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Place-based data, methods, and analysis: Past, present, and future

Andresen, M.A., & Hodgkinson, T. (2019). Place-based data, methods, and analysis: Past, present, and future. In M.D. Krohn, G.P. Hall, A.J. Lizotte, & N. Hendrix (Eds.), Handbook on crime and deviance (2nd ed.) (pp. 3 – 19). New York, NY: Springer.

Published onJan 01, 2019
Place-based data, methods, and analysis: Past, present, and future


Place-based research in criminology considers the micro-place (street segments, for example) as the unit of analysis. Though research considering criminal events, or police calls for service, occurring at the micro-place has a long history, the contemporary “crime and place” literature that considers citywide analyses of criminal events or police calls for service emerged 30 years ago. This research has shown that the micro-place is an important component of understanding the spatial dimension of criminal events, both descriptively and inferentially. In this chapter, we review the crime and place literature, considering place-based data, methods, and forms of analysis. We discuss the significant strides that have been made within the spatial criminology literature using a place-based approach, but conclude that there remains work to be done to move the field forward.

Keywords: crime and place; micro-geography; place-based; spatial


Most criminological literature focuses on the offender: why and how they offend. The places criminal events occur, however, consistently show that location matters for understanding crime. The academic examination of “problem places” began with the Chicago School in the early 1900s, but more recently, this focus has begun to shift to include the micro-place, as practitioners and academics acknowledge the role of problem places in understanding crime and its prevention/reduction. Place-based research in criminology considers the micro-place (specific addresses, street segments, street intersections) as the primary unit of analysis when studying criminal events (official incident) and police activity (calls for police service) data.

Micro-level place-based research, as it is currently understood, began with the work of Sherman et al. (1989), when they undertook a micro-place analysis of predatory crimes (robbery, rape, and automotive theft) across the entire city of Minneapolis, MN for an entire year. Also referred to as crime and place research (Eck and Weisburd, 1995), the micro-place has proven to be a critical component of understanding the spatial patterns of crime. For example, a small percentage of micro-places account for a significant percentage of crime across many cities: the “typical” reporting is that five percent of micro-places (street segments, street intersections, actual addresses, and so on) account for 50 percent of crime—when individual crime types are considered, this percentage of micro-places can drop to less than one percent (Weisburd, 2015).

The importance of the micro-place to understanding spatial patterns of crime has been shown to be critical by some recent research that has investigated the proportion of the variability in spatial patterns that can be explained at different levels of geography: the micro-level (street segments, for example), the meso-level (larger areas approximately the size of one square kilometre, neighbourhoods or census tracts, for example), and macro-level geographic areas that are larger than neighbourhoods but regions within a city. For example, Steenbeek and Weisburd (2016) investigated the proportion of the variability in spatial crime patterns that could be attributed to the micro-, meso-, and macro-levels of analysis in The Hague, Netherlands. They found that approximately 60–70 percent of the spatial variability could be attributed to the micro-level, with most of the remaining percentage of the spatial variability attributed to the macro-level; they even go as far as stating that the meso-level of analysis (neighbourhoods) do not add value to understanding spatial patterns of crime. Schnell et al. (2017) found similar results in Chicago, IL, with 55–65 percent of the spatial variability attributed to the micro-level. In another research study, O’Brien and Winship (2017) found that 95–99 percent of the spatial variability of crime can be attributed to the street address. These findings indicate that while research comparing cities or neighbourhoods may be important, statistically, the most significant variance occurs from street to street, showing that criminological research needs to take into account these micro-locations. It is also important to note here that such high percentages of spatial variability being accounted for by the micro-place does not mean that larger areal units of analysis are not important for understanding the geography of crime. Rather, this simply shows that place-based analyses should not be ignored if one wishes to understand the spatial dimension of crime.

In this chapter, we outline the empirical consistency of crime concentration, the nature of the data, theoretical implications, methods of measurement, and methods of analysis most common in place-based criminology. Our goal here is to provide the reader with an understanding of the primary ideas and issues with place-based criminology, concluding with our view on how and where the field can progress in the future.

The law of crime concentration at places

Sherman, Gartin, and Buerger (1989) were the first to report a Pareto-type principle for understanding spatial crime concentration at places: three percent of micro places were able to account for 50 percent of predatory crime in Minneapolis; considering specific crime types, these concentrations are 2.2 percent for robbery, 2.7 percent for motor vehicle theft, and 1.2 percent for rape. This is a considerable level of concentration that is similar to, and consistent with, the study by Wolfgang et al. (1972) who found that a small percentage of offenders committed a significant portion of criminal events.

Several years later, Weisburd et al. (2004) studied crime concentrations and stability in Seattle, Washington. Similar to Sherman et al. (1989), these researchers found that approximately five percent of street segments accounted for 50 percent of all calls for police service. Moreover, they found that this high degree of spatial concentration carried over a 14-year time period. In subsequent research, Weisburd et al. (2009, 2012) confirmed these results in other contexts in Seattle, Washington: young offenders over the original 14-year time period and their previous analyses over a 16-year time frame. Braga et al. (2010, 2011) found similar results for shootings and robbery in Boston, Massachusetts; over 29 years, less than 3 percent of street segments and intersections accounted for 50 percent of shootings and 8.1 percent of street segments and intersections accounted for 50 percent of robberies. In cities of varying sizes across the United States, Weisburd (2015) has found this general pattern of spatial crime concentrations to be present. And more recently, Haberman et al. (2017) confirmed these tendencies at three different temporal scales.

These patterns of spatial concentration have also been found in international contexts. In Canada, Andresen and Malleson (2011) found that approximately five percent of street segments accounted for 50 percent of crime in Vancouver (1991 to 2001), and that levels vary by crime type: assault (1.62 %), burglary (7.61 %), robbery (0.84 %), sexual assault (1.12 %), theft (2.58 %), theft of vehicle (5.97 %), and theft from vehicle (2.64 %). More recently, Andresen et al. (2017a) found that these concentrations increased over time (1991 through to 2006) and Andresen et al. (2017b) found that these spatial concentrations continued to increase (2003 through to 2013) for property crime. Also in Canada, Andresen and Linning (2012) found that for Ottawa in 2006, crime was incredibly concentrated spatially in order to account for 50 percent of that crime: total burglary (1.67 %), total robbery (0.38 %), and theft of vehicle (0.99 %). Outside of North America, Weisburd and Amram (2014) found that 50 percent of crime occurred on 4.5 percent of street segments and all crime could be accounted for by considering 36.8 percent of street segments in Tel-Aviv-Jaffa, Israel in 2010. And in Campinas, Brazil considering various forms of robbery and theft (commercial, residential, vehicle, street, and public transportation), Melo et al. (2015) found that 50 percent of crime is accounted for by 0.1–3.66 percent of street segments over the years 2010–2013 depending on the crime type.

