J Quant Criminol
DOI 10.1007/s10940-014-9223-8
ORIGINAL PAPER
Early Warning System for Temporary Crime Hot Spots
Wilpen L. Gorr • YongJei Lee
Springer Science+Business Media New York 2014
Abstract
Objectives We investigate the potential for preventing crimes at temporary hot spots in
addition to chronic hot spots. Using data on serious violent crimes from Pittsburgh,
Pennsylvania, we investigate an early warning system (EWS) for starting/stopping police
deployments at temporary hot spots in coordination with constant prevention work at
chronic hot spots.
Methods We estimate chronic hot spots using kernel density smoothing. We use simple
rules for detecting flare-ups of temporary hot spots, predicting their persistence, deploying
police, and stopping deployments. We also consider a combination program including the
hottest chronic hot spots, with EWS applied to remaining areas. Using 2000–2010 data, we
run computational experiments varying the size of chronic hot spots and varying rule
thresholds to tune the EWS. Tradeoff curves with percentage of crimes exposed to prevention versus percentage area of the city with crime prevention workload provide tools for
coordinating chronic and temporary hot spot programs.
Results The combination program is the most efficient, equitable, and responsive program. After first allocating police prevention resources to the hottest chronic hot spots, the
marginal benefits of adding more chronic hot spot area is not as high as adding temporary
hot spots. Chronic hot spots are limited to large commercial and adjoining residential areas.
Temporary hot spots are widely scattered throughout Pittsburgh.
Conclusions Temporary hot spots exist outside of chronic hot spots and are targets for
prevention as supplements to chronic hot spots. A combination program targeting both
chronic and temporary hot spots is recommended.
W. L. Gorr (&)
School of Public Policy and Management, H. John Heinz III College, Carnegie Mellon University,
Pittsburgh, PA 15213, USA
e-mail: gorr@cmu.edu
Y. Lee
School of Criminal Justice, College of Education, Criminal Justice, and Human Services, University of
Cincinnati, Cincinnati, OH 45221, USA
e-mail: lee2yj@mail.uc.edu
123
J Quant Criminol
Keywords Hot spots Crime prevention Police deployment Early
warning system
Introduction
Sherman (1995) defined crime hot spots as ‘‘small places in which the occurrence of crime
is so frequent that it is highly predictable, at least over a one-year period.’’ There are
several other, similar definitions of crime hot spots (e.g., Grubesic 2006; Braga and Weisburd 2010; Braga et al. 2012). In regard to duration, Weisburd et al. (2004) used trajectory analysis (Nagin 1999) with annual data to show that crime hot spots in Seattle made
up of block-long street segments can persist for many years, even more than a decade.
These can be termed ‘‘chronic hot spots.’’ The practical implication for police decisionmaking is that chronic hot spots are constant and therefore good targets for crime prevention efforts. All that is needed is to determine the street segments or boundaries of
chronic hot spots and then to assign prevention resources to them over the long term.
Wilcox and Eck’s (2011) ‘‘iron law of troublesome places’’ assures a constant series of
crimes in such places.
This paper investigates temporary hot spots as targets for crime prevention in addition
to chronic hot spots. Temporary hot spots, like chronic hot spots, have high crime density
but persist only for months instead of years and thus require a dynamic approach for
allocating crime prevention resources. We therefore propose and investigate a hot spot
early warning system (EWS) for managing temporary hot spots that includes rules for (1)
detecting the start or flare-up of a temporary hot spot, (2) predicting persistence of crimes
after detection given no prevention work beyond existing policing efforts, (3) deploying
police for prevention work at a temporary hot spot, and (4) stopping prevention work after
the hot spot is extinguished temporarily if not permanently.
Computational experiments using offense-report data on part 1 violent (P1V) crimes
(homicide, rape, robbery, and aggravated assault) from Pittsburgh, Pennsylvania during
2000–2010 are used to calibrate, investigate, and compare the performance of chronic,
EWS, and combined chronic and EWS hot spot programs. Pittsburgh is an ideal test bed
because while it has used modern crime mapping and CompStat approaches for tactical
deployment of police, putting ‘‘cops on the dots,’’ it has not had either sustained or
centralized hot spot programs during the study period.1 Thus the empirical work in this
paper assesses the potential for preventing crimes beyond current good policing practices.
