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Policing and Society: An International
Journal of Research and Policy
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Predictability of gun crimes: a
comparison of hot spot and risk terrain
modelling techniques
Grant Drawvea, Stacy C. Moaka & Emily R. Berthelota
a Department of Criminal Justice, University of Arkansas at Little
Rock, Little Rock, AR, USA
Published online: 05 Aug 2014.
To cite this article: Grant Drawve, Stacy C. Moak & Emily R. Berthelot (2014): Predictability of gun
crimes: a comparison of hot spot and risk terrain modelling techniques, Policing and Society: An
International Journal of Research and Policy, DOI: 10.1080/10439463.2014.942851
To link to this article: http://dx.doi.org/10.1080/10439463.2014.942851
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Predictability of gun crimes: a comparison of hot spot and
risk terrain modelling techniques
Grant Drawve*, Stacy C. Moak and Emily R. Berthelot
Department of Criminal Justice, University of Arkansas at Little Rock, Little Rock, AR, USA
(Received 17 January 2014; accepted 26 June 2014)
The current study was designed to assess the possible differences in the accuracy and
precision of two methodological mapping techniques as predictors of future gun crimes
in Little Rock, AR: (1) risk terrain modelling (RTM) and (2) nearest neighbour
hierarchical (Nnh), a traditional hot spot technique, which relies on past crime to
predict where future crime is likely to occur. Data from the Little Rock Police
Department, the Little Rock Treasury Department and the 2000 census were used to
examine Nnh hot spot and RTM methods of gun crime prediction. The RTM
incorporated measures of crime generators and crime attractors, while Nnh hot spots
were constructed from 2008 gun crime data. The two measures were compared using
their predictive accuracy index (PAI) and recapture rate index (RRI) values. Six of the
seven social and physical environmental measures in the RTM significantly predicted
future gun crime locations and the Nnh hot spots predicted 7% of future gun crime.
PAI and RRI values suggested the RTM was more precise than the Nnh hot spot
technique and the Nnh hot spot technique was more accurate than the RTM technique.
Relying on one spatial prediction technique may create problems with accuracy and
reliability. Multiple techniques may be needed to fully assess the phenomenon.
Accuracy is a potential limitation of RTM when compared to other techniques,
however, RTM is more reliable than Nnh hot spots due to the inclusion of the
environmental backcloth. The findings were discussed in relation to crime prediction
and policing efforts.
Keywords: risk terrain modelling; hot spot; crime generators and attractors
Introduction
Police departments regularly try to understand where crime will occur in the future based on
past crime locations. Criminal events are not uniformly distributed geographically
(Brantingham and Brantingham 1982), and due to this, crime tends to be concentrated in
small geographical areas (Sherman et al.1989). These small geographical areas are referred
to as ‘hot spots’. Hot spot analysis is a technique that is often used by police departments
to identify clusters of past crimes, which are then used to determine where police
resources should be distributed (Townsley et al.2000). Although hot spot analysis is a
useful technique for the examination of crime clusters and subsequent distribution of
police resources, it lacks a theoretical foundation. Additionally, hot spot techniques
traditionally rely on past locations of crime in an attempt to predict future crime locations,
creating a retrospective approach.
*Corresponding author. Email: grdrawve@ualr.edu
Policing and Society, 2014
http://dx.doi.org/10.1080/10439463.2014.942851
© 2014 Taylor & Francis
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Ratcliffe (2004) suggested that the academic field had two interests in hot spots:
(1) the different theoretical explanations and (2) the different techniques for identifying
hot spots. Baldwin (1979) stated that there were many explanations for the spatial
concentration of crime, but there was little theoretical agreement because technology had
surpassed the development of different theoretical explanations. One could still argue that
a gap remains between technology and theory but a new spatial technique, risk terrain
modelling (RTM), offers a better theoretical framework that can close this gap.
RTM allows for a theoretical foundation to be incorporated in the spatial analysis of
crime (Caplan et al.2011). With a basis in environmental criminology, RTM includes
many concepts from crime pattern theory. RTM is capable of measuring Brantingham and
Brantingham’s(1995) concepts of crime generators and crime attractors (CGAs) that help
explain the environmental backcloth of crime. RTM is used to predict where crime is
likely to occur in the future based upon multiple physical and social characteristics of the
environment (Caplan et al.2011). Accounting for these additional characteristics allows
for more accurate predictions of future crime locations and will improve the allocation of
police resources to designated areas with higher predicted levels of criminal activity.
Taking the spatial environment into consideration will also improve the theoretical
implications of research on the geography of crime.
The current study examined gun crimes in Little Rock, AR, comparing two different
prediction techniques: RTM and a traditional hot spot technique. The researchers sought
to extend a previous study conducted by Caplan et al.(2011) examining differences
between retrospective techniques and RTM. Negative binomial regression was used to
assess the spatial risk factors used within the RTM, diverging from past RTM studies
(Caplan et al.2011) but following suit in the current direction of RTM methodology (Piza
2012, Moreto et al.2013). The two methods were then compared to determine which
technique was better at predicting future gun crime locations. To compare these two
different techniques, the predictive accuracy index (PAI) and the recapture rate index
(RRI) were examined to assess the accuracy and precision of the two methods,
respectively. Traditionally, these measures are applied to hot spot techniques (see
Chainey et al.2008, Levine 2008, Van Patten et al.2009) and have been limited in the
application to RTM (Drawve, in press, Dugato 2013).
The focus of this research is not to test whether one technique is better than the other
but to compare the two techniques. Kennedy et al.(2011) discussed the utility of using
multiple techniques together for application purposes. Additionally, Drawve (in press)
discussed the importance of using multiple techniques jointly for analysis when
comparing multiple hot spot techniques and RTM on their prediction accuracy and
reliability values. The purpose of the current study was to further examine differing
techniques to understand differences and/or similarities between the two techniques. The
results could allow for police departments to tailor their policing strategies for prevention.
For example, based on which technique is more accurate, police agencies could use this
knowledge to better deploy their resources. Furthermore, by examining two distinct
techniques, the results could be used to guide future research on spatial crime prediction,
enhancing the understanding of the spatial attribute of crime.
