and each of the non-places (balance of the county) would have all associated independent variables at that level of geography, pertinent to their respective populations.

The development of the geographic coverage for analysis was somewhat more complicated. First, using basic GIS operations from the geo-processing wizard in ArcGIS, the place level polygons had to be clipped from the county level polygons, leaving a county level map with a number of 'holes' where places used to be, akin to a piece of Swiss cheese. This coverage of counties, sans place polygons, is the spatial boundary of the non-place territory. Next, the place level polygons had to be merged back to the NPT, in order to fill in the holes left by the original operation. This resulted in a consolidated spatial data coverage with places and non-place territories in the same polygon file for a given year (e.g. 1990, 2000).

Crime Rate Variables

The dependent variables consist of counts and constructed rates of crime obtained from the F.B.I.'s Uniform Crime Reporting Program (UCR). Following the literature, this study makes use of three separate variables at two different time periods. First, the total crime rate, which is the sum of the seven index crimes reported to the F.B.I. The seven index crimes consist of murder, rape, robbery, burglary, assault, motor vehicle theft and larceny. The variable is computed by simply summing all cases for each geographic unit, dividing that figure by the total population within that geographic unit, and multiplying it by 100 000, in order to compute a rate consistent with the literature. It is important to note that some of the earlier literature used eight index crimes and included arson, but more recently the literature has moved to using seven following the UCR programs omission of arson as an index crime.

The other two dependent variables will be subsets of the total crime rate consisting of violent crime and property crime. The violent crime rates will be computed via the same technique as the total rate using only murder, rape and assault. Likewise, the property crime rate will consist of only burglary, robbery, larceny and motor vehicle theft. All rates will be per 100 000 population and all three crime rates will be computed for both 1990 and 2000, ultimately resulting in six variables across two time periods.

Analytic Techniques

The analytic strategy employed concerns an exploratory approach to the detection of possible spatial mobility of crime via the combination of a number of theoretical approaches outlined above. These frameworks include the core-periphery relationship associated with the transmission

of information and behaviour, the concentric model of spatial arrangement introduced by the Chicago School, and the contiguous nature of the transmission of information and behaviour, based on the spatial arrangement of places within non-places.

The statistical procedure employed in this examination will implement the bivariate LISA statistic as an extension of the work done by Cohen and Tita (1999). This is labelled as an exploratory approach due to the fact that, first, the approach is part of a family of tests known as exploratory spatial data analysis (ESDA) and, second, because previous work has only implemented the use of the univariate LISA. However, it is anticipated that the use of the bivariate LISA, which is inherently designed to handle temporal analyses (see Anselin and Sridharan, 2000), can further add to the methodological value of this project.

Building upon the innovative work by Cohen and Tita (1999), this analysis will examine the spatial mobility via a bivariate examination of crime as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where

s2 = 1/N [N.summation over (i=1)](Yi-[bar.Y])[conjunction]2

Equation 2 is very similar to the equation for the univariate LISA; however, as you can see, the Yj has been replaced with the Xi. Within this analysis, the Yi will be the type-specific crime rate at T1 (1990), while the Xj will be the type-specific rate at T2 (2000).

This equation is akin to the Pearson correlation coefficient, as mentioned earlier, with a simple weight indicator ([[omega].sub.ij]). The measure of spatial dependence is equal to a measure of variation in the area unit specific rate and the overall mean rate ([s.sup.2]), multiplied by the neighbour weight indicator ([[omega].sub.ij]), times the product of each unit's (Yi) proportion of crime at t1, minus the overall mean of the same variable and each average neighbourhood's (Xj) per cent change in the proportion of crime accounted for in the county, minus the overall mean, divided, again by the weight indicator and summed across all units (i) and across all neighbourhoods (j) for both the denominator and the numerator (Anselin, 1995; Waller and Gotway, 2004).