Indeed the results show that 33.3 % of Pittsburgh’s P1V crimes (with 95 % confidence
interval [32.6, 33.9]) could have been exposed to hot spot prevention efforts with only an
average of 3 % of Pittsburgh’s area under prevention workload using the combination hot
spot program as described below.
1
The status of hot spot policing in Pittsburgh over 2000–2010 was confirmed by reading annual reports of
the Pittsburgh Police Bureau and from interviews of commanders of the two zones with the highest violent
crime rates. Authority to use hot spot programs rests with the six zone commanders, and they used saturation
patrols in only two locations for short periods. A 2012 master’s student project in the Heinz College of
Carnegie Mellon University designed chronic hot spots using the methods provided in this paper for one of
the commanders, who has since implemented the design. In the early 1990s, one Pittsburgh neighborhood,
Homewood, famously had intensive hot spot policing for an entire summer, supported by a DMAP crime
mapping project (Olligschlaeger 1998) but that kind of effort was not repeated in the study period.
123
J Quant Criminol
We use grid cells as potential temporary hot spots (Chainey and Ratcliffe 2005) for
computational convenience as well as a practical way for police to implement EWS. We
optimize temporary hot-spot grid size and rule thresholds in the computational experiment
over sets of values for grid sizes and rule thresholds. The result of each experimental run is
plotted as benefits versus costs represented by percentage of city-wide P1V crimes exposed
to prevention measures (and thus possibly prevented) versus average percentage area of the
city under prevention workload. The frontier of all points from the experiment is the
optimal EWS tradeoff curve.
We use kernel density smoothing (KDS), a non-parametric spatial smoothing method,
for estimating chronic hot spots (Chainey et al. 2002; McGuire and Williamson 1999; Gorr
and Lee 2012). KDS estimates crime density maps (crimes per unit area). KDS places a
kernel, generally a three-dimensional Gaussian density centered over each mapped crime
point (as is the case in this paper), and sums all kernels to yield the density surface. Crime
densities above a selected crime density threshold for KDS maps estimated over a multiple-year period define chronic hot spot boundaries. The KDS map has the appearance of
topography with hills and the threshold is a plane whose intersection with hilltops defines
the chronic hot spot boundaries. This method of defining chronic hot spots has the
advantage of allowing us to vary the crime density threshold and estimate performance for
a range chronic hot spots of increasing size. We create tradeoff curves for chronic hot
spots, with the same dimensions as those for temporary hot spots, by varying the KDS
threshold.
The combined hot spot program first allocates resources to chronic hot spots up to a
maximum size in area and then applies the EWS to remaining areas outside of the chronic
hotspots, optimizing over grid sizes and rule thresholds. The combined tradeoff curve uses the
chronic hot spot curve up to the maximum size and then uses the optimal EWS tradeoff curve
for additional areas added to the end point of the chronic curve. The rationale for the combined
program is based on two observations. First, an analysis of chronic hot spots shows their crime
densities are steeply peaked so that crime densities fall off exponentially as chronic hot spot
areas are increased. For example, the hottest chronic hot spots in Pittsburgh covering roughly
1 % of Pittsburgh’s area have a crime density of 738 P1V crimes per square mile over a year
while the additional ring of chronic hot spot area from roughly 1–2 % has a density of 372 and
that for 2–3 % has a density of 214. Thus chronic hot spots in Pittsburgh degrade quickly to
behaving more like temporary hot spots as sizes are increased. Second, the feasible areas for
chronic hot spots are a subset of feasible areas for temporary hot spots, so that after the hottest
areas are assigned to chronic hot spots there may exist better or simply more of the best
temporary hot spots such as adjacent to the hottest chronic hot spots.
The results demonstrate comparative advantages of chronic and temporary hot spot
programs, with the combination program capturing the best of both, providing overall the
best efficiency as well as more equitable and responsive allocations of police prevention
resources. We provide evidence that (1) chronic hot spots, with constant deployment of
prevention resources, are the most efficient means for crime prevention, but only for the
very hottest (highest crime density) areas; (2) temporary hot spots are more efficient than
relatively large chronic hot spots for crime prevention as supplements to hottest hot spots
of the same total area under prevention workload; (3) chronic hot spots tend to occur in
large commercial areas of impoverished neighborhoods; and (4) temporary hot spots
provide crime prevention services more equitably across the urban landscape where needed
and especially in widely-scattered residential and small commercial areas.