Review of literature
The more precisely a crime location can be determined in advance, the greater the
likelihood for prevention and detection (Polvi et al.1991). The need to identify location
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was highlighted by the works of Sherman (1995). His study found that when comparing
criminal careers of places and criminal careers of offenders, the estimates of future crimes
were six times more predictable by the location. Ratcliffe and McCullagh (1999) stated
that a main aspect of spatial crime analysis was to identify areas of the highest crime
concentration.
Hot spot analysis and RTM were utilised to predict future crime in the current study.
Based on the differences in the types of analyses, the hot spot technique relied solely on
past crime clusters to predict future crime while RTM included measures of the physical
and social environment for prediction (see Drawve, in press). Hot spot analysis indicates
just that, hot spots, and is retroactive by design. That is not to say crime generators and/or
attractors do not influence the presence of crime hot spots. According to extant literature
(Roncek and Maier 1991, Kautt and Roncek 2007, Weisburd et al.2009), hot spots
commonly form in or around areas that have higher amounts of CGAs (i.e., schools and
bars). Hot spot analyses provided the groundwork in helping identify criminogenic
businesses/establishments that RTM can further use in a forecasting model. Because of
the clustering of crime that can be a result of the presence of CGAs and RTM
incorporating CGAs as risk factors, crime pattern theory (Brantingham and Brantingham
1993) was reviewed to offer insights into the spatial element of crime. Crime pattern
theory includes aspects of routine activities theory (Cohen and Felson 1979) and includes
more environmental-based measures to offer a better understanding of the geography of
crime. Further, crime pattern theory incorporates elements of the built environment that
correlate with crime locations, such as the types of establishments located in a particular
place.
Theoretical framework
Cohen and Felson’s(1979) routine activities theory suggests that criminal opportunities
are identified throughout peoples’daily activities. For crime to occur, a motivated
offender, a suitable target and a lack of capable guardianship must converge in time and
space to create a criminal opportunity. The movements of individuals throughout the day
generate and reduce opportunities for crime to converge in space (Cohen and Felson
1979). A main hypothesis of routine activities theory posits that increased activity away
from home creates criminal opportunities and generates higher crime rates (Cohen and
Felson 1979). When people are away from their homes, guardianship is naturally
decreased which allows more crime to occur. This hypothesis was supported by Cohen
and Felson’s(1979) findings.
Cohen and Felson (1979) stated that individuals have three broad areas where routine
activities occur: at home, jobs away from their home and other activities away from their
home. These locations shape the ‘activity space’of individuals. Activity spaces refer to
locations where people spend a majority of their time and start to establish their
awareness space (Brantingham and Brantingham 1984) when travelling to and from
different ‘nodes’. Nodes are locations where people can identify criminal opportunities
and are common place areas in their lives such as their homes, work, school, shopping
malls/centres and recreation sites (Brantingham and Brantingham 1995). The more often
people travel to and from different nodes, the greater their awareness space becomes.
Opportunities for criminal acts to be recognised and committed arise within the awareness
space but the individual has to choose to commit the criminal act.
1
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Brantingham and Brantingham (1993) stated that routine activities influence the
patterns of opportunistic crime (i.e., shoplifting, theft from automobile) such that peoples’
routine activities throughout the day are capable of shaping when and where a crime
occurs. Those individuals follow distinct paths that are important in forming their routine
activities. Brantingham and Brantingham (1993) developed crime pattern theory to extend
routine activities theory and encompass more environmental influences that affect where
crime takes place. Crime pattern theory employs the location element from routine
activities theory and expands upon it to examine the influence specific locations have on
the built environment in relation to crime locations.
The location of where crime takes place can be influenced by a multitude of measures
(personal, social, physical and structural characteristics). The environmental backcloth
has interconnected attributes that are not static and consist of interactions between
physical, social, legal, cultural, economic and temporal environments (Brantingham and
Brantingham 1999). Brantingham and Brantingham (1999) stated that the backcloth
encompasses the routine activities that shape awareness spaces. Individuals’routine
activities may rely on factors that influence their awareness space such as, age, social
status, income and education; all of which rely on space–time convergence.
Similar to awareness space, people develop cognitive maps. Tolman (1948) classified
cognitive maps as, ‘this tentative [cognitive] map, indicating routes and paths and
environmental relationships, which finally determines what responses, if any, the animal
will finally release’(p. 192). Offenders develop cognitive maps through their routine
activities (routes and paths) and identify environmental relationships that are favourable
for crime to occur (response). Individuals use these maps when determining where to
commit crime.
Cognitive maps are shaped by activities that people complete in their everyday lives.
Brantingham and Brantingham (1993) developed multiple propositions about an
individual’s cognitive map. The first proposition they suggested was that, ‘cognitive
maps, knowledge of spatial relations influences crime location’(p. 22). This pertains to
the environmental relationships of an area that influence a criminal response in the
offender. Offenders may be able to establish locations within their cognitive maps that
have criminogenic characteristics (contain suitable targets that lack capable guardianship).
Brantingham and Brantingham’s(1993) second proposition stated that, ‘the cognitive
representations reflect high activity nodes and the paths between them and through those
representations shape the location of crime’(p. 22). The routes (paths) travelled to
different activity spaces (nodes) increases individuals’awareness space of the surround-
ing environment and increase the potential for identifying criminal opportunities.
Brantingham and Brantingham (1995) suggested that paths refer to the routes taken
when travelling from one node to another and establish areas where criminal
opportunities exist.
Extant literature suggests that many types of crime occur in close proximity to activity
nodes. Eck and Weisburd (1995) stated that certain types of establishments may impact
the immediate environment by increasing or decreasing crime such as convenience stores,
churches and public housing projects. For example, Brantingham and Brantingham
(1995) found that sports clubs, youth clubs and other clubs were the most frequently
burgled establishments. Those types of locations not only draw large numbers of people
to them for non-criminal reasons (generators) but also increase the amount of awareness
space of that location. Brantingham and Brantingham (1995) ascertained the clientele that
attended those facilities were young, males, with lower incomes. Thus, the type of people
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who are attracted to various establishments can also influence the types of activities that
occur there, and not all are for criminal purposes.