This high degree of spatial concentration in a variety of international contexts has led Weisburd (2015) to assert a law of crime concentration at places. This law of crime concentration at places states that “for a defined measure of crime at a specific micro-geographic unit, the concentration of crime will fall within a narrow bandwidth of percentages for a defined cumulative proportion of crimes” (Weisburd, 2015, 138). Though this law has been shown to be present in a variety of contexts over space, time, and crime types, the data used for these measurements are far from perfect, needing consideration for future research.

Data and its issues in place-based research

Three primary data issues exist in place-based criminology research: police data and the dark figure of crime, georeferencing/geocoding at the micro-place, and how to account for intersections. Place-based research in criminology primarily relies on police calls-for-service data (police activity) and incident data (Uniform Crime Reports, for example) obtained from various police services. The former represents calls for police service through an emergency service such as 911, requests for police service made by the public directly to a police service, and internal calls for service made by police officers (Sherman et al., 1989), and the latter represent official incident data that are reported to government statistical organizations.

Since the late 1980s, calls for service data has become more available and used more frequently in research. However, because of the sensitivity of criminal event data (or any data concerning any interactions between the public and the police), many police services do not provide address level (micro-place) data for analyses unless there is a pre-existing relationship between the researcher and that police service. Moreover, these calls for service data have been criticized for not appropriately representing criminal events because a call for service does not necessarily mean a crime has actually occurred (Klinger and Bridges, 1997; Sherman et al., 1989). Because of this potential, calls for service data are, at times, referred to as police activity data (Andresen, 2014). Despite these concerns regarding calls for service data, the potential for the inclusion of any unfounded calls would likely be dwarfed by the volume of calls even reported to the police and the importance of catching low level social disorder that often does not translate into official incident data but is still important for understanding what is happening at the street (Black, 1970; Bulwer, 1836; Perreault, 2015; Perreault and Brennan, 2010).

The most significant concern regarding the use of official crime data is that it may not actually be representative of crime patterns; this concern dates back to at least the early 1800s (Bulwer, 1836). The issue is that if a significant portion of criminal events are never reported to the police, those criminal events that do get reported may be biased, potentially leading to improper inferences relating to theoretical testing and, more importantly, subsequent policy implementations. For example, data drawn from the Canadian victimization survey in 2014 indicate that 31 percent of total criminal victimization was reported to the police, steady at 31 percent in 2009, down from 34 percent in 2004, and from 37 percent in 1999 (Perreault, 2015; Perreault and Brennan, 2010).. It should be obvious that with more than two-thirds of criminal event data not even being present in official crime records that the potential for bias in the crime data that we do study is great; this is particularly the case for any investigation of spatial crime patterns, especially for studies considering the micro-place because criminal/police events are so rare for any particular micro-place. The trouble is that we do not have any studies that are able to investigate this potential spatial bias due to the high costs of undertaking a micro-level victimization survey, or even the neighbourhood level survey, for example. The only study we are aware of that considers this issue, and tests it, was undertaken by Ceccato and Lukyte (2011), where they found that the victimization patterns were significantly different from official crime data patterns. This study was for one country and rather coarse spatial units of analysis, but shows the potential for problems with 200 years of spatial criminological research. Regardless, their research is important and points to an issue for which we need to be aware.

Overall, the under-reporting for criminal event data is problematic for place-based, or any spatial, analysis of crime in a manner similar to how offender-based theories often only rely on interviews of offenders in prison, not those who do not get caught. However, in order to address under-reporting, researchers have begun to look at individual crime types that may have better reporting rates, allowing for more confident analyses—it is assumed that reporting issues within these individual crime types are consistent over time and space. Homicide, for example, is commonly known to have the highest reporting rates because the victims either disappear or are found deceased. Though some homicide victims may be reported as missing persons for some (indefinite) period of time or the cause of death for a person may be mis-identified, homicide-related crime data are considered the most complete (David, 2017; Forst, 2004). The question, then, is how well other crime types are reported to the police? Research in Canada has shown that there is substantial variation across the following individual crime types: sexual assault, robbery, physical assault, residential break and enter (residential burglary), motor vehicle/parts theft, theft of household property, vandalism, and theft of personal property (Perreault, 2015; Perreault and Brennan, 2010). As shown in Table 1, property crimes have much greater levels of reporting to the police, especially break and enter and theft related to motor vehicles; this may simply be due to those criminal events often requiring a police report for insurance claims. Despite having higher reporting rates to the police, for the crime types reported in Table 1, rarely are the reporting rates greater than 50 percent, revealing that biases in these data are likely systemic. Though this is less consequence for the actual analyses of criminal event data, the reasons listed for not reporting a crime to the police range from “not important enough” (almost 70 percent) to “fear of publicity or news coverage” (approximately 5 percent) (Perreault, 2015; Perreault and Brennan, 2010).

<Insert Table 1 About Here>

Another georeferencing issue for place-based research is geocoding: the placement of a criminal event on a map (using a dot to represent an address, for example). This is an issue because this process has the potential for error that may impact subsequent analyses. At times, criminal events, or any other location data for that matter, do not have an address or set of geographic coordinates provided. This may be due to a lack of reporting, unknown locations, or human error in data reporting, for example. If these missing geographic locations are repeatedly occurring in the same places this may be problematic for subsequent analyses to understand spatial crime patterns. However, Ratcliffe (2004) has found that even when data are missing at random, 85 percent of the data must be geocoded to prevent bias occurring in the spatial patterns of crime. But even when data are geocoded at an acceptable rate, there is still the issue of the availability of micro-level geocoded police data for place-based analyses.

Police data (calls for service or incident) measured at the micro-place level are increasingly becoming available in a variety of different cities and countries (see Weisburd,2015). In some cases, these data are provided at the street segment level, suitable for place-based analyses, but in other cases data are not provided at such a fine resolution. Of course, we must work with the data that are available to us as researchers, but this limits the reproducibility, and generalizability, of place-based criminological research.

Lastly, an issue that has emerged in place-based criminology research is the inability to properly georeference police calls for service or incident data to intersections. Depending on the research study, Weisburd (2015) has found that 0 to 33 percent of police calls for service data are georeferenced at intersections. These intersections are removed from the analysis in some research (Weisburd et al., 2004; Curman et al., 2015), but other research has incorporated intersections into the analyses (Andresen et al., 2017a, 2017b; Braga et al., 2010, 2011; Wheeler et al., 2016) as separate units of analysis. Very few police incidents that are not traffic-related actually occur within an intersection, but if the incident occurred very close to the intersection (a motor vehicle theft, for example, that was parked at the end of a street segment) it often is georeferenced to that point rather than on the street segment itself. The issue is that removing intersection data, especially when it can represent as much as one-third of the police calls for service data, only adds to the “dark figure of crime” issue, but placing police calls for service at an intersection when they did not occur at that intersection imposes some spatial bias. If the number, or percentage, of intersections is low, then either one of these situations will generate very little bias.