Next, local areas of significance will be detected via the bivariate LISA statistic. The LISA statistic provides a significance value for each case based on local neighbourhood deviations from the overall expected rates of crime (Waller and Gotway, 2004). The equation for the bivariate LISA is as follows:

Ii = [N.summation over (j=1)] [[omega].sub.ij] (Yi - [bar.Y]) (Xj - [bar.X]) (3)

From Equation 3, you can see that the random variable, Ii, is equal to the weight indicator, multiplied by the product of the type-specific crime rate in 1990 (Yi) and the type-specific crime rate in 2000 (Xj), summed across all neighbourhood units (j). Simply put, the LISA value for a given location is simply equal to the relationship between the two variables of interest (correlation), multiplied by the weight indicator (one if considered a neighbour, zero if otherwise). This approach will, then, allow for the examination of pockets of significant spatial mobility of crime within each county.

Identifying Within-County Neighbourhoods

As mentioned above, the LISA statistic is sensitive to the definition of the neighbourhood and the resolution at which the social process of interest is examined (Anselin, 1995; Agnew, 1993). Furthermore, it is important to define your given neighbourhood as being grounded in some theoretical framework, which in this case is interested in the identified relationships of articulation between neighbouring places and non-places within the same county (Waller and Gotway, 2004). In ancillary analyses, the spatial 'neighbourhoods' were defined using a number of differing approaches in order to maximize the within-county relationships (Anselin, 1995). Maximizing the within county connectivity is important due to the fact that one of the goals of this paper is to identify patterns of urban-to-rural crime mobility within the same county. Implementing some of the work outlined above, the transmission of social processes, behaviours and information is often found to take place in a core-to-periphery fashion (Agnew, 1993; Lightfoot and Martinez, 1995). It is evident, then, that the transmission of criminal behaviour should move outward in a contiguous manner to the periphery areas, or non-places, from the core areas, or places. This method, then, should allow for the better understanding of the mobility processes of crime, using a mobility framework, in a contagious model of urban-to-rural criminological processes (Park et al., 1925; Agnew, 1993; Lightfoot and Martinez, 1995).

The identification and understanding of place to non-place mobility requires a definition aimed at maximizing the within-county connectivity. For this purpose a k nearest neighbours approach will be employed (4). By aggregating (summing) the number of places within a given county and computing simple descriptive statistics on that count, it is possible to identify potential k's to be used in the definition of the within-county neighbourhoods. The range of places within a county varies greatly from 0 to 77, with a mean of 2.75, a median of 2.34 and a standard deviation of 3.01. However, they concentrate heavily between two and four, with 70 per cent of the counties having two places, 81 per cent having two or three places and 87 per cent having between two and four places.

Ultimately, three was chosen as the number of nearest neighbours for each locality (5). Figure 1 provides an illustration of the k-nearest neighbour's definition with k equal to three. One can see, in this illustration, that there is one centroid associated with each locality. For example, the county of interest (in green), has three places and four centroids, one extra for the non-place. The figure shows a two-way arrow, demarcated by a letter representing the line, and a table to the right of the figure containing the distance between the points. The distances in the table show that line segments A, B and C represent the three shortest distances between any points ending in the county of interest. Since the non-place is the focal point of the mobility, this nearest neighbours approach looks to be more efficient in identifying within-county neighbourhoods when compared to the 'queen's matrix' because, on average, the places within the county will be the non-places only neighbours.

There will be some instances where there are less than three places, in these cases a place from neighbouring non-place, or the neighbouring non-place itself, will be included as a neighbour. This will lead to a few instances where between-county mobility may be identified. However, from the simple statistics above, one can see that this will be the exception as opposed to the norm. For the purposes of maximizing the within-county connectivity and following the results of ancillary analyses, it seems that the k = 3 nearest neighbours approach is the most efficient definition.

Ultimately, this function will allow for both the intra-county examination of the spatial mobility of type-specific crime rates across the entire country and the proper specification of the spatial neighbourhood will allow for the intercounty spatial mobility by not allowing geographic entities, within different counties, to be considered neighbours. Each of these is further outlined in the model specification section outlined in greater detail below.

[FIGURE 1 OMITTED]

RESULTS

Mobility: Univariate Versus Bivariate LISA Results

Building on the work of Cohen and Tita (1999), this study compares the obtained empirical results against the replicated results laid out by the authors. The results are presented in tabular form in Table 1. This replication and cross-tabulation allows for a degree of 'ground-truthing' in which the theoretical interpretations of the bivariate analyses can be checked against the 'known' univariate interpretations from the Cohen and Tita work. Since this study is interested in the within-county redistribution of criminal offending from core places to periphery non-places, the values used in the LISA analysis are related to the proportion of the overall crime in the larger county accounted for by the ith locality.