The third proposition put forth by Brantingham and Brantingham (1993) was, ‘the
type of crimes are varied, but some are highly opportunistic and highly dependent on
daily activities and the physical availability of suitable targets and suitable situations,
frequently including lack of surveillance or a feeling of anonymity’(p. 22). The activities
that take people throughout a city provide different locations within it that have varying
opportunities for crimes, based on the concepts of routine activities theory. For example,
offenders are able to identify locations where they are more likely to successfully rob
someone because of the criminogenic characteristics of the environment. Murray and
Roncek (2008) established that the immediate area surrounding a bar was able to take
advantage of the diffusion of benefits from the security present at the bar but, the blocks
further away from the bar had an increase in crime due to lower levels of guardianship
present.
The three cognitive map propositions provide a backcloth for where crime occurs
based on the activity spaces of individuals. The criminogenic locations of a study area
begin to establish why offenders commit crimes at specific locations. Brantingham and
Brantingham (1995) stated there are two main types of locations: crime generators and
crime attractors (CGAs). Crime generators are areas where a large number of people
congregate for non-criminal purposes like a sports stadium or entertainment venues
(nodes); however, crime attractors are areas where motivated offenders are drawn to
because of the criminal opportunities at them like shopping malls or drug areas (nodes).
Bernasco and Block (2011) measured multiple CGAs (bars/clubs, fast food, beauty
salons, liquor stores, grocery stores, etc.) in relation to street robberies in Chicago. They
found support for the influence that crime generators and attractors had on a block, which
increased the amount of robberies present on blocks that had crime generators and/or
crime attractors. In previous studies, CGAs influenced the amount of criminal
opportunities differently from one location to another. Thus, CGAs were included in
the current study as an important environmental variable.
These different elements of crime pattern theory lay out the groundwork for more
contextual studies on the geography of crime. Based on individuals’routine activities,
they start to develop cognitive maps through paths that they travel to different nodes. The
more that a path is travelled the more people become familiar with the surrounding area,
creating opportunities for crime to arise at specific locations. The incorporation of
locations known as CGAs advances the understanding of the geography of crime and
how the built environment influences crime differently. An argument could be made that
difficulties in the operationalisation and testing of criminal opportunities of routine
activities theory has led research to assess the risk of crime in an area. By assessing the
riskiness of an environment, tangible concepts such as CGAs can be included to
operationalise risk.
Current study
The current study compared two different predictive techniques, RTM and Nnh hot spot,
for forecasting future gun crime. Our research differs from Caplan et al.’s(2011) by using
a hot spot technique that is more suited for short-term forecasting and incorporated PAI
and RRI measures. The primary question guiding the research was to compare two
predictive techniques in terms of accuracy and precision when forecasting future crime
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locations. The goal was not to have competing techniques but to identify possible
differences between the techniques.
Traditional hot spot techniques examine past crime locations to determine where
crime clusters (see Eck et al.2005). The past crime clusters are used as areas where crime
would be expected to occur in the future. With this notion, there is an expectation that
crime will remain, for the most part, static. The issue arises though that crime is not
inherently static but dynamic in nature because of temporal patterns. This issue could
partially be resolved by the utilisation of RTM. By only including past crime within hot
spot techniques, the built environment is often left unaccounted for when trying to predict
future crime. RTM is capable of including risk factors of the environment that are
expected to create riskier areas. That is, RTM creates a model that diagnoses risky areas
for crime. That does not mean that all risky areas have crime but that the characteristics of
that area make it more criminogenic (see Levine et al.1986 for similar argument). If
crime were to move, RTM could predict where it occurs because RTM includes
criminogenic characteristics of the environment as risk factors, not solely past crime.
This study fills a gap in extant RTM literature in many ways. First, by examining all
Part I Index crimes that involved guns, rather than shootings specifically, we expanded
previous work (Caplan et al.2011) to include gun crimes that do not always result in a
shooting. Similar measures from Caplan et al.’s(2011) analyses were applied in the
current study offering validation of predictive measures. The current study diverged from
prior literature by separating CGAs into individual risk factors to determine significance
of each measure rather than grouping multiple CGAs into one measure.
Next, we sought to compare two distinctly different techniques for predicting future
crime locations. Specifically, we used the nearest neighbour hierarchical (Nnh) hot spot
analysis technique which is different from the hot spot technique used in previous
comparisons of the two techniques (Caplan et al.2011).
2
Caplan et al.(2011) used a hot
spot technique that examined the density of shootings across their study area and
identified highly dense areas of past shootings for prediction of future shootings. Their
technique was a grid-based approach to assessing density of past crime while we used a
cluster analysis technique that indicated significant clusters of crime in the form of
ellipses (discussed more later).
Based upon the differences in the techniques, we expected that the Nnh hot spot
technique would provide a more accurate prediction of gun crimes. This is because the
Nnh hot spot technique is using past crime to predict future crime. RTM includes
numerous physical and social measures that might diagnose risky areas but not all risky
areas are dangerous (i.e., gun crimes occurring), resulting in RTM being less accurate
than Nnh hot spot analyses. On the other hand, we expected that RTM would provide
more reliable predictions of gun crimes. Since RTM is constructed from characteristics of
the environment, the ability to identify risky areas could aid in RTMs’reliability over
time. The social and physical characteristics could create a more stable criminogenic area
that benefits RTM in reliability but hindering the accuracy of the technique compared
to Nnh.
We also examined the PAI and RRI between the RTM and Nnh hot spots, which has
been applied sparingly to RTM (Drawve, in press, Dugato 2013). This approach allowed
researchers to compare predictive techniques and to compare them with more finite
measures of accuracy and precision. Thus, the research effort supported two equally
important goals. The first was to extend the application of previous studies beyond only
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those gun crimes that involved shootings to encompass gun crimes in general. Second,
we sought to compare the two predictive techniques, Nnh hot spot analysis and RTM.
3
Data and methods
The current study specifically examines the city of Little Rock, AR, located within the
USA, which has a population around 200,000 and covers about 120 square miles with a
surrounding metro-area population around 700,000. In 2008 and 2009, the years for
which data are analysed for this study, crime rates in the city of Little Rock were two and
half and three times that of the national average (FBI 2010). Crime data were provided by
the Little Rock Police Department (LRPD) and consisted of all crime incidents involving
agun
4
that occurred between January of 2008 and June of 2009 (n= 946 for 2008 and
n= 483 for 2009). Along with these data, drug incident data from LRPD were included in
the analysis. Business data were obtained from the Little Rock Treasury Department for
all permitted businesses. All data that contained addresses were geocoded (above 95%)
for spatial analyses. Census block group data were used from the 2000 decennial census
summary file three to measure social characteristics of Little Rock.