Theory testing in place-based research

Though related to the previous section, another issue with micro-place data that is important to highlight is the lack of correlates with crime measured at the micro-place. These correlates relate to most of the traditional variables used in the spatial criminology literature to test theories, evaluate interventions, or generate criminal justice policy and are simply not available at this scale. The lack of availability may be related to privacy (statistical agencies will not release the data) or the cost of obtaining these measures at the micro-place (most censuses only sample 20% of individuals), but these variables are important to control for in any analyses.

For example, in the cases of social disorganization theory (Sampson and Groves, 1989; Shaw and McKay, 1942, 1969), theoretically informed variables have been measured at the neighbourhood level; in the case of routine activity theory, theoretically informed variables have been measured at the national level (Cohen and Felson, 1979), the neighbourhood level (Andresen, 2006, 2011), and the individual level (Kennedy and Forde, 1990). Very few theoretically informed variables tend to be available at the micro-geographic level. Rather, these variables tend to be available in various censuses considering areal units such as census tracts and census block groups. The availability of theoretically-informed variables at the micro-place matters and is important for moving place-based research forward in criminology because, as shown in Figure 1, one census tract may include 10 census block groups, and each census block group may include 20 street segments and intersections.

<Insert Figure 1 About Here>

To date, the only two known studies testing theory at the micro-place are Smith et al. (2000) and Weisburd et al. (2012). Smith et al. (2000) undertook a citywide study of spatial crime patterns at a micro-spatial unit of analysis, street segments, but also larger areal units of analysis. They used data from a medium-sized southeastern city in the United States, integrating routine activity theory and social disorganization theory in a place-based analysis. They noted that the empirical support in past research for integrating routine activity theory and social disorganization theory has not been strong. However, they note that is was not because routine activity theory and social disorganization theory should not be integrated, rather that the spatial units of analysis have not been appropriate, such as census tracts or census block groups. In their theoretical integration that used the street segment as the spatial unit of analysis, Smith et al. (2000) had far more success, in the context of street robbery. They argued that their success was because of the heterogeneity within neighbourhoods that was averaged out when other researchers had used larger areal units.

Weisburd et al. (2012) conducted the most recent, and comprehensive, place-based investigation of crime. In their book, Weisburd et al. (2012) extended their previous research on crime at places in Seattle, Washington. In addition to investigating trajectories of micro-places over time, they also examined the characteristics of the chronic street segments. Weisburd et al. (2012) analyzed the characteristics of this type of trajectory (time path) from a theoretical perspective. Using logistic regression, they incorporated explanatory variables that represented routine activity theory and social disorganization theory. For routine activity theory, they found the following: the presence of high-risk juveniles (motivated offenders) doubled the probability of high-crime street segments; each additional employee on a street segment (industrial/business land use) increased the probability of a presence of a chronic street segment by eight percent; a public facility (community centre or high school, for example) within 400 meters of a street segment increased the probability of a chronic street segment being present by 25 percent; and street segments with a greater resident population had a greater probability of being a chronic street segment. Moreover, each additional bus stop increased the probability of a high crime street segment by a factor of two, a street segment on an arterial road was at an increased probability of being a chronic street segment, and the presence of vacant land on a street segment had a very larger impact of a street segment (a one percent increase in the area of vacant land increases the probability of a street segment being chronic by almost 50 percent).

In the context of social disorganization variables, the results showed that increases in the residential property value were associated with a large magnitude decrease in the probability of a street segment being chronic, and the presence of subsidized housing was associated with a moderate increase in the probability of a street segment being chronic. Weisburd et al. (2012) also found statistically significant effects for the presence of physical disorder, the presence of truant juveniles and, lastly, the presence of residents who are involved in public affairs in that all increase the probability of a street segment being chronic).

This research that is able to incorporate theoretically informed variables in a place-based context has been instructive. However, because of a lack of citywide data that measures these theoretical constructs, there is very little of this research. Though more research is emerging that incorporates more theoretically informed (routine activity theory and social disorganization theory) place-based variables with more traditional variables in the spatial criminology literature (Andresen and Hodgkinson, 2018a), it is often necessary for the place-based variable to be aggregated to larger census-based areal units of analysis such as census tracts and census block groups. The generation, and use, of these more traditional theoretically informed variables at the level of the micro-place are available through the census, but involve confidentiality concerns. As such, in order to move the place-based criminology research agenda forward, this data constraint, and the others named above, need to be addressed.

Measuring crime at places

As outlined above, the law of crime concentration at places holds across time, space, and crime types. However, it is important to note that when the spatial units of analysis become increasingly smaller, the spatial concentration of any activity will appear to increase. For example, if there are 1000 events occurring within 10,000 spatial units, the minimum level of concentration is 5 percent of spatial units of analysis accounting for 50 percent of the events; this replicates the Pareto Principle nature of crime concentrations with a (potentially) completely random or uniform distribution of criminal activity.

Although this is a completely hypothetical scenario, this phenomenon has been shown to be present in the crime and place literature. For example, Andresen et al. (2017b) showed that 100 percent of property crime in Vancouver, Canada occurred in just over 25 percent of street segments and intersections; moreover, this level of concentration has been increasing over time: 35 to 25 percent, 2003 to 2013. In the context of specific crime types, 100 percent of crime can be accounted for considering 5 to 20 percent of street segments and intersections. Most often, this is an artefact of crime counts versus the number of spatial units of analysis, but not always. As such, this crime concentration measure should be evaluated critically whenever there are more spatial units of analysis than there are criminal events—see Hipp and Kim (2017) and Levin et al. (2017) for other discussions of issues with measuring spatial crime concentrations.

Accounting for this limitation in the crime concentration measure, Andresen and Malleson (2011) not only reported the percentage of criminal events accounted for by 50 percent of street segments, but also reported the percentage of street segments with any crime and the percentage of street segments with any crime that account for 50 percent of crime. This allows for the reader to place the standard concentration measure within a context: given how many places crime actually occurs, how concentrated is crime? In the aggregate, this tends to show that approximately 10 to 15 percent of street segments and intersections account for 50 percent of crime, depending on the year. Though this provision of context is a step forward and, most often, supports the law of crime concentration at places, it still has its limitations.

Bernasco and Steenbeek (2017) standardize the measurement of spatial crime concentrations using a generalized Lorenz curve and Gini coefficient: the Lorenz curve is a function that graphs the cumulative distribution of one variable compared to the cumulative function of another variable (the percentage of crime compared to the percentage of micro-places, for example), and the Gini coefficient is a statistic measuring inequality. The Lorenz curve has a long history (over a century) of being used to measure the magnitude of inequality in the distribution of wealth. As shown in Figure 2, in the graph showing the Lorenz curve there is a line of equality that represents an even distribution; 25 percent of micro-places account for 25 percent of crime, 50 percent of micro-places account for 50 percent of crime, 75 percent of micro-places account for 75 percent of crime, and so on. The Lorenz curve shows the actual distribution: 5 percent of micro-places account for 50 percent of crime, for example. As such, the further away the Lorenz curve is from the Line of equality, the greater the degree of inequality present with regard to the distributions of the two variables of interest.