Section 2 reviews relevant literatures. Section 3 describes the Pittsburgh crime data
used for testing alternative hot spot strategies. Section 4 describes the proposed hot spot
123
J Quant Criminol
EWS, and Sect. 5 provides the results of computational experiments. Section 6 discusses
the results further and suggests future work, and Sect. 7 summarizes the paper.
Literature Review
This section reviews the literatures on crime hot spots, temporary hot spots, fear of crime,
and crime detection and prediction methods.
Crime Hot Spots
Many scholars have suggested crime hot spots as targets for crime prevention by police
because of their high crime density and stability over long periods of time. Sherman et al.
(1989a) found that about 3 % of street addresses produced over 50 % of service calls to
police officers in Minneapolis. Spelman (1995) found a large number of police service calls
concentrated in high risk places such as high schools, subway stations, and parks in Boston
for a relatively long period. Weisburd et al. (2004) found that 5 % of block-long street
segments accounted for 50 % of crime in Seattle and the hottest hot spots chronically
persisted longer than a decade. Recently, Braga et al. (2010) found that about 5 % of street
units (e.g., street-segments and cross-streets) accounted for 74 % of gun crimes in Boston
from 1980 through 2008. Additionally Braga et al. (2011) found that only 1 % of street
units generated about 50 % of commercial robberies during a 29-year (1980–2008) study
period. Wilcox and Eck (2011) coined a term for the concentration of crime in a very few
bad places as ‘‘The Iron Law of Troublesome Places.’’
One criticism of police interventions in crime hot spots has been the possibility that
criminals and their crimes merely displace to other locations, often nearby. There had been
a mixed literature on crime displacement (Reppetto 1976; Miethe 1991; Scherdin 1986;
Braga et al. 1999; Clarke and Weisburd 1994; Hesseling 1995; Ratcliffe et al. 2011). More
recently, however, Weisburd et al. (2006) found that certain crimes, illegal drug dealing
and prostitution, do not readily displace and thus benefit from prevention efforts. Moreover, Braga et al. (2012) concluded that policing hot spots not only has a moderate effect
size in reducing crime, but also a diffusion of benefits (crime reduction) in contiguous
areas rather than crime displacement. To the extent that displacement of crime exists, EWS
would be responsive to it while chronic hot spots would not. Both crime prevention at
chronic and EWS hot spots could enjoy diffusion of benefits.
Another important finding from Braga et al. (2012) was on the impact of police hot spot
programs on community members. Regardless of the early critiques on police misconduct
and force abuse in New York City (Greene 1999), the skepticism surrounding the effectiveness of hot spot policing tactics (Tonry 2011), as well as the disagreement between the
police and residents when assessing and prioritizing neighborhood problems (Rosenbaum
2006), Braga et al. found that community members in residential areas expressed positive
reactions to hot spot policing. We recommend that a key policy of any hot spot program
should be that field officers build positive relationships with citizens—being responsive to
crimes that have occurred and working to prevent future crimes.
Paralleling the development of hot spot policing has been development of methods for
automatically estimating hot spot boundaries, including point mapping (Jefferis 1999),
spatial ellipses (Block 1995; Levine 2013), thematic mapping (Harries 1999), grid-system
maps (Chainey and Ratcliffe 2005), and surface smoothing methods (Chainey et al. 2002;
McGuire and Williamson 1999; Gorr and Lee 2012). One of the commonly-used surface
123
J Quant Criminol
smoothing methods is kernel density smoothing (KDS) which is a simple non-parametric
method that estimates crime density (crimes per unit area) from point data (Haining 2012).
Chainey et al. (2008) generated hot spots using alternative mapping techniques and
compared them based on persistence of crimes in the next month after estimation. Controlling total hot spot area in each hot spot mapping technique to be 3 % of the study area
in Central/North London, the study generated hot spots using the previous 3 months’ crime
data. Though the percentage of crimes persisting varied by types of crime from only 8 to
20 %, KDS outperformed other commonly-used hotspot mapping techniques: standard
deviational ellipses, thematic mapping of boundary areas, and grid thematic mapping.
Temporary Crime Hot Spots
Mohler et al. (2011) provide a methodology that models and simultaneously estimates both
short-term and long-term crime hot spots using a marked point process. Their model,
however does not identify or distinguish chronic hot spots versus temporary hot spots.
Instead they compute a total crime density for grid cells, summing long-term average and
short-term flare up contributions. They recommend ranking all grid cells daily and allocating the top x % for police prevention work depending on available resources.