The present study applies two different spatial analysis methods to determine
differences in prediction techniques using a metric comparison. RTM and Nnh hot spots
are further discussed as follows and are used as prediction methods for future gun-related
incidents. The current study was modelled based on previous RTM analyses (Caplan
et al.2011, Kennedy et al.2011) and expanded based on a call for new methodological
techniques within RTM research (Piza 2012).
Risk terrain modelling
RTM is a technique that incorporates multiple map layers that each identify a risk factor
associated with a specific crime in space and time then combines the map layers based on
the grid system of the study area (Caplan and Kennedy 2011). RTM is built upon past
research pertaining to hot spots coupled with environmental criminology and offers a
statistical basis to validate the findings (Caplan and Kennedy 2011). More specifically,
RTM could be used to predict where crime is likely to occur based on physical and social
characteristics of a city. In a general sense, RTM is able to diagnose a study area for the
risk of crime occurring given a certain time frame. The different characteristics that make
an area risky are examined to construct spatial risk values across Little Rock.
The RTM study area, Little Rock, was divided into 300 ft × 300 ft cells (total 38,760
cells).
5
The locations of the built environment measures were expected to influence
criminal activity beyond the immediate physical location of the establishment. Due to
this, the incorporation of awareness space expanded the spatial influence of the
businesses used in the current study to encompass about a block and a half (600 ft).
Using a grid system, the spatial influence (risk factor) of each map layer is combined into
one spatial risk assessment map of Little Rock, once the significance is determined. Each
risk map layer is based on the presence, absence or intensity of factors throughout the
study area (Caplan and Kennedy 2011).
Predictors of gun crime
The current research incorporated similar predictors of gun crime as used in Caplan
et al.’s(2011) analysis of shootings. The first four predictors of gun crime were
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businesses and their influences were operationalised similarly. Based upon past literature,
the influences certain businesses had on the blocks in which they were located on were
taken into consideration. The spatial influence that each business had on the surrounding
environment was expressed as 600 ft (about a block and a half). Although the influence
of a business on a block can increase crime, the influence may extend beyond 300 ft (cell
size used in the current analysis) due to the awareness space people had of the
surrounding area. With an increased knowledge of the environment surrounding of a
business, the larger spatial influence of that environment on crime can be examined.
Based on past literature related to alcohol establishments (Roncek and Bell 1981,
Roncek and Pravatiner 1989, Homel and Tomsen 1993, Brantingham and Brantingham
1995, Gorman et al.2001), fast food establishments (Brantingham and Brantingham
1982, Spelman 1995, Bernasco and Block 2011) and pawn shops (Wright and Decker
1994, Fass and Francis 2004, Cancino et al.2007) were included in the analysis.
The alcohol establishments were separated into two types: on-site consumption and off-
site consumption, creating four measures of the built environment. It is expected that the
presence of any of these establishments increases the risk of a gun crime occurring.
Caplan et al.(2011) included similar business measures in their analysis of shootings.
In their study, they grouped numerous businesses together into one risk factor (pawn
shops, fast food restaurants, liquor stores and among others). In the current study,
businesses were not grouped together as one risk factor; they were kept separate to
determine if specific business types were related to gun crimes. Also building from their
analysis, our analysis separated alcohol into two categories, on-site and off-site
consumption, further breaking down business types to assess the influence they have
on gun crime. Similar to Caplan et al.’s(2011) study, previous drug crime was included
as a spatial risk factor.
Based on past literature on drugs and crime (Gorman et al.2005, Bernasco and Block
2011, Caplan et al.2011), past drug incidents were included in the RTM model. Gorman
et al.(2005) found that drug crime density accounted for 72% of the variance in violent
crime. Density estimates were examined using the ArcView’s Spatial Analyst Extension.
The values of the density map were reclassified based on cell values that had a value
greater than +2 standard deviations (SD). The areas that had a value greater than +2 SD
were classified as more risky and were expected to have a greater likelihood for gun
crimes to occur in that area.
Lastly, we included block group census data. Past research suggested areas with larger
male populations, areas with larger populations between the ages of 15 and 25 and areas
with larger black populations tend to experience higher rates of violent crime
(Brantingham and Brantingham 1995, Pizarro and McGloin 2006, Braga et al.2011).
The current analysis incorporated two census measures, per cent black and per cent male
between 15 and 24 years old in the analysis. Since census block groups have distinct
boundaries, the census block group boundaries needed to be smoothed with surrounding
values. The block group data were converted to raster maps, grid-based maps, then
smoothed based on the nearest neighbour distance of the mean centres for each centre
block (3174 ft).
6
The conversion process does not significantly change the values of
census data (see Caplan 2010). Similar to the drug density measure, per cent black and
per cent male between 15 and 24 years old were reclassified based on their cell value. It
was expected that cells with a value greater than +2 SD to increase the likelihood of gun
crime in that area.
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RTM procedures
RTM relies on a grid system, therefore it is important to examine adjacent cells for
possible influencing effects.
7
The evaluation of Moran’s I values from ArcMap indicated
that spatial autocorrelation does exist in the data examined.
8
The value of Moran’s I for
gun crimes was 0.06 and was significant at the .01 level. This indicates that there was
spatial autocorrelation in the distribution of gun crimes and a spatial lag was needed in
the model.
Before constructing the full RTM, the independent variables had to be examined to
identify if they were each significantly correlated with the Part I Index gun crimes.
9
To
thoroughly assess the RTM, we employed a more appropriate statistical procedure than
previous researchers of RTM had used in their analyses, negative binomial regression.