<Insert Figure 2 About Here>

In order to summarize the degree of inequality in one statistic, the Gini coefficient can be calculated as the ratio of the area between the Line of equality and the Lorenz curve (Area A in Figure 2) to the area between the Line of equality and the “Line of perfect inequality” (Areas A and B in Figure 2): A/(A + B). If there is no inequality, the Area A is zero, so the Gini coefficient is equal to zero, but if all crime happens in one place (perfect inequality) Area A is equal to Areas A + B, so the Gini coefficient is equal to unity. This provides a simplistic graph and easily interpreted statistic for comparisons of crime concentrations across different studies. Though instructive, the Lorenz curve and corresponding Gini coefficient have a limitation that can be problematic for such comparisons.

In the crime and place literature, the Lorenz curve and the Gini coefficient are limited when there are more micro-places than there are criminal events: 1000 criminal events and 10,000 street segments, for example. In this situation, the line of equality would not represent what equality would actually be. Even if each criminal event were on a separate street segment, 10 percent of the street segments would account for all the criminal events and a Gini coefficient close to unity. Visually, Area A would be much larger than it should be. Rather, the actual Line of Equality would be much steeper.

With their generalized Lorenz curve and Gini coefficient, Bernasco and Steenbeek (2017) modified the calculations such that the Line of equality is represented in a manner that accounts for this small number problem. In the crime and place context, if the number of criminal events (or calls for service) is greater than or equal to the number of micro-places their generalized Lorenz curve and Gini coefficient gives the same output as the traditional Lorenz curve and Gini coefficient. Consequently, using the generalized Lorenz curve and Gini coefficient developed by Bernasco and Steenbeek (2017), researchers can confidently compare concentration rates across all contexts.

Methods of analysis in place-based research

There are a number of ways to measure spatial crime concentrations, as well as the stability of those spatial crime concentrations over time. This stability is critically important within spatial criminology, more generally, and place-based criminology, specifically. If spatial patterns are not stable over a reasonable length of time, it is not possible to make good predictions regarding the levels of crime, or police activity, at other times or in other places. In other words, if there is no spatial stability in our data, we can only report on historical spatial crime patterns that have no relevance today.

The importance of this spatial stability has been recognized for almost a century, with Shaw et al. (1929) and Shaw and McKay (1931, 1942, 1969) noting how neighbourhoods maintained their spatial patterns of juvenile delinquency over time, despite the change in ethnic composition of those neighbourhoods. However, it is important to re-assess spatial stability because many North American inner cities have become gentrified as the nature of industry changes (Lees et al., 2007; Florida, 2010).

The methods within the place-based criminology literature have primarily consisted of group-based trajectory modeling, growth curve modeling, and a longitudinal spatial point pattern test. In addition, some more traditional statistical methods have been used in the analysis of placed-based (crime) data. Each is covered briefly, in turn.

Group-based trajectory modeling and k-means clustering

Within investigations of the criminal career debate, Nagin and Land (1993) were the first to use trajectory analysis in criminology. Commonly referred to as “group-based trajectory modelling” (GBTM), this semi-parametric method was used to identify subgroups of individual offenders who follow a similar pattern of change over time (Andruff et al., 2009; Nagin, 1999, 2005). Effectively, GBTM is a form of cluster analysis that groups individual observations (individuals or places) into groups that have similar time paths. The number of groups identified is identified based on the variance between the different trajectories and is most often measured using the Bayesian Information Criteria (BIC) score. As such, the number of trajectory groups is identified by increasing and decreasing the number of groups in an effort to minimize the BIC. This statistical method has been used in a number of contexts within place-based criminological research (Andresen et al., 2017a; Curman et al., 2015; Griffiths and Chavez, 2004; Groff et al., 2010; Weisburd et al., 2004, 2009, 2012; Wheeler et al., 2016).

Though instructive, this statistical method has two assumptions that can prove to be problematic. First, GBTM assumes the independence of repeated measures over time for each observation, or unit of analysis. With regard to place-based research, this means that the number of criminal events or call for police service for a group of streets in one particular trajectory for one year (e.g. 2018) is completely independent of the number of criminal events or call for police service on those same streets for the following year (e.g. 2019). This assumption is clearly problematic because of the known stability of crime patterns (Weisburd et al., 2004). And second, GBTM does not control for spatial correlation. With regard to criminal events or call for police service, the respective count for the “300 block of Main Street” is assumed to be independent from the count on its neighbouring street segments, the 200 or 400 block of Main Street. This assumption is problematic because criminal events do not exist on an isotropic plane; rather, criminal events, and calls for police service more generally, cluster close to one another (Andresen, 2014). Regardless, this statistical method has proven to be instructive for place-based research in criminology. Different places (often street segments) are treated as individuals and grouped together based on similar time paths. This has been used to identify different subgroups of places similar to the subgroups of individual offenders: chronic street segments, discussed further below.

In order to address the two limitations of GBTM, outlined above, k-means clustering has been used to identify these different subgroups (Andresen et al., 2017a; Curman et al., 2015). As opposed to semi-parametric GBTM, k-means is a non-parametric statistical method that analyzes longitudinal data in order to identify clusters of observations that share similar time paths (Calinski and Harabasz, 1974; Genolini and Falissard, 2010). Though not as common as GBTM, k-means longitudinal clustering has been used in criminology: Huizinga et al. (1991) used k-means to examine the offending trends of 1,530 Denver youth over a two-year period (1987-1988), and Mowder et al. (2010) used k-means to investigate the resilience of 215 male and female juvenile offenders who were committed to a juvenile facility.

Given that k-means longitudinal clustering is a non-parametric statistic, it does not require data to fit a specific distribution, not being sensitive to the (lack of) autocorrelation and spatial dependence in GBTM. Genolini and Falissard (2010) have noted that when k-means longitudinal clustering is supplemented by GBTM, the researcher is given a thorough picture of longitudinal patterns within a large dataset. Moreover, when the distributional assumptions of GBTM are met, the two methods output comparable results, but when the assumptions are not met, GBTM does not produce the known clusters in the test data whereas k-means longitudinal clustering is able to reproduce those groups. The advantage of using GBTM; however, is that control variables may be introduced. This cannot be done within k-means longitudinal clustering.