Gorr and Lee (2012) defined temporary hot spots as areas with crime densities (crimes
per unit area per time period estimated using KDS) that are comparable to chronic hot spots
but typically persist for periods of time less than a year, generally months. Temporary hot
spots flare up, persist, extinguish, and can reoccur. Gorr and Lee found chronic hot spots to
be relatively few in number and concentrated in commercial and poverty-stricken areas of
Pittsburgh while temporary hot spots are smaller in area, greater in number, and widely
dispersed across the city. Craglia et al. (2000) pointed out the importance of different crime
prevention responses in accordance with differences in neighborhood characteristics as
well as offender, victimization and incident rates across neighborhoods. For example, an
urban area with high offense rates requires long-term policing tactics to reduce crime,
while a residential area with low offense rate but relatively high victimization needs more
sophisticated approaches such as dynamic proactive policing. In this vein, temporary hot
spots can be potential targets, in addition to chronic hot spots, for police if the temporary
hot spots persist long enough after initial detection for police to prevent crimes or can be
forecasted in advance. This paper shows that early detection is promising. Forecasting
crime flare-ups is more challenging.
Chronic to temporary hot spots define a spectrum of cases from always hot, to mostly
hot, to sometimes hot. The empirical work in this paper provides evidence that, depending
on where the line is drawn to define chronic hot spots, some designated chronic hot spots or
their parts may exhibit the on-and-off behavior of temporary hot spots and thus may benefit
from a dynamic pattern of police resource allocation for prevention. This section reviews
four theories for temporary hot spots: near repeat crimes, routine activity theory, hardening
of soft crimes, and relocation of poor populations.
Near Repeat Crimes Morgan (2001), Townsley et al. (2003), Johnson and Bowers
(2004a, b) found ‘‘near repeat’’ burglaries in their studies; namely, that residences nearby
an initial burglary were more likely to be targeted for burglaries soon afterwards than
otherwise expected. Also, near-repeat burglaries are more prevalent than repeat burglaries
at the same location. Similar to the crime preventive benefit of focusing on repeat victims
(Pease 1998), focusing on particular dwellings at or nearby the initial burglary could also
predict and prevent future crimes. Johnson and Bowers (2004a) found that properties
within 400 m on an initial burglary suffered from the elevated risk of burglaries for
123
J Quant Criminol
2 months after the initial burglary. For burglaries in a portion of Los Angeles, Mohler et al.
(2011) estimated areas of elevated risk to be 50–100 m.
Ratcliffe and Rengert (2008) studied near repeat patterns of shootings. Their study
showed that near-repeat shootings typically occurred within 400 feet from an initial
shooting within a few weeks. Their reasoning was that the near-repeat shootings were
retaliation between offenders and victims.
Also, disputes arising from illegal activities such as drug dealing can cause near repeats.
In this case, shootings may be the most certain and swiftest means to punish another given
that criminals cannot report crimes they suffer to the police. If legitimate means, such as a
law enforcement, were available offenders would not have to retaliate. Another possibility
is retaliation gang shootings (Cohen and Tita 1999; Tita and Ridgeway 2007). Initial
shootings between the rival gangs trigger not only serial shootings, but also other types of
violent acts. Repeat victimization theories (Jacobs et al. 2000) and near-repeat phenomena
in regard to location can explain this case.
In sum, near-repeat criminal behavior is one theory that leads to temporary crime hot
spots. This theory appears, however, to only pertain to limited crime types: burglary, gangrelated violence, and shootings. It may be able to be extended to other crime types, for
example, aggravated assault and homicide, as the result of shootings. It also may pertain to
the certain types of criminals, for example, gang members who seek revenge from recent
acts of violence.
Routine activity theory According to routine activity theory (Cohen and Felson 1979;
Felson 1986, 1987; Sherman et al. 1989b; Eck 1994, 1997), any situational change among
the three necessary elements—potential victim (suitable target), motivated offender, and
capable guardianship—can either deter or provoke crime. If a motivated offender finds a
suitable target without any situational barrier that increases the risk of being arrested, the
likelihood of the offender committing crimes will increase. Crime-prone places provide
potential offenders with higher opportunity to be involved in criminal acts due to the lack
of guardianship and existence of potential victims.