Piza (2012) suggested that the use of logistic regression techniques in previous RTM
research led to an undercount of incidents by collapsing them into categorical dependent
variables. Collapsing the data decreases model validity and statistical power. Piza (2012)
suggested that negative binomial regression techniques were more appropriate for RTM
models because they allow researchers to analyse count data and control for the
overdispersion of data that contain large numbers of spatial units with counts of zero (0)
rather than being bound by the limitations of categorical data which was required by
logistic regression techniques. Therefore, negative binomial regression was used to
determine the probability of a gun crime occurring within areas classified by spatial risk
values. The dependent variable for this stage in the analysis was a count measure of ‘gun
crime’in each cell occurring between January and June 2009.
Once the negative binomial results indicated which risk factors significantly predicted
counts of gun crime, logistic regression
10
was then used to assess how well the risk
assessment scale predicts whether or not gun crime occurred within the identified risky
areas (cells). The dependent variable was a dichotomous measure of ‘gun crime’creating
using data from 2008 (base year), which measured whether or not gun crime occurred
within the grid cell during the predicted time frame (January–June 2009).
11
The
independent variable was a five category measure of spatial risk values (discussed later).
The output was interpreted relative to the reference category that had a risk value of zero
(0), which was the category that corresponded to areas with the least risk. Each of the
four subsequent risk value categories was interpreted relative to the reference category. A
one unit increase in the spatial risk value of Little Rock had a corresponding change in
the probability of having a gun crime occur within cells with that specific risk value.
Once the RTM procedures were completed the PAI and RRI (discussed later) were
examined in comparison to the Nnh hot spot analysis.
Hot spot technique
For hot spots to form, past gun crimes must be clustered. Distance analysis was first
conducted to determine if gun crimes were significantly clustered. Ripley’s(1976,1981)
Kfunction, a measure of non-randomness, was used to determine clustering of gun
crimes.
12
The locations of gun crimes in Little Rock were more clustered than what
would be expected by chance, signifying that the gun crime locations were not randomly
distributed geographically. Once the clustering of gun crimes was established, the hot
spot analysis was administered to identify the geographical clusters.
There are a multitude of techniques to measure crime hot spots (see Eck et al.2005).
With no set standard on which technique to use, the application of using hot spots to
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predict future crime becomes difficult for researchers and practitioners.
13
This could
partially be a result in the different general types of hot spot mapping, thematic, point and
density. To address this, research has paired different hot spot techniques against one
another to better understand the accuracy and precision (Chainey et al.2008, Levin 2008,
Van Patten et al.2009).
With the examination of multiple hot spot techniques, a standard for a ‘go to’hot spot
technique is still debated. Chainey et al.(2008) concluded the kernel density estimates
(KDE) were the most accurate at predicting crime while Van Patten et al.(2009)
emphasised how one technique cannot fit all possible circumstances due to the spatial
element of crime.
14
This created differences in the applicability of certain hot spot
techniques. For instance, Van Patten et al.(2009) indicated that Nnh hot spot techniques
(ellipses and convex hulls) surpassed other hot spot techniques when predicting short-
term future crime such as one year predicting the following year.
15
As the time element of
prediction was increased, Van Patten et al.(2009) found that KDE becomes a stronger hot
spot technique for prediction (2–3 years).
In the current study, Nnh hot spot technique was used to indicate clusters of 2008 Part
I Index gun crimes.
16
Numerous studies (Paulsen 2004, Newton and Hirschfield 2009,
Van Patten et al.2009, Calvo et al.2012) within criminology and criminal justice have
measured hot spots using the Nnh hot spot technique. Nnh was chosen as the hot spot
technique since the current study was predicting short-term future crime, which Van
Patten et al.(2009) proposed was the most accurate technique for this type of analysis.
The 2008 Part I Index gun crimes were used to assess their predictability for future gun
crimes that occurred in the first six months of 2009.
Within CrimeStat, the researcher is able to select which parameters define a hot spot.
Due to the subjectivity of this approach, there has not been a set standard of a minimum
number of points (gun crimes) needed to represent a hot spot. Past research has used a
range of minimum points needed, from 5 to 15 (see Paulsen 2004, Newton and
Hirschfield 2009, Van Patten et al.2009, Calvo et al.2012). The current study used a
conservative minimum of 15 Part I Index gun crimes in 2008 to form a hot spot to
indicate the high areas of clustering. When searching for points within CrimeStat, a
search radius needs to be set to determine clustering. A random nearest neighbour
distance was implemented, which is not limited by a fixed distance search radius (see
Levine 2010).
17
With the parameters set, CrimeStat indicates whether or not hot spots
were found and allows for comparison to the risk terrain model.
The risky areas of Little Rock were viewed in a similar mindset as hot spots would be
viewed. While there are distinct differences between the techniques, both were used to
examine the predictability of future crime. Traditional hot spots are constructed from
previous crime while RTM is constructed from numerous social, physical and crime-
related factors. These techniques indicate small geographical areas within a study area
that are expected to have crime occur within them in the future (prediction phase). Since
RTM identifies riskier areas for crime with specific geographical boundaries (cells), those
areas are viewed as ‘hot areas’allowing for comparison between techniques (similar to
Drawve, in press).
Metric comparison
When comparing different hot spot techniques to one another, there must be a base of
reference since different techniques are used. Chainey et al.(2008) suggested the
10 G. Drawve et al.
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implementation of a metric for assessing different hot spot techniques known as the PAI.
PAI provides a method of testing the accuracy of hot spots on predicting future crime,
allowing for comparisons of techniques. PAI is a ratio constructed from the number of
future crimes within retrospective hot spots in relation to the overall number of crimes in
the future divided by the area within the retrospective hot spots in relation to the overall
study area, measured as:
ðnÞ
N100
ðaÞ
A100
The numerator becomes known as the hit rate and the denominator as the area percentage.
Chainey et al.(2008) discussed higher PAI values are a result of a greater number of
future crime events in a hot spot that is smaller in size (area) compared to the whole study
area (121.54 square miles for Little Rock). Multiple studies have incorporated the PAI as
a means for assessing the accuracy of hot spots at predicting future crime and discussed
the usefulness of the measure (Chainey et al.2008, Van Patten et al.2009, Tompson and
Townsley 2010, Hart and Zandbergen 2012, Dugato 2013).
To further supplement the utility of PAI, Levine (2008) suggested the RRI. The RRI is
the recapture ratio of PAI of the future crime to the PAI of the base crime [PAI
t
/PAI
t−1
].