Growth curve modeling

Another statistical method used in place-based criminological research is growth curve modeling. Growth curve modeling, similar to GBTM is based on a count-based regression method (negative binomial). This method is multi-level and longitudinal, predicting

within unit variation at level 1 and between unit variation at level 2—level 1 intercepts and slopes are the outcomes (Braga et al., 2010, 2011; Gelman, 2005; Singer and Willet, 2003). Similar to GBTM, this statistical method analyzes the overall trend in a data series for each of the spatial units of analysis (street segments and/or intersections), with each spatial unit of analysis having its own slope and intercept such that each spatial unit of analysis can have its own starting level and overall trend.

The advantage of using growth curve modeling instead of GBTM is that rather than estimating trends and subsequently clustering subgroups of trends together such that they “share” a slope coefficient (GBTM), growth curve modeling estimates trend slopes for all spatial units of analysis (see Eggleston et al., 2004 and Nagin, 2004 for discussions of the relative merits of these different statistical methods). Regardless, growth curve modeling allows for the trends of individual spatial units of analysis to be estimated such that the researcher may identify the complete nature of the temporal patterning of each spatial unit of analysis for the entire study period through an assessment of individual slope parameters (Braga et al., 2010, 2011; Kubrin and Herting, 2003).

In their analyses of patterns of gun violence and robbery in Boston, MA, Braga et al. (2010, 2011) used a number of control variables in their growth curve models: lagged values of the crime type counts under analysis, street segment length or a variable to differentiate between street segments and street intersections, street type, and a linear trend. This more traditional statistical estimation that includes a set of control variables has a clear advantage over non-parametric and semi-parametric approaches, but does need to be concerned with any distributional assumptions of the data. Additionally, estimating the trends (stability) for each spatial unit of analysis has a clear advantage because clustering may mask interesting, and critical, variation from street to street.

Longitudinal spatial point pattern test

Another statistical method that considers change at the level of each spatial unit of analysis is a longitudinal spatial point pattern test. The spatial point pattern test developed by Andresen (2009, 2016) identifies spatial stability through the identification of similar spatial patterns between multiple spatial point pattern datasets. This spatial point pattern test has been used in a variety of contexts: the similarity of spatial patterns across crime types (Andresen, 2009), changing patterns of international trade (Andresen, 2010), the stability of crime patterns (Andresen and Malleson, 2011), the spatial impact of the aggregation of crime types (Andresen and Linning, 2012), the spatial dimension of the seasonality of crime (Andresen and Malleson, 2013a; Linning, 2015), the impact of modifiable areal units on spatial patterns (Andresen and Malleson, 2013b), the role of local analysis in the investigation of crime displacement (Andresen and Malleson, 2014), the comparison of open source crime data and actual police data (Tompson et al., 2015), the changing spatial patterns of crime with regard to the crime drop (Hodgkinson et al, 2016; Pereira et al., 2016), the spatial dimension of police proactivity (Wu and Lum, 2017), and the stability of crime concentration at micro-places (Andresen et al., 2017b; Vandeviver and Steenbeek, 2017).

The details of this test are available in Andresen (2009, 2016), but essentially it involves identifying differences in the spatial patterns of two, or more, spatial data sets at the micro-level, or whatever spatial unit of analysis is employed. Moreover, in addition to the original version of this spatial point pattern test, Wheeler et al. (2018) have implemented a Chi-square version and Steenbeek et al. (2018) have produced bootstrap versions of this spatial point pattern test. The output of this test is a global index of similarity, S, that ranges between 0 (no similarity) and 1 (perfect similarity), calculated as follows:

S=i=1nsinS = \frac{\sum_{i = 1}^{n}s_{i}}{n}


where si is equal 1 if the pattern of two datasets are similar within an individual spatial unit of analysis and 0 otherwise, and n is the number of areas. Simply put, the similarity index measures the percentage of areas (street segments, census tracts, etc.) that share a similar spatial pattern. Though there are no strict guidelines for a value of S to indicate similarity, a rule of thumb has emerged that relates to the rule of thumb in the context of multicollinearity and regression. Specifically, the variance inflation factor (VIF) is used as a diagnostic tool for regression analysis to identify potentially problematic multicollinearity that may lead to issues with inference: most often with a range of 5 to 10 (O’Brien, 2007). In a bivariate context, this represents a correlation ranging from 0.80 to 0.90, so an S-Index value of 0.80 is often used to identify when two spatial point patterns are similar. In addition to this global index of similarity, the results of this test can be mapped, showing the local level results and the researcher where the two spatial point patterns are different (Andresen, 2009). As such, this statistical method works well in the place-based criminology literature.

The original version of this spatial point pattern test considered pairwise comparisons: two different years of the same crime type or two different crime types, for example. Though instructive, and indicated by Andresen et al. (2017b), this version of the spatial point pattern test may lead to spurious results when considering changing spatial patterns over time. Even if S >= 0.90 for a number of consecutive pairwise comparisons, if the 10 percent of non-similar spatial units of analysis changes with every subsequent pairwise comparison, by the time 10 years have passed spatial similarity will actually be quite low. In order to address this limitation, Andresen et al. (2017b) extended the original spatial point pattern test making it longitudinal in order to assess the stability of spatial trajectories. In doing so, these researchers also modified the S-Index to better represent longitudinal spatial trajectories.


The place-based criminological research that has investigated the spatial stability of crime patterns has found remarkably consistent results. Weisburd et al. (2004), the first to investigate the stability of spatial crime patterns (calls for police service), found that the vast majority of street segments had stable trajectories over a 14-year time period—this was confirmed in their subsequent work for a 16-year time period (Weisburd et al., 2012). Additionally, these researchers found that the crime drop that occurred in their case study, Seattle, WA, could be accounted for by a small percentage of the street segments, 14 percent (see also Hodgkinson et al., 2016). As such, the seemingly omnipresence of the international crime drop (Farrell et al., 2011, 2015), though present in a large number of contexts, is a rather localized effect. These results have also been confirmed for Seattle, WA in the contexts of juvenile delinquency and the spatial patterns of different street segment trajectories (Weisburd et al., 2009; Groff et al. 2010).

In their analyses of gun violence and robbery in Boston, MA, Braga et al. (2010, 2011) found strong evidence for spatial stability over a 29-year time period. Curman et al. (2015) also found that the vast majority of street segments were stable over a 16-year study period in Vancouver, BC, with Andresen et al. (2017a) confirming this stability for disaggregated crime types; moreover, in these studies of spatial stability in Vancouver, BC, a relatively small percentage of street segments and intersections accounted for the crime drop in Vancouver over the study period. In a 14-year study of spatial stability in Albany, NY, Wheeler et al. (2016) found similar results to previous research, particularly those from Vancouver, BC.