This change in the proportion of crime is important in order to understand how areas involved in the mobility of high criminal offending from places to non-places were identified, one would expect the proportion of criminal offending that takes place in the nonplaces to have risen. However, due to the unique relationships among each individual locality, it is possible that a High-High cluster may be associated with place-to-place mobility, which is not the subject of the current project. Therefore, if a High-High cluster exists and a place is high in 1990 and the non-place gains in crime and is high in 2000 (via a shift in the within-county proportion of crime), there is evidence of potential contagious mobility. On the same point, a Low-Low cluster that involves a non-place, which decreases its proportion of crime over the time, would be considered an area in which lower rates of crime existed in the places and spread outward in a mobility pattern to the nonplaces.

Table 1 is organized around three sub-sections, each representing a type-specific crime rate. Within each of the three sections, there is a

crosstabulation of Cohen and Tita's univariate method (rows) by the bivariate method (columns). The results support the work of Anselin and Sridharan (2002), which suggests that positive spatial autocorrelation (High-High and Low-Low) is associated with contagious mobility while negative spatial autocorrelation (High-Low and Low-High) is associated with spatial outliers or hierarchical mobility. In all three tables, about 90 per cent of the cases that were identified as having contagious mobility, using Cohen and Tita's method, are in columns representing positive spatial autocorrelation. In relation to cases identified as hierarchical by the Cohen and Tita method, between 80 and 100 per cent are classified as negative spatial autocorrelation by the bivariate method. The combined results show that the bivariate LISA is a consistent predictor of spatial mobility within the theoretical framework put forth by Cohen and Tita (1999). Furthermore, it seems to capture more of the space-time interaction with a higher proportion of cases being identified as being part of a statistically significant cluster of spatial mobility involving reported criminal offending.

Geographic Distribution of Bivariate LISA Results

In Table 2, the type of mobility by type-specific crime rate is broken down by metropolitan status and region. In relation to metropolitan status, the table shows that, across the board, at least 90 per cent of counties had no significant mobility. However, there does seem to be a noticeable difference with metropolitan counties having a higher occurrence of significant mobility compared to non-metropolitan counties. Within metropolitan counties, there is a higher occurrence of high place-to-non-place mobility of total crime and violent crime. On the other hand, there is not much difference in occurrence of high and low mobility between places and non-places in regards to property crime. The findings reported in this table are very interesting in that they point to areas of higher levels of immigration, and population mobility in general, as being disproportionately more likely to have a significant cluster of mobility (Lichter and Fuguitt, 1982; Lichter et al., 1985; Frey, 1987; Fuguitt et al., 1988; Wilkinson, 1991; Frey and Spear, 1992; Brown and Zuiches, 1993; Isserman, 2001; Johnson et al., 2005).

In relation to differences by U.S. Census Region, most of the counties do not fall into either the 'high' or 'low' mobility categories. However, there is noticeable difference in occurrences between the regions. The West and South both have higher levels of mobility then do the Northeast and Midwest. Within the South, there is no real difference in occurrence of trends in mobility for both total and property crimes; however, high crime mobility occurs at a meaningfully higher rate than low crime mobility, concerning violent crime. Within the West region, a similar pattern exists, with a six percentage point difference in violent crime occurrence. This is also important to note as it relates back to the earlier exploratory work where high crime rates were found in these two areas, especially relating to violent crime.

Identifying Counties with Significant Within-Unit Contagious Mobility

Because of the embedded nature of places within non-place territories, this project is mainly interested in the process of contagious mobility. Therefore, only areas of positive spatial association will be examined further in an attempt to identify localities of high type-specific crime mobility, through either expansion or relocation, from places to non-places. The bivariate LISA procedure only identifies significant relationships among localities that are neighbours, based on the nearest neighbours' definition. While this explicitly takes temporal relationships into account, it does not discriminate between place to non-place mobility or vice-versa. Since this project is interested in identifying significant place to non-place contagious mobility, the data were aggregated to the county level. If the bivariate cluster of the non-place was High-High and the non-place increased in crime, then the county is identified as having high place-to-non-place mobility.