The RRI measures the rate of change from one time period (base) to another time frame
prediction (Van Patten et al.2009). While the PAI examines the accuracy of the model,
the RRI supplements that analysis by examining the precision of the model.
Results
In the current study, RTM was examined in relation to gun crimes. After completing this,
Nnh hot spot analysis examined the clustering of past gun crimes. Each technique is
discussed in relation to their general findings then the PAI and RRI of the two techniques
were compared.
Risk terrain model
Little Rock was divided into 300 ft × 300 ft cells creating 38,670 cells. The independent
variables were each expressed spatially and given a risk value of one (1) depending on
their spatial influence. To determine which variables in the RTM analysis significantly
predict future gun crime locations, negative binomial regression was used. Six of the seven
independent variables used in the study significantly predict future gun crime locations.
Pawn shops did not significantly predict gun crime in Little Rock. The strongest predictor
of future gun crime was past drug incidents and the lowest was on-site liquor
establishments.
The six independent variables were combined into a final risk value map of Little
Rock that ranged from 0 to 4.
18
Figure 1 shows the risky areas of Little Rock in relation
to the Nnh hot spot locations. Table 1 provides the breakdown of the risk value, the
number of cells with that value and the number of gun crimes that occurred within each
risk value. The spatial risk value five (5) cells were collapsed with the spatial risk value
four (4) cells because of the low quantity of cells with the risk value of five (5) (n= 3).
As the spatial risk value increased, the number of cells decreased but the average number
of gun crimes per cell increased. This was consistent with our expectations that increased
presence of CGAs leads to increased gun crimes.
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The results of the logistic regression analysis are presented in Table 1. The odds of a
Part I Index gun crime occurring in an area with a spatial risk value of one (1) was about
five and a half times greater than areas with a spatial risk value of zero (0) (odds ratio =
5.67). The odds of a gun crime occurring in a cell with a spatial risk value of two (2) was
nearly 12 times that of areas with a spatial risk value of zero (0) (odds ratio = 11.90).
When an area has a spatial risk value of three (3), the odds of a gun crime increase to
nearly 35 times the odds of gun crime occurrence in areas with a spatial risk value of zero
(0) (odds ratio = 34.63). Areas with a spatial risk value of four (4) experience over 55
times the odds of gun crime relative to areas with a spatial risk value of zero (0) (odds
ratio = 55.05). The variance of the model was about 14% when predicting Part I Index
gun crimes.
Figure 1. RTM risky areas and Nnh hot spots in Little Rock, Arkansas.
Table 1. Logistic regression and spatial risk of Little Rock.
Odds ratio No. of cells
No. of gun
crimes
Average gun
crimes per cell
Spatial risk 0 Reference 30,682 125 0.004
Spatial risk 1 5.675* 5527 127 0.023
Spatial risk 2 11.895* 1621 80 0.049
Spatial risk 3 34.634* 678 111 0.164
Spatial risk 4 55.053* 162 40 0.252
Spatial lag 0.316
*p< .001.
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The results of the logistic regression were consistent with the assumptions presented
in the literature pertaining to RTM. The combination of drug incidents, on-site liquor, off-
site liquor, per cent of population black and per cent of population males between 15 and
24, were all significant predictors of future gun crimes. The physical and social
characteristics of Little Rock greatly increased the odds of identifying where gun crimes
were predicted to occur in the future.
Nnh hot spot technique
Before performing the Nnh hot spot technique, the spatial dependency had to be
established through the Ripley’sKfunction. Monte Carlo simulations were run on the
2008 Part I Index gun crimes and identified that the gun crimes were highly concentrated
compared to the expected values (determined by the simulations). 2008 Part I Index gun
crimes were found to be clustered which allowed for further analysis of the spatial
distribution of the gun crimes.
In Figure 1, the map depicts the locations of the Part I gun crime Nnh hot spots in
relation to the RTM map. The Nnh hot spot analysis identified seven significant hot spots
(.001 level).
19
The Monte Carlo simulations run in congruence for this analysis did not
find any clusters of gun crimes using random crime locations. The Nnh hot spots
contained from 16 to 27 gun crimes within them from 2008. One of the more southern
Nnh hot spots was difficult to distinguish because it is more linear than round. The
locations of these seven Nnh hot spots were used to predict the location of 2009 gun
crimes from January to June.
There were 483 Part I Index gun crimes that occurred in the first six months of 2009.
When the 2009 gun crimes were added to the analysis, 36 gun crimes occurred within the
2008 Nnh hot spots. Retrospective areas were able to predict 7% of future gun crime
within Little Rock. The Nnh hot spot analysis was further examined in relation to the risk
terrain model findings.
Comparing techniques
The PAI and RRI values were examined to determine the accuracy and precision of the
two models. The PAI prediction value for the RTM was 19.246: calculated as:
40
483
100
:5229
121:54
100
There were 40 gun crimes that occurred in 2009 within the highest risk area
(4, area = 0.5229 square miles) of the total 483 crimes that occurred within the first six
months of 2009. The Nnh hot spot technique had a PAI prediction value of 21.05,
calculated as:
36
483
100
:4303
121:54
100
There were 36 gun crimes that occurred in 2009 within the seven hot spots (area = 0.4303
square miles). This indicated that the Nnh hot spot technique was more accurate at
predicting future Part I Index gun crimes than the Nnh hot spot technique.
It is possible to be accurate without being precise so the RRI was examined within the
two models. When examining the RTM, 66 Part I Index gun crimes of 946 total in 2008
occurred within the highest risk area (4). These numbers were used to construct the PAI
value for the base year, 2008. The RRI for the RTM was 1.18 (19.246/16.214). For the
Policing and Society 13
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Nnh hot spot technique, 151 of 946 Part I Index gun crimes in 2008 occurred within the
Nnh hot spots. These numbers were also used to construct the PAI value for the base year
(2008). The RRI value for the Nnh hot spot technique was 0.467 (21.049/45.077). This
concluded that the RTM was more precise than the Nnh hot spot technique for Part I
Index gun crimes. This indicated that while the Nnh hot spot technique was more
accurate than the RTM technique, it was less precise.