Thus, by eliminating the opportunity that a crime-prone location offers to motivated
offenders, police can reduce the likelihood of crime before it happens or reduce the
opportunity of repeated occurrence of crime (Weisburd and Braga 2006; Sherman et al.
1989b). Proactive policing could achieve this goal by increasing the presence of police
officers or increasing the frequency of police patrol in crime-prone locations. Once special
police resources are removed from such locations, however, crimes can start up again after
criminals perceive the changed circumstances (e.g., Cohen et al. 2003).
Thus on and off behavior of crime hot spots can be caused by police, location managers,
and other involved persons affecting the target/offender/guardianship situations of locations.
Soft crimes harden Theoretical reasoning on certain criminal behaviors suggests that an
increase in certain lesser crimes in a small geographic area may lead to an increase in
serious crimes later in that area. Empirical research has borne this possibility out, giving
rise to an additional theory for temporary hot spots.
Contributing to this development is that criminals tend to be generalists, committing a
wide range of disorder and crime types (e.g., Blumstein et al. 1988; Piquero 2000; DeLisi
2001). Additionally, criminals generally do not travel far from their residences to commit
crimes (e.g., Rengert et al. 1999). So if there is a new criminal element in a neighborhood,
say due to new gang activity or release of a prisoner from jail, we expect to have a variety
of crime types occurring in a relatively small area. Disorderly behavior and lesser crimes
are much more prevalent than serious violent crimes; hence, by chance alone one would
expect to experience lesser crimes first and serious violent crimes later by a specific group
123
J Quant Criminol
of criminals. Broken windows theory suggests that crime hardens over time as neighborhoods decay, and can occur over a variety of time scales including short time intervals
(Doran and Burgess 2012, p 13).
A test of this theory is to determine if large increases in soft crime in small areas lead to
large increases in hard crimes in the same areas. Cohen et al. (2007) and Gorr (2009)
developed and tested a leading-indicator forecast model to forecast serious property and
violent crimes from time-lagged soft crimes. They found that increases in particular soft
crimes and police calls for service often precede increases in serious violent crimes in
small areas. For example, approximately 25 % of all large increases in serious P1V crimes
were forecasted one month ahead of occurrence with a false positive rate of 15 %, whereas
a chance mechanism would forecast 15 % of such P1V crimes increases at the 15 % false
positive rate. Cohen et al. (2009) in analyzing Pittsburgh Police crime analysts’ preferences
found a 15 % false positive rate to be optimal in the tradeoff between signaling P1V crime
increases for prevention versus cost of false positives.
Displacement of poor populations Reports on the ‘‘moving to opportunity for fair
housing’’ demonstration program conducted by the U.S. Department of Housing and Urban
Development (e.g., Popkin et al. 2002; Kling et al. 2007; Sanbonmatsu et al. 2011) found
that displacing poor people may result in poverty displacement and, in turn, displacement
of crime places. After 10–15 years of experiments, the researchers found that there was no
significant difference in serious forms of anti-social or criminal behavior between treatment and control groups. These findings indicated that movement of poor and high-risk
people to other places may cause displacement of crime, resulting in hot spot displacement.
As a case study, public housing developments in Pittsburgh were demolished from the
mid-1990s to the early 2000s with former inhabitants scattered throughout poor areas of
the city. Prior to that, gangs tended to form in isolated housing developments and in
relation to surrounding neighborhoods, leading to established territories, boundaries, and
crime hot spots. When relocated and scattered, members of rival gangs no longer had
established territories and thus had chance encounters, with temporary sequences of violent
crimes resulting (Garland 2012). For example, aggravated assaults increased substantially
in poor areas of Pittsburgh as relocation progressed.
Therefore local government policy on housing can have an adverse effect on crime,
causing increased levels of serious violent crimes in previously low-crime areas, and
because housing relocations are scattered as opposed to concentrated, the result can be
temporary hot spots.
Fear of Crime
While this paper uses potential reductions in crime counts as a measure of performance, it
is also worthwhile to consider potential reductions in fear of crime, especially in residential
areas where crime prevention workload at temporary hot spots has the potential to be
effective. Fear of crime is considered by some researchers to be more important than crime
itself, with fear exceeding actual crime rates (Doran and Burgess 2012, p 24). Crimes have
a multiplier effect in residential neighborhoods because interpersonal social networks
spread second-hand information on crimes widely (Skogan 1986). For example, Skogan
and Maxfield (1981) reported that 48 % of interviewees knew about robberies in a
neighborhood in which only 5 % of the neighborhood population had been victimized. Due
to the second-hand information effect, a community may gradually lose its neighborhood
cohesiveness as fear of crime elevates (Nasar et al. 1993).