In a recent special issue of a journal on place-based criminology, Braga et al. (2017), a number of its articles further investigate the stability of spatial crime patterns. Hibdon et al. (2017) extend the research on crime concentrations and spatial stability in Seattle, WA considering drug activity, confirming previous research. Also consistent with previous research, Gill et al. (2017) reproduced a high degree of spatial stability in a suburban, as opposed to an urban, context. Needless to say, there is a remarkable degree of consistency in place-based criminological research. What we know is most definitely well-established, but now we need to know where to move next in the field to go forward.

Where we need to go to move the field forward

The place-based criminological literature has firmly established a number of empirical regularities, some of which may be referred to as stylized facts, or in one case, a law (Weisburd, 2015). However, this area of criminology is still quite young and there is much work to be done. Though there are many ways in which research may proceed in the future, there are a number of pressing issues that should be addressed. Namely, there are still concerns regarding data quality (common in most empirical research), details, specifics, or nuances of the empirical regularities that should be explored, methodological issues, and the role of theoretical development because of its importance to proper policy development.

The primary data quality issue in place-based research is that this research relies on police records management systems for data. These systems are improving and increasingly available for research purposes but, as discussed above, the dark figure of crime still looms over any research that uses such data. As shown by Ceccato and Lukyte (2011), actual victimization and police data may not be well-aligned. What is needed at this juncture is a set of victimization surveys at the smallest geography possible in multiple cities to confirm or deny the similarity in the spatial patterns of reported and total crime. As noted above, if these spatial patterns are similar enough, previous work in spatial criminology, more generally, and place-based criminology, specifically, regarding patterns remains useful, only the levels of criminal/police activity will be incorrect. However, if it is repeatedly shown that actual crime and reported crime have different spatial patterns, this is problematic for all of spatial criminology, place-based or not, because any relationships found would be spurious.

In a similar way, the details, or nuances, of these empirical regularities needs to be fleshed out. Yes, “crime” and/or “police activity” overall may be spatially concentrated, but the different aspects of crime and police activity may prove to be different. As outlined above, spatial concentrations are greater when measured for specific crime types. Although this is partially due to having fewer data points, these concentrations tend to remain true after controlling for the fewer locations crime may actually occur. It is also important to note that crime only comprises 20–30 percent of police calls for service, over relatively long periods of time (Wuschke et al., 2018). As such, 70–80 percent of police activity is ignored when only criminal events are analyzed. For example, Vaughan et al. (2016) found that the spatial patterns of mental health related calls for police service (approximately two percent of calls for police service) are notably different from crime-related calls for police service. Moreover, mental health related calls for police service are more concentrated than crime-related calls for police service.

With regard to statistical methods, traditional statistical methods have their limitations within place-based criminological research. There is not a lot of inferential research (with control variables) simply because of a lack of data, as discussed above. However, the research that does include more traditional statistical methods tends to be rather sophisticated, spatial, count (Poisson and negative binomial), and discrete choice (logistic) regression models. However, in addition to a lack of theoretically informed variables, because of the extremely rare nature of events at the micro-place, there tends to be very little variation in the counts of criminal events or other police activity: most micro-places have zero events, a few micro-places have a few events, and a very small percentage of micro-places have a large magnitude of events. Though there are statistical methods to deal with low counts of events (count-based and zero-inflated count-based regression models, for example), events at the micro-place are so rare that even using these statistical methods there can be difficulties finding statistical significance for independent variables that have been shown to be critical in previous research (Andresen and Hodgkinson, 2018b). This may be simply because these variables do not matter at the micro-place, but it could be because of a lack of variation in the variables used in the analyses. One way this field may move forward is through the gathering of more theoretically informed variables and, perhaps, considered statistical methods not currently used in criminology such as rare event modelling.

Finally, there is the issue of theoretical development/testing at the micro-place. Do social disorganization theory and routine activity theory (the two most prominent explicitly spatial theories in spatial criminology) still matter when the unit of analysis is the micro-place? As shown by Smith et al. (2000) and Weisburd et al. (2012) routine activity theory and social disorganization theory, respectively, have been shown to be important at the micro-place. In fact, as discussed above, Smith et al. (2000) was able to show that the integration of routine activity theory and social disorganization theory performed best at the micro-place. However, because of a lack of theoretically informed variables and constructs, this work is difficult, if not cumbersome, to undertake. But understanding why there is a high degree of spatial concentration at micro-places and why those spatial concentrations are stable over time at micro-places is critical for not only understanding the micro-place for theoretical interest, but the proper development of criminal justice policy to make our cities safer places to live, work, and play.


Andresen, M.A. (2006). A spatial analysis of crime in Vancouver, British Columbia: A

synthesis of social disorganization and routine activity theory. Canadian

Geographer, 50(4), 487 - 502.

Andresen, M. A. (2009). Testing for similarity in area-based spatial patterns: A

nonparametric Monte Carlo approach. Applied Geography, 29(3), 333 - 345.

Andresen, M. A. (2010). Canada - United States interregional trade: Quasi-points and spatial

change. Canadian Geographer, 54(2), 139 - 157.

Andresen, M.A. (2011). The ambient population and crime analysis. Professional

Geographer, 63(2), 193 - 212.

Andresen, M.A. (2014). Environmental criminology: Evolution, theory, and practice. New

York, NY: Routledge.

Andresen, M.A. (2016). An area-based nonparametric spatial point pattern test: The test, its

applications, and the future. Methodological Innovations, 9, Article 12.

Andresen, M.A., & Hodgkinson, T. (2018a). Predicting property crime risk: An application of

risk terrain modeling in Vancouver, Canada. European Journal on Criminal Policy

and Research,

Andresen, M.A., & Hodgkinson, T. (2018b). Evaluating the impact of police foot patrol at the

micro-geographic level. Policing: An International Journal, 41(3), 314 - 324.

Andresen, M. A., & Linning, S. J. (2012). The (in)appropriateness of aggregating across

crime types. Applied Geography, 35(1-2), 275 - 282.

Andresen, M. A., & Malleson, N. (2011). Testing the stability of crime patterns: Implications

for theory and policy. Journal of Research in Crime and Delinquency, 48(1), 58 - 82.

Andresen, M. A., & Malleson, N. (2013a). Crime seasonality and its variations across space.

Applied Geography, 43, 25 - 35.

Andresen, M. A., & Malleson, N. (2013b). Spatial heterogeneity in crime analysis. In M.

Leitner (Ed.), Crime modeling and mapping using geospatial technologies (pp. 3 - 23).

New York, NY: Springer.

Andresen, M. A., & Malleson, N. (2014). Police foot patrol and crime displacement: A local

analysis. Journal of Contemporary Criminal Justice, 30(2), 186 - 199.

Andresen, M. A., Curman, A. S. N., & Linning, S. J. (2017a). The trajectories of crime at places:

Understanding the patterns of disaggregated crime types. Journal of Quantitative

Criminology, 33(3), 427 - 449.