Discussion
The purpose of the current study was to compare RTM and Nnh hot spots when trying to
predict future crime, with the notion that the results could help aid police departments for
crime prediction. Nnh hot spot analysis is a technique that relies on past crime to predict
future crime, making it more difficult to apply a theoretical framework. The RTM
methodology allows for a more theoretical foundation to be incorporated into the
analysis. The results from the PAI and RRI revealed that the RTM technique was less
accurate than the Nnh hot spot analysis but more precise when predicting gun crime.
This finding brings up an important point within spatial prediction, relying on one
technique could create accuracy and reliability problems. Kennedy et al.(2011) discussed
the utility of using RTM jointly with more traditional hot spot methods rather than
substituting one technique for another. Just as Van Patten et al.(2009, p. 28) distinguished,
‘It depends’is the acceptable answer to what technique is the best. Depending on the type
of research, multiple techniques may be needed to fully assess the phenomenon.
Additionally, this identified a potential limitation of RTM that has not been examined
thoroughly, the accuracy when compared to other prediction techniques. On the other hand,
since RTM is constructed from social and physical measures, it makes sense that it is more
reliable over time compared to the Nnh hot spot technique. Incorporating characteristics of
the built environment allows for the findings to be discussed in relation to crime pattern
theory and future directions.
Brantingham and Brantingham (1999) discussed the elements of the environmental
backcloth and integration of social and cultural characteristics. The social characteristics
of Little Rock were taken into account within the RTM model. The three spatial risk
factors: per cent black, per cent male between 15 and 24 and drug density were found to
be positively significant for predicting gun crime. These factors provided context of the
population variations within Little Rock and where past crimes occurred. These measures
combined with the physical characteristics of the built environment of Little Rock started
to develop the environmental backcloth of the city.
The routine activities of individuals take them to various CGAs where criminal
opportunities can be established. It is possible that numerous individuals frequent the
locations measured in the current study and become aware of the surrounding
environment around the CGAs. The findings suggest that the CGAs measured influence
the surrounding crime levels. The three positive and significant CGAs that were
incorporated into the model, on-site liquor establishments, off-site liquor establishments
and fast food establishments were found to predict gun crimes. The on-site liquor
establishments and fast food establishments attract high volumes of people, increasing
informal guardianship in that area. Due to the nature of the crime being analysed, Part I
Index gun crimes, and the informal guardianship, who can act as witnesses, offenders
may choose targets that truly lack capable guardianship. The smaller size of the
coefficient for on-site liquor establishments may be a result of many of informal
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mechanisms of social control (i.e., bartenders and bouncers) being used in these
establishments (i.e., bars and taverns) to prevent escalation of potentially violent
situations in lieu of making formal complaints to the police. Pawn shops were found to
be non-significant and were excluded from the spatial risk measures. The small number
of pawn shops within Little Rock could attribute to their inability to predict gun crime.
The inclusion of CGAs allowed for researchers to take into account locations in which
individuals frequent in Little Rock and compare those with gun crime. Additionally, crime
pattern theory pertains to the environmental backcloth that includes numerous attributes
(see Brantingham and Brantingham 1999) that construct it to understand a study area. The
current study included social and physical measures of Little Rock to account for elements
of the environmental backcloth. The social measures and physical were found to be
significant predictors of gun crimes, supporting crime patterns theory assertion of
incorporating numerous attributes of the environment backcloth.
The Nnh hot spot analysis did accurately predict future gun crimes but not to the
extent the RTM was able to predict future gun crime. There are two primary reasons we
believe RTM was a better predictor than Nnh hot spot analysis. First, when examining the
location of the identified hot spots, each hot spot is positioned in a medium to high spatial
risk area when compared to the RTM map. This finding indicated that the RTM measures
of the current study were able to account for past crime clusters without including a
measure risk factor of past Part I crime. Second, RTM was able to identify the risky areas
where hot spots formed, but was also able to identify risky areas in Little Rock that the
Nnh hot spot analysis did not identify. For example, when looking at Figure 1, no hot
spots formed in west Little Rock but the RTM accurately predicted gun crimes that
occurred in that area.
20
Based on suggestions by Piza (2012), our second goal was to integrate the use of
negative binomial regression into RTM to reduce problems with undercounting within the
dependent variable. We first analysed the data using negative binomial regression, which
allowed us to both account for the large number of zeros in our dependent variable and to
increase statistical power and validity by not collapsing the data into categories. Using
this method of analysis, we were also able to determine the individual effects of each
of the CGAs within each cell (on and off premise liquor establishment, fast food
establishments and pawn shops) and each of the social characteristics within each cell
(density of past drug incidents, per cent of the population that is black, and per cent of
males between the ages of 15 and 24). Because pawn shops did not significantly predict
gun crime, the measure was excluded from the analyses. All other measures of CGA and
social characteristics significantly predicted gun crime.
21
Using both negative binomial and logistic regressions in tandem allowed us to narrow
down significant predictors of gun crime and determine which areas are at highest risk for
gun crime across the city of Little Rock. Additionally, including the built environment
into the analysis allowed for locations where individuals frequent to be taken into
consideration. Where there are higher intersections of victim and offenders, there are
more opportunities for crimes to occur. Accounting for the significant CGAs and social
characteristics alone, we were able to predict nearly 14% of the variance in gun crime.
Since RTM takes into account the built environment and was found to relate to the
location of the Nnh hot spots, prevention and policing strategies can be implemented.
Increased policing within crime hot spots is not a new application. Braga’s(2005)
overview of five police enforcement efforts on crime hot spots revealed that targeted
police efforts do, in fact, reduce the calls for service in treatment hot spots. Hot spot
Policing and Society 15
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techniques rely on past crime/calls to determine clustering, providing a basis for future
policing areas, but those areas may not be where crime moves (see Johnson and Bowers
2004) or where crime remains stable. The application of targeted policing can be
expanded to encompass risky areas (RTM) for crime that hot spot techniques may not
identify. Furthermore, the RTM technique was more precise over time making it more
reliable than the Nnh hot spot technique. If crime were to move, RTM provides a basis for
predicting where crime could likely move to based on the spatial riskiness of an area
while taking CGAs into account, further helping policing efforts.