123
J Quant Criminol
Those who live in communities with crime hot spots nearby are more likely to experience emotional instability as well as continuous fear of crime (Grohe 2007). Citizens in
such areas are more likely to devote large amounts of effort to protect themselves from
crime or stay in-doors rather than enjoying out-door activities (Moore and Trojanowicz
1988). Fear of crime is amplified for the old (Box et al. 1988), females (Keane 1998), and
the poor (Taylor and Hale 1986). These groups are more vulnerable to crime due to
potential psychological, physical, and economic weaknesses, so they are less likely to cope
with the fear of crime. Also, the propensity for fear of crime is higher among residential
communities than urban settings. Citizens in urban areas may accept crime as a part of their
life while those in residential areas do not (Grohe 2007). People can take safeguards when
visiting commercial areas, but avoiding crime risks is much more difficult where they live
and their children play.
At the present time, there is little evidence suggesting that police can reduce fear of
crime through hot spot enforcement (Braga et al. 2012), although if done properly there is
the possibility that it may. Police need to engage in crime prevention proactively with
problem- and community-oriented policing in partnership with communities (Doran and
Burgess 2012, p 51). If, however, policing tactics become overly aggressive such as with
zero tolerance, then community relations suffer and fear of crime may increase (Rosenbaum 2006; Tonry 2011). Also, unexplained increased police presence may increase fear
of crime as an indication or reminder of nearby dangers of crime (Hinkle and Weisburd
2008). Nevertheless, Box et al. (1988) found police presence a crucial means for reducing
the fear of crime among citizens. Weisburd et al. (2011) did not find evidence of negative
impacts on community perceptions of police by hot spot enforcement while Braga et al.
(2012) found residents favorable to hot-spot crime enforcement. If community members
are aware that police presence has the purpose of preventing crimes, then perhaps fear of
crime can be reduced.
Detection and Forecasting of Temporary Crime Hot Spots
Forecasting the on-and-off behavior of temporary crime hot spots, when they start and end,
would be highly desirable for efficient prevention of crimes by police. So far forecasting
the timing of changes in time series has not been addressed adequately in the literature
although there is a small literature on detecting and forecasting the start of crime flare ups.
The great majority of demand forecasting methods use space and time series data with
fixed service or product categories (crime types in this case), fixed time increments (e.g.,
days, weeks, months, quarters, etc.), and fixed spatial units (e.g., service or sales territories,
census tracts, etc.). A disadvantage of such data, relative to temporary hot spots, is that
some crimes can occur across boundaries of fixed units and therefore be missed. For
example, a crime flare up might be split between adjacent grid cells and, while not detected
as tabulated, would be detected in a new, custom area unit that combines affected portions
of areas from the adjacent cells. The same is possible for a flare up split across sequential
time intervals.
Some methods exist that build custom spatial units, such as Corcoran et al. (2003) and
the spatial scan statistic (Neill and Gorr 2007). The latter assembles the best set of custom
areal units from small, ‘‘atom’’ units, such as blocks, searching over all possible subsets of
atom units. Recent results make the spatial scan statistic computationally feasible for many
applications (Neill 2009). Nevertheless, each time new data is available, the analyst is
confronted with having to create new custom observation units to communicate to field
123
J Quant Criminol
officers, the computational burden is large, and as yet there is no empirical validation that
such methods are accurate enough for crime prevention work.
The space and time series data of temporary hot spots is best characterized as ‘‘intermittent.’’ Intermittent time series data have very low demand (such as demand for spare
aircraft parts) or are tabulated at such a fine-grained level, that there are many zeros in the
time series data with occasional positive demand points, often clustered in time (Croston
1972; Regattieri et al. 2005). The intermittent time series forecasting literature, however, is
exclusively devoted to inventory management policies and estimation of optimal safety
stocks in order-quantities to minimize inventory holding costs. The objective is to have
enough stock on hand to meet demand with a fairly high probability, given a run with
positive demand, while at the same time not to have excessive stocks. Thus while the
models in this area include estimation of separate parameters for arrival time and demandlevel distributions, they are not concerned with precise timings of demands or durations of
runs. All that is needed is enough stock on hand to meet demand, and that is assured at a
high probability by optimizing the safety stock. The temporary crime hot spot problem,
however, is concerned with precise timing—start up and stopping time points—so that
police resources for crime prevention are not wasted. So intermittent forecast methods in
the literature are not applicable to temporary hot spots.