Figure 2 focuses on the area of Fort Worth, TX (Tarrant). In the top two panels, the logged total crime rate for 1990 and 2000 are set side by side, with the same standardized legend across all figures (using an average of the natural breaks method). The difference in the rates is also illustrated in the lower panel. In the Fort Worth area, one can see that, in 1990, the crime rate was relatively higher in the place than the non-places. However, in 2000, the non-places have a similar high crime rate in comparison to the places. The difference mapped in the bottom panel shows that, while the area of Fort Worth decreased, the non-place and many other surrounding nonplaces increased.

[FIGURE 2 OMITTED]

DISCUSSION AND CONCLUSIONS

Identifying the proper, theoretically driven, neighbourhood is important to the subsequent understanding of macro-level social processes. Here a within-county nearest neighbour approach was employed to the identification of spatial neighbourhoods with k = 3 as the number of neighbours each locality would have. Using this approach, each non-place has three neighbours, which is about the average number of places within counties in this analysis. While it is understood that there exist a number of limitations to this analysis concerning the variation in numbers of places per county, the empirical support for setting the neighbourhood definition at k = 3 simply maximizes the within-county connectivity.

Furthermore, a multivariate approach was employed to identify articulated patterns of spatial mobility between the theoretically linked places and non-places following the work of Cohen and Tita (1999). The neighbourhood definition proved to work well as the bivariate results closely matched what was expected based on a replication and crosstabulation of Cohen and Tita's (1999) univariate use of the LISA for mobility detection. Again, while limitations exist concerning potential within period variation, it is evident that the application of the multivariate LISA is both reliable and efficient as an identifier of mobility processes.

Upon initial inspection, the results very closely matched those of Cohen and Tita (1999), upon which they were built. Again, the challenging part was defining and identifying a neighbourhood that would maximize the within-county connectivity while minimizing any between-county connectivity of places and non-places. Ultimately, the k-nearest neighbours approach was chosen and a series of counties where significant mobility of crime had occurred were identified, with a subset of those being presented as exemplars for further graphic illustration of the apparent mobility processes.

Geographically, all three type-specific crime rates proved to have significant patterns of mobility identified, both locally and globally. Globally, the Moran's I suggests that there are non-random patterns of clustering at a national level and, locally, the locations of these nonrandom clusters identified local areas of significant articulated mobility. These clusters noticeably were more prevalent in the South and West regions, in comparison to relatively lower numbers of occurrences in the Northeast and Midwest. Identified clusters of mobility also occurred at a higher rate in metropolitan counties when compared to non-metropolitan counties.

Ultimately, this examination of reported crime explored a new method for the examination of spatio-temporal processes related to the spread of criminal offending behaviour. The primary interest of this paper was to marry such methods to the place-level geography in order to identify counties within the U.S where significant spatial mobility of crime could be identified through patterns of mobility. The results suggest that there, do exist, such patterns and they are identifiable using the methods employed here. There also exist specific patterns associated with areas that were identified as counties in which significant mobility of criminal behaviour, from places to non-places, occurred during the time period of 1990 to 2000. (6) These processes occurred in adjacent non-metropolitan counties at a higher rate than they did in metropolitan or nonadjacent non-metropolitan counties. They also occur more often in the South when compared to all other regions.

Theoretically, it seems that this high level of spatial mobility in these areas may be linked to the high level of general population mobility. Meaning that, as population has deconcentrated from cities to suburbs and moved in a southward trend nationally, there may be a link between the mobility of behavioural processes such as criminal offending and the mobility of people through migration or even commuting. This brings to light another interesting connection concerning the substantive articulation of demography and crime. As individuals are the perpetrators of acts such as crime, it is generally plausible that the bulk of identifiable mobility in such processes will follow the trends of population mobility as outlined by more traditional demographic analyses. Therefore, one would expect to see the highest activity of crime mobility in areas that have been empirically identified as having the highest activity of population mobility. This will be the focus of further study based upon these data.