Andresen, M. A., Linning, S. J., & Malleson, N. (2017b). Crime at places and spatial

concentrations: Exploring the spatial stability of property crime in Vancouver BC,

2003-2013. Journal of Quantitative Criminology, 33(2), 255 - 275.

Andruff, H., Carraro, N., Thompson, A., Gaudreau, P., & Louvet, B. (2009). Latent class

growth modelling: A tutorial. Tutorials in Quantitative Methods for Psychology, 5(1),

11 – 24.

Bernasco, W., & Steenbeek, W. (2017). More places than crimes: Implications for evaluating

the law of crime concentration at place. Journal of Quantitative Criminology, 33(3),

451 – 467.

Black, D. J. (1970). Production of crime rates. American Sociological Review, 35(4), 733 –

748.Braga, A. A., Andresen, M. A., & Lawton, B. [Eds.] (2017). Special issue: The law of crime

concentration at places. Journal of Quantitative Criminology, 33(3), 421 - 674.

Braga, A., Hureau, D. M., & Papachristos, A. V. (2010). The concentration and stability of gun

violence at micro places in Boston, 1980–2008. Journal of Quantitative Criminology,

26(1), 33 – 53.

Braga, A., Hureau, D. M., & Papachristos, A. V. (2011). The relevance of micro places to

citywide robbery trends: A longitudinal analysis of robbery incidents at street

corners and block faces in Boston. Journal of Research in Crime and Delinquency,

48(1), 7 – 32.

Bulwer, H.L. (1836). France, social, literary, political, volume I, book I: Crime. London, UK:

Richard Bentley.

Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications

in Statistics, 3(1), 1 – 27.

Ceccato, V., & Lukyte, N. (2011) Safety and sustainability in a city in transition: The case of

Vilnius, Lithuania. Cities, 28(1), 83-94.

Cohen, L. E., & Felson, M. (1979). Social change and crime rate trends: A routine

activity approach. American Sociological Review, 44(4), 588 – 608.

Curman, A.S.N., Andresen, M.A., & Brantingham, P.J. (2015). Crime and place: A longitudinal

examination of street segment patterns in Vancouver, BC. Journal of Quantitative

Criminology, 31(1), 127 - 147.

David, J-D. (2017). Homicide in Canada, 2016. Ottawa, ON: Statistics Canada.

Eck, J. E., & Weisburd, D. (1995). Crime places in crime theory. Crime Prevention

Studies, 4, 1 – 33.

Eggleston, E. P., Laub, J. H., & Sampson, R. J. (2004). Methodological sensitivities to latent

class analysis of long-term criminal trajectories. Journal of Quantitative Criminology,

20(1), 1 – 26.

Farrell, G., Tilley, N., & Tseloni, A. (2015). Why the crime drop? Crime Justice: An Annual

Review of Research, 43, 421 – 490.

Farrell, G., Tseloni, A., Mailley, J., & Tilley, N. (2011). The crime drop and the security

hypothesis. Journal of Research in Crime and Delinquency, 48(2), 147 – 175.

Florida, R. (2010). The great reset: How new ways of living and working drive post-crash

prosperity. Toronto, ON: Vintage Canada.

Forst, B. (2004). Errors of justice: Nature, sources and remedies. Cambridge, UK:

Cambridge University Press.

Gelman, A. (2005). Analysis of variance: Why it is more important than ever. The Annals of

Statistics, 33(1), 1 – 33.

Genolini, C, & Falissard, B. (2010). KmL: K-means for longitudinal data. Computational

Statistics, 25(2), 317 – 328.

Gill, C., Wooditch, A., & Weisburd, D. (2017). Testing the “Law of Crime Concentration at

Place” in a suburban setting: Implications for research and practice. Journal of

Quantitative Criminology, 33(3), 519 – 545.

Griffiths, E., & Chavez, J. M. (2004). Communities, street guns, and homicide in Chicago,

1980–1995: Merging methods for examining homicide trends across space and time.

Criminology, 42(4), 941 – 978.

Groff, E. R., Weisburd, D., & Yang, S-M. (2010). Is it important to examine crime

trends at a local “micro” level? A longitudinal analysis of street to street

variability in crime trajectories. Journal of Quantitative Criminology, 26(1), 7 – 32.

Haberman, C. P., Sorg, E. T., & Ratcliffe, J. H. (2017). Assessing the validity of the law of

crime concentration across different temporal scales. Journal of Quantitative

Criminology, 33(3), 547 – 567.

Hibdon, J., Telep, C. W., & Groff, E. R. (2017). The Concentration and stability of drug

activity in Seattle, Washington using police and emergency medical services data.

Journal of Quantitative Criminology, 33(3), 497 – 517.

Hipp, J. R., & Kim, Y-A. (2017). Measuring crime concentration across cities of varying sizes:

Complications based on the spatial and temporal scale employed. Journal of

Quantitative Criminology, 33(3), 595 – 632.

Hodgkinson, T., Andresen, M. A., & Farrell, G. (2016). The decline and locational shift of

automotive theft: A local level analysis. Journal of Criminal Justice, 44(1), 49 - 57.

Huizinga, D., Esbensen, F., & Weiher, A. W. (1991). Are there multiple paths to delinquency?

Journal of Criminal Law and Criminology, 82(1), 83 – 118.

Kennedy, L. W., & Forde, D. R. (1990). Routine activities and crime: an analysis of

victimization in Canada. Criminology, 28(1), 137 – 152.

Klinger, D. A., & Bridges, G. S. (1997). Measurement error in calls-for-service as an indicator

of crime. Criminology, 35(4), 705 - 726.

Kubrin, C. E. & Herting, J. (2003). Neighborhood correlates of homicide trends: An analysis

using growth-curve modeling. Sociological Quarterly, 44(3), 329 – 350.

Lees, L., Slater, T., & Wyly, E. K. (2007). Gentrification. New York, NY: Routledge.

Levin, A., Rosenfeld, R., & Deckard, M. (2017). The law of crime concentration: An

application and recommendations for future research. Journal of Quantitative

Criminology, 33(3), 635 – 647.

Linning, S. J. (2015). Crime seasonality and the micro-spatial patterns of property crime in

Vancouver, BC and Ottawa, ON. Journal of Criminal Justice, 43(6), 544 – 555.

Melo, S. N., Matias, L. F., & Andresen, M. A. (2015). Crime concentrations and similarities in

spatial crime patterns in a Brazilian context. Applied Geography, 62, 314 - 324.

Mowder, M. H., Cummings, J. A., & McKinney, R. (2010). Resiliency scales for children and

adolescents: Profiles of juvenile offenders. Journal of Psychoeducational Assessment,

28(4), 326 – 337.

Nagin, D. (1999). Analyzing developmental trajectories: A semiparametric group-based

approach. Psychological Methods, 4(2). 139 – 157.