The great majority of time series models and methods are for regular (non-intermittent)
data, meaning that almost every observation has positive magnitude. The greatest number
of time series forecasting papers are on extrapolative methods that merely extend experienced time trends and seasonal adjustments into the future. The temporary hot spot/
intermittent forecast problem cannot be forecasted by extrapolation. Before positive
demand forecasts are biased low (zero) and after a demand point they biased high (positive
when the demand is again 0).
A smaller time series literature is devoted to models that are ‘‘causal’’ in the sense that
they are multivariate with independent variables. Causal forecast models using lesser
crimes as leading indicators of serious crimes have had some success (Cohen et al. 2007;
Gorr 2009). If leading indicator events/crimes (e.g., shots fired 911 calls, drug 911 calls,
simple assaults) have recently had a large step increase in a spatial unit (or neighboring
areal units), then serious violent crimes (homicide, rape, robbery, and aggravated assault)
will likely have a near-term future increase in the spatial unit. While these models are
much better than chance decisions, they have relatively high false positive rates. A further
limitation of such models is that they require relatively large spatial units (e.g., census
tracts) in order to have accurate estimates of model coefficients, while crime hot spots
generally are much smaller, on the order of blocks. Given a leading-indicator forecast of a
crime flare up, crime analysts must then use expertise, crime mapping, field intelligence,
etc. to determine where exactly and if to intervene within the larger area flagged.
Time series monitoring methods (Brown 1959, 1963; Trigg 1964; McClain 1988; Cohen
et al. 2009) provide an alternative to time series forecasting. These methods have the
objective of detecting an unexpected, large change in time series data as soon as possible.
They are based on decision rules analogous to hypothesis testing using a test statistic based
on departures from extrapolative forecasts. A large, one-step-ahead forecast error (or series
of errors of the same sign) provides evidence of a departure from ‘‘business as usual.’’
Generally time series monitoring is more accurate than time series forecasting (having
higher true positive rates for given false positive rates) but at the cost that initially-detected
crimes can have no prevention exposure, by definition. In contrast, if it were possible to
accurately forecast a temporary hot spot, then the initial crime or crimes could also be
exposed to prevention. Also, as with leading indicator forecasts, the crime analyst must use
123
J Quant Criminol
additional information and expertise to pinpoint locations within larger areal units monitored. Nevertheless, time series monitoring is promising because of their relatively high
true positive rates for given false positive rates (compared to forecasting). For example,
CrimeStat IV (Levine 2013) implements time series monitoring for crime space and time
series data, based on Cohen et al. (2009).
In summary, none of the existing time series models and methods meets the needs of
temporary hot spot management by police for crime prevention. At this time, detection
appears to be the only feasible approach to managing temporary hot spots in a EWS at the
spatial scale of multiple blocks.
Data
Altogether this study had available 2 months less than 21 years of crime offense reports
from the Pittsburgh Bureau of Police—January 1990 through October 2010. These are
official, hierarchy offense reports listing the highest UCR offence for each crime incident.
We chose to analyze part 1 violent (P1V) crimes in aggregate (murder/manslaughter,
forcible rape, robbery, and aggravated assault) because they are the highest priority of
police. We did not filter these crimes to eliminate those not amenable to street-level
prevention measures such as domestic crimes; all P1V crimes were used. Future work with
field experimentation should include such screening, thereby improving accuracy.
We decided to use the 1990–1999 data for exploration work only because conditions in
the city of Pittsburgh and Police Bureau changed significantly by the year 2000. The city
accomplished much in terms of redevelopment of several crime-prone neighborhoods and
had demolished the majority of its public housing developments. Overall violent crime
decreased in Pittsburgh after the peak in 1993 due to the decline of the crack cocaine
epidemic. Also, by the early 2000’s crime mapping was available citywide to both field
officers and police management on a real-time basis, and the police department had
instituted a CompStat process that included reviewing crime patterns. High-density crime
areas became recognized and good targets for police. The share of crime in chronic hot
spots was 50 % less in the 2000’s than it had been in the 1990’s while the percentage of
crime in temporary hot spots increased (Gorr and Lee 2012).