As mentioned, there are some important limitations that must be formally acknowledged. First and foremost, when dealing with any temporal modelling concerned with spatial mobility, it is good practice to introduce a number of different time lags for sensitivity analyses (Anselin, 1995). This project chose a 10-year period in which to examine the mobility of crime in 1990 to 2000, but future research should take into account yearly or even monthly lags in the associated articulation. While this analysis did provide evidence of the spatial mobility of crime within counties through patterns of contagious mobility, it may have missed other important within-period temporal processes. If that is in fact the case, then this examination simply uncovered time series related differences at [T.sub.1] and [T.sub.2], while not fully understanding the within-period variability that ultimately led to the identified net change.

Another important limitation is the aggregation of crime type. The ability to make distinctions between crime types is certainly important and more than worthy of future study. In fact, certain types of crimes are expected to be person specific (robbery) and some place specific (burglary) even though in this analysis both are treated as property crimes. In either case, the disaggregation of the crime types may provide insight into the differing mobility patterns of each and thus lend insight into approaches to combat them independent of one another. This, not unlike temporal and spatial aggregation, remain important issues that require the continued attention of researchers.

With the noted limitations, this examination makes a number of important contributions centred on moving the analysis of spatio-temporal processes forward and in the general area of ecological analyses. Methodologically, the use of the multivariate LISA as an identifier of spatial mobility has proven to successfully compare with earlier work using a univariate approach (Cohen and Tita, 1999). Even more beneficial is the fact that this approach appears to be more sensitive to such mobility as it identified many more cases of significant non-random clustering than the previous univariate method. This allows for the ability to identify much more of the space time interaction while efficiently examining the two in a single procedure. Furthermore, this procedure has implication beyond the analysis of crime, particularly in the analysis of more traditional demographic count data such as population mobility.

These implications lay the groundwork for a potentially rich line of future research. First, a sensitivity analysis should be under taken in order to better understand the appropriate time lag for within-decade examinations of the spatial mobility of reported crime. It is obvious that a decade may not be the most optimal choice and with-period examinations should continue to build on this work; however, as the goal of this analysis was to test this method against the univariate method, a simple 10 year difference was used for comparative purposes. Since the UCR data are collected on a monthly basis, this can be done. From this analysis, a template can be developed, from which a series of future analyses may sprout. Thus, providing an almost real-time algorithm for the allocation of resources in the ever evolving 'war on crime'.

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(1) The 'mobility' of crime refers to the geographic movement of reported crimes and not the travel of criminals themselves.

(2) 'Place-level' classification is in reference to the U.S. Census Bureau's identification of designated places (CDPs). These are areas that are designated as having a 'concentration of population'. In direct opposition to CDPs is a new conceptual geography, non-places. These nonplaces make up the balance of the county and represent areas that the U.S. Census Bureau has not designated as a 'place' or CDP.

(3) Robinson (1950) introduced the term ecological fallacy as a recognized error in the interpretation of statistical data through the use of inferences about the nature of individuals based aggregate statistics collected for the group to which those individuals belong. This fallacy is related to the idea that all members of the group are alike and can be described using aggregate data.

(4) The k nearest neighbors approach identifies a theoretically grounded number of meaningful neighbors based on locality centroids and Euclidean distance (Anselin, 1995).

(5) For sensitivity purposes, the analyses were run with k = 2, 3, and 4. k = 3 was ultimately chosen based on the balance between meaningful significant results compared to k = 2 and k = 4.

(6) Among those counties that were identified as having significant spatial mobility from places to non-places over the 10-year period, 40% were adjacent non-metropolitan counties while metropolitan and non-adjacent non-metropolitan counties both made up 30% of the cases. This large influx of crime in the adjacent counties is likely to be associated with notable in creases and mobility of crime in the suburbs. The largest percent, 49%, of the cases occurred in the South, with the next highest proportion occurring in the Midwest with 30%. Lastly, 12% took place in the West, while 9% occurred in the northeast.