Nagin, D. (2004). Response to “Methodological sensitivities to latent class analysis of long-

term criminal trajectories”. Journal of Quantitative Criminology, 20(1), 26 – 37.

Nagin, D. (2005). Group-based modeling of development over the life course. Cambridge,

MA: Harvard University Press.

Nagin, D. S., & Land, K. C. (1993). Age, criminal careers and population heterogeneity:

Specification and estimation of a nonparametric, mixed Poisson model. Criminology,

31(3), 327 – 362.

O’Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation

factors. Quality & Quantity, 41(5), 673 – 690.

O’Brien, D. T., & Winship, C. (2017). The gains of greater granularity: The presence and

persistence of problem properties in urban neighborhoods. Journal of Quantitative

Criminology, 33(3), 649 – 675.

Pereira, D. V. S., Mota, C. M. M., & Andresen, M. A. (2016). The homicide drop in Recife,

Brazil: A study of crime concentrations and spatial patterns. Homicide Studies,

21(1), 21 - 38.

Perreault, S. (2015). Criminal victimization in Canada, 2014. Ottawa, ON: Statistics Canada.

Perreault, S., & Brennan, S. (2010). Criminal victimization in Canada, 2009. Ottawa, ON:

Statistics Canada.

Ratcliffe, J. H. (2004). Geocoding crime and a first estimate of a minimum acceptable hit

rate. International Journal of Geographical Information Science, 18(1), 61 - 72.

Sampson, R. J., & Groves, W. B. (1989). Community structure and crime: Testing

social-disorganization theory. American Journal of Sociology, 94(4), 774 – 802.

Schnell, C., Braga, A. A., & Piza, E. L. (2017). The influence of community areas,

neighborhood clusters, and street segments on the spatial variability of violent

crime in Chicago. Journal of Quantitative Criminology, 33(3), 469 – 496.

Shaw, C. R., Zorbaugh, F., McKay, H. D., & Cottrell, L. S. (1929). Delinquency areas:

A study of the geographic distribution of school truants, juvenile delinquents,

and adult offenders in Chicago. Chicago, IL: University of Chicago Press.

Shaw, C. R., & McKay, H. D. (1931). Social factors in juvenile delinquency, Washington, DC:

U.S. Government Printing Office.

Shaw, C. R., & McKay, H. D. (1942). Juvenile delinquency and urban areas: A study of

rates of delinquency in relation to differential characteristics of local

communities in American cities. Chicago, IL: University of Chicago Press.

Shaw, C. R., & McKay, H. D. (1969). Juvenile delinquency and urban areas: A study of

rates of delinquency in relation to differential characteristics of local

communities in American cities (revised edition). Chicago, IL: University of

Chicago Press.

Sherman, L. W., Gartin, P., & Buerger, M. E. (1989). Hot spots of predatory crime: Routine

activities and the criminology of place. Criminology, 27(1), 27 – 55.

Singer, J. D., & Willet, J. B. (2003). Applied longitudinal data analysis: Modeling change and

event occurrence. New York, NY: Oxford University Press.

Smith, W. R., Frazee, S. G., & Davison, E. L. (2000). Furthering the integration of

routine activity and social disorganization theories: Small units of analysis and the

study of street robbery as a diffusion process. Criminology, 38(2), 489 – 524.

Steenbeek, W., & Weisburd, D. (2016). Where the action is in crime? An examination of

variability of crime across spatial units in The Hague, 2001–2009. Journal of

Quantitative Criminology, 32(3), 449 – 469.

Steenbeek, W., Vandeviver, C. Andresen, M.A., Malleson, N., & Wheeler, A. (2018). sppt:

Spatial Point Pattern Test. R package version (0.1.5, 0.1.6). Retrieved from:

Tompson, L., Johnson, S., Ashby, M., Perkins, C., & Edwards, P. (2015). UK open source crime

data: Accuracy and possibilities for research. Cartography and Geographic

Information Science, 42(2), 97 - 111.

Vandeviver, C., & Steenbeek, W. (2017). The (in)stability of residential burglary patterns on

street segments: The case of Antwerp, Belgium 2005 - 2016. Journal of Quantitative

Criminology, DOI

Vaughan, A., Hewitt, A., Andresen, M. A., & Brantingham, P. L. (2016). Exploring the role of

the environmental context in the spatial distribution of calls-for-service associated

with emotionally disturbed persons. Policing: A Journal of Policy and Practice, 10(2),

121 - 133.

Weisburd, D. (2015). The law of crime concentration and the criminology of place.

Criminology, 53(2), 133 – 157.

Weisburd, D., & Amram, S. (2014). The law of concentrations of crime at place: The case of

Tel Aviv-Jaffa. Police Practice and Research, 15(2), 101 – 114.

Weisburd, D., Bushway, S., Lum, C., & Yang, S-M. (2004). Trajectories of crime at places: A

longitudinal study of street segments in the City of Seattle. Criminology, 42(2), 283 –


Weisburd, D., Morris, N. A., & Groff, E. R. (2009). Hot spots of juvenile crime: A longitudinal

study of arrest incidents at street segments in Seattle, Washington. Journal of

Quantitative Criminology, 25(4), 443 – 467.

Weisburd, D., Groff, E. R., & Yang, S-M. (2012). The criminology of place: Street segments and

our understanding of the crime problem. New York, NY: Oxford University Press.

Wheeler, A. P., Worden, R. E., & McLean, S. J. (2016). Replicating group-based trajectory

models of crime at micro-places in Albany, NY. Journal of Quantitative Criminology,

32(4), 589 – 612.

Wheeler, A. P., Steenbeek, W., & Andresen, M. A. (2018). Testing for similarity in area-based

spatial patterns: Alternative methods to Andresen's spatial point pattern test.

Transactions in GIS, in press.

Wolfgang, M. E., Figlio, R. M., & Sellin, T. (1972). Delinquency in a birth cohort. Chicago, IL:

University of Chicago Press.

Wu, X., & Lum, C. (2017). Measuring the spatial and temporal patterns of police proactivity.

Journal of Quantitative Criminology, 33(4), 915 - 934.

Wuschke, K. E., Andresen, M. A., Brantingham, P. J., Rattenbury, C., & Richards, A. (2018).

What do police do and where do they do it? International Journal of Police Science

and Management, 20(1), 19 - 27.

Table 1. Percent of Self-Reported Victimizations Reported to the Police

Crime Type





Total victimization





Sexual assault










Physical assault





Total violent victimization





Break and enter





Motor vehicle/parts theft





Household property theft










Total household victimization





Theft of personal property





Source. Perreault and Brennan (2010) and Perreault (2015).

Figure 1. Census tracts, dissemination areas, and street segments

A close up of a map Description generated with high confidence

Source. Andresen and Malleson (2011).

Figure 2. Lorenz curve

A close up of a map Description generated with very high confidence

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