The inclusion of CGAs into the RTM has practical meaning for policing and city
policy-makers. Place managers (see Eck 1994) can influence the presence of crime at a
location via ineffective managing or complete absence from the place. Extant literature
supports the argument that effective place management at various types of businesses can
lower crime in an area (see Eck and Wartell 1998, Madensen and Eck 2008). With this
knowledge, policy-makers can hold businesses more accountable for effectively managing
their properties in an effort to reduce crime in the area. This approach could allow for a
dual target of prevention efforts, increasing effective business management with targeted
policing efforts. For example, Nnh hot spot analysis indicated clusters of Part I crimes and
RTM constructed the riskiness of that area. From this, the CGAs within the Nnh hot spots
could benefit from policies increasing effective management while police increase their
presence in the area.
A limitation to the study is that hot spot analysis technique relies on the minimum
requirements to be met for a hot spot ellipse to form (varies by technique). If there are not
enough crimes in close proximity to one another a hot spot will not form even though
crime regularly occurs in a small area. Additionally, the Nnh hot spot analysis was not
able to identify all of the most risky areas (value = 4) in Little Rock due to the use of past
crime only. These downfalls can be overcome through the use of RTM that takes into
account the built environment that influences where crime is likely to occur.
Future research should include similar methodology put forth in this paper. Hot spot
analysis is a technique that indicates clustering of past crime, but may not always be the
most precise technique, as found in this study. Furthermore, it would be advantageous to
construct predictive models separate, RTM and Nnh hot spots, and explore the utility of
joining the two models into one. While RTM could include past crime as a risk factor, by
including it as a risk factor could produce a bias model. Specifically, future research
should utilise constructing RTM models based on the built environment then supplement-
ing it with hot spot analysis. By doing so, one technique concentrates on past crime while
the other utilises CGAs. Research needs to continue to address the differences in
predictive techniques with the emergence of RTM in respect to the PAI and RRI. RTM
allows for the built environment and social characteristics of an area to be included within
an analysis, possibly allowing for a more static environment to be used for prediction
rather than dynamic crime hot spots. Additionally, future research should examine the
difference in ‘high risk’areas of RTM where crime actually does not occur with areas
where crime does occur. Differences in the areas could allow for more precise measure of
risk factors.
Notes
1. Numerous factors are incorporated into the decision-making process (Cornish and Clarke
1986).
16 G. Drawve et al.
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2. Their hotspot technique relied on raster data output for comparison. The current study
incorporates vector data output that identified gun crime clusters.
3. The purpose of this study is not to generalise the findings to any particular population, but to
compare the two analytical methods.
4. An important limitation of using official crime statistics, such as LRPD data, is that only crimes
reported to the police are included in the data. This may create systematic bias in the results due
to crimes that involved a gun going unreported.
5. The average street length in Little Rock was about 430 ft, but the nature of RTM used in the
current study relies on a smaller cell size that allowed for the incorporation of awareness space.
6. The current study conducted five smoothing iterations to take into account surrounding block
group values.
7. Caplan and Kennedy (2013) released a RTM specific programme known as RTMDx to aid in
the operationalisation and building of the ‘best’model. The programme was not utilised in the
current study because it operates on point data alone when creating the ‘best’model. It would
be possible to take the current study’s point data and input it into RTMDx to help
operationalised measures but the ‘best’model would be misspecified. That is, because the
model only used the point data and not the block group data, the ‘best’model would not reflect
the entire risk factor list. The social characteristics at the block group level could alter how the
point data were operationalised but RTMDx cannot currently account for that possibility.
8. Moran’s I determines whether there is any correlation, positive or negative, and compares the
values of nearby areas to look for similar rates (Anselin et al.2000). Moran’s I tests against the
null hypothesis of clustering, that incidents are randomly distributed. The z-score identifies
the significance of the correlation and the Moran’s I signifies the direction (positive or negative).
The values range from –1, dispersion, to +1, highly clustered incidents. A corresponding
significance value is given with the Moran’s I value. For the use within RTM, a value near 0 is
wanted to signify independence among the distribution of gun crimes.
9. Each independent variable map layer was trimmed to the Little Rock boundaries so the 300 ft ×
300 ft grid would line up correctly when the variables were combined.
10. The results to the binary logistic regression analysis were robust across zero inflated negative
binomial regression, ordinal logistic regression and penalised likelihood logistic regression.
11. Gun crimes were collapsed into a binary measure due to the small number of block groups in
the sample that contained more than one gun crime.
12. Lum (2008) discussed how Ripley’sKfunction tests for statistical significance of clustering by
comparing observed data points to random data points. The comparisons between observed
and expected are based on Monte Carlo simulations. Levine (2006) stated that Monte
Carlo simulations must be run to achieve statistical significance of the findings. Monte Carlo
simulations consist of randomly distributed points that were run with the same parameters
defined by the user to determine if the findings of the actual data were significant when
compared to random simulations. The output gives the approximate confidence intervals
(minimum and maximum) of the simulations and the observed value of the actual data.
13. The researchers acknowledge the work completed by Weisburd et al.(2004,2009), but the
focus of the current paper is not street segments.
14. Chainey et al.’s(2008) assertion that KDE was the best hot spot technique was met with
criticism due to various reasoning (see Levine 2008, Pezzuchi 2008).
15. Their study examined five hot spot techniques: STAC Ellipses, STAC Convex Hulls, Nnh
Ellipses, Nnh Convex Hulls and KDE.
16. Nnh is a hot spot technique that is part of the CrimeStat III programme and the output was in
ellipse form (see Levine 2010). The researchers are aware of the arbitrariness of ellipses in
regards to the distribution of crime within the ellipses.
17. The search radius was set to random distance with a significance level set to .001%. Similar to
Ripley’sKfunction, Nnh uses Monte Carlo simulations to determine if the results of the
analysis were by chance.
18. Pawn shops were found to be non-significant predictors for gun crimes, excluding them from
the analysis. The non-significance can be due to the few pawn shops that were located in Little
Rock, AR.
19. The technique was also run at the .05 level to determine if more hot spots would be identified
but no new hot spots formed at the .05 level.
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20. On the other hand, RTM does identify many areas as risky when in reality those areas are not
dangerous for criminal activity.
21. All significant measures predicted gun crime in the predicted direction, positively, other than
fast food establishments, which predicted a reduction in gun crime.
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