DOI: 10.1002/sres.1076

Jeremy R. Porter *

Department of Finance and Business Management, Brooklyn College, City University of New York, USA

* Correspondence to: Jeremy R. Porter, Department of Economics, 218 Whitehead Hall, CUNY-Brooklyn College, 2900 Bedford Avenue, Brooklyn, NY 11210, USA. E-mail: jeremy.reed.porter@gmail.com
Table 1 Crosstabulation of univariate versus bivariate LISA
classification of the proportion of type-specific crime in
the overall county accounted for by each locality, 1990 and 2000

Type-specific
crime rate by       Bivariate classification (row percentage)
univariate
classification       Not
                 significant   High-high    Low-low    Low-high
Total crime
  Stationary         7369           351         270         187
  Contagious       3 (7%)      26 (58%)    14 (31%)           0
  Hierarchical     1 (7%)       2 (14%)           0    11 (79%)
  Column total       7373           379         284         198
Property crime
  Stationary         7367           334         287         184
  Contagious        2(4%)      28 (61%)    15 (33%)      1 (2%)
  Hierarchical          0             0           0   16 (100%)
  Column total       7359           362         302         201
Violent crime
  Stationary         7250           450         273         174
  Contagious       5 (9%)      24 (45%)    23 (43%)           0
  Hierarchical     2(10%)             0           0    18 (90%)
  Column total       7257           474         296         192

Type-specific       Bivariate
crime rate by     classification
univariate       (row percentage)
classification
                 High-low   Total
Total crime
  Stationary          246    8423
  Contagious            0      45
  Hierarchical          0      14
  Column total        248    8482
Property crime
  Stationary          248      20
  Contagious            0      46
  Hierarchical          0      16
  Column total        248    8482
Violent crime
  Stationary          262    8409
  Contagious       1 (2%)      53
  Hierarchical          0      27
  Column total        263    8482

Univariate classifications from Cohen and Tita (1999).

Table 2 Count and per cent of counties by type-specific crime rate
and mobility trend, 1990-2000

Descriptives                      Type specific crime by mobility
                                  (type-specific row percentages)

                                            Total crime

                                   Not sig.     High       Low
Metropolitan status
  Metropolitan                     776 (90%)   54 (7%)    21 (3%)
  Adjacent non-metropolitan       1161 (95%)   30 (2%)    33 (3%)
  Non-adjacent non-metropolitan    989 (96%)   12 (1%)    34 (3%)
Region
  Northeast                        215 (98%)    2 (1%)   1 (0.5%)
  Midwest                         1027 (97%)   14 (1%)    14 (1%)
  West                             380 (92%)   16 (4%)    16 (4%)
  South                           1304 (92%)   64 (5%)    57 (4%)

Descriptives                      Type specific crime by mobility
                                  (type-specific row percentages)

                                            Property crime

                                   Not Sig.     High       Low
Metropolitan status
  Metropolitan                     782 (91%)   38 (5%)   31 (4%)
  Adjacent non-metropolitan       1161 (94%)   29 (3%)   34 (3%)
  Non-adjacent non-metropolitan    990 (95%)   15 (2%)   30 (3%)
Region
  Northeast                        216 (99%)    2 (1%)     0.00
  Midwest                          133 (98%)   12 (1%)   10 (1%)
  West                             381 (96%)   15 (6%)   16 (4%)
  South                           1303 (91%)   53 (4%)   69 (5%)

Descriptives                      Type specific crime by mobility
                                  (type-specific row percentages)

                                            Violent crime

                                   Not Sig.     High       Low
Metropolitan status
  Metropolitan                     769 (90%)   71 (9%)   11 (1%)
  Adjacent non-metropolitan       1143 (94%)   54 (4%)   27 (2%)
  Non-adjacent non-metropolitan    996 (96%)   20 (2%)   19 (2%)
Region
  Northeast                        206 (64%)    6 (3%)    6 (3%)
  Midwest                         1017 (95%)   28 (3%)   10 (1%)
  West                             371 (90%)   31 (8%)   10 (2%)
  South                           1314 (92%)   80 (6%)   31 (2%)
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Title Annotation:Research Paper
Author:Porter, Jeremy R.
Publication:Systems Research and Behavioral Science
Article Type:Report
Geographic Code:1USA
Date:May 1, 2011
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