We geocoded offense report data using ArcMap 10, TIGER street centerlines projected
to State Plane coordinates as spatial reference data, and an ArcMap locator using default
settings. The match rate for 2000–2010 data was 86 % which meets to the minimum of
85 % prescribed by Ratcliffe (2004). We used the Grid Index Feature tool of ArcToolbox
to create three grids of polygons with square grid cells, all with the same arbitrary origin,
with cell sizes 500, 750, and 1,000 feet on a side. Spatial overlay of grids on geocoded
crime locations allowed aggregation to monthly time series by grid cell.
Table 1 provides average counts for P1V crimes for Pittsburgh for the 2000–2010 study
period with residential and commercial area crimes broken out. Only 5.5 % of Pittsburgh is
commercial while 48.2 % is residential. The balance of Pittsburgh in addition to commercial and residential areas is not broken out but includes institutional and industrial land
use areas along with large areas that are not inhabited such as steep hillsides, parks, and
cemeteries. With this makeup of Pittsburgh, from Table 1 we calculate that the average
P1V crime density for commercial areas is 128 crimes per percent land area while that of
residential areas is 31. So while there are twice as many residential P1V crimes as commercial, commercial crimes are four times dense than residential crimes. To impact total
123
J Quant Criminol
Table 1 Annual part 1 violent crime statistics: Pittsburgh, 2000–2010
Residential areas of
Pittsburgh
Commercial areas of
Pittsburgh
All of Pittsburgh
Annual
average
Annual
average
Annual
average
Percentage
residential (%)
Percentage
commercial (%)
Percentage
total (%)
Murder-Manslaughter
28
2
7
1
39
2
Rape
68
5
19
3
107
4
Robbery
654
44
458
65
1,302
50
Aggravated assault
741
50
223
32
1,140
44
1,491
100
707
100
2,588
100
Part 1 violent crime
P1V crimes with prevention, it is very desirable, while challenging, to find ways to impact
residential areas.
Ninety-four percent of the P1V crime aggregate is made up of robberies and aggravated
assaults in Pittsburgh as well as its residential areas; however, the percentage of robbery is
higher in the former while the percentage of aggravated assault is higher in the latter, as
might be expected. Furthermore, 58 % of all P1V crimes occur in residential areas,
including 72 % of murder-manslaughter and the majority of rapes and aggravated assaults.
Rule-Based Early Warning System and Experimental Design
The Law of Parsimony suggests simple explanations. Along this line, too often sophisticated methods are no more accurate than simple methods in the realm of prediction and
forecasting (e.g., Makridakis et al. 1982; Makridakis and Hibon 2000), therefore simple
methods should always be considered. The EWS of this paper is simple, has positive
results, is readily implementable by police departments, and provides a baseline for
comparison with more sophisticated methods in future work. It uses the following components for dynamic management of temporary hot spots.
Grid System
For simplicity of data analysis and ease of implementation by police, we decided to
aggregate data by fixed grid cell, rather than spatial buffers of flare-up crime points as is
done for near-repeat crimes or KDS maps. While feasible and perhaps desirable in practice,
buffering or KDS adds geoprocessing steps as well as additional communication
requirements with field police as boundaries change. It is an empirical question as to
whether dynamic boundaries for temporary hot spots provide additional performance over
fixed grids to justify additional effort, and we leave that to future work. The use of fixed
grid cells in this paper provides a proof of concept for temporary hot spots as targets for
crime prevention.
The key question of grid design is the size or scale of hot spot to be considered.
Weisburd et al. (2004, 2012) established that chronic hot spots are composed of micro
areas on the order of one-block long street segments. Ratcliffe (2012), using change point
regression, found elevated densities of violent crimes within 85 feet of bars in Philadelphia.
Gorr and Lee (2012) showed that Pittsburgh’s chronic hot spots are indeed micro areas, but
generally include several adjacent street segments along linear commercial corridors or
123
J Quant Criminol
several contiguous blocks of major commercial areas such as the central business district.
We imagine that temporary hot spots are smaller in size than chronic hot spots. Exploratory
data analysis using Pittsburgh P1V crimes from 1990 through 1999 showed that temporary
crime hot spots cluster both spatially and temporally but over small numbers of blocks as
opposed to a single street segment or block. The near-repeat crime literature (e.g., Johnson
and Bowers 2004a; Ratcliffe and Rengert 2008; Mohler et al. 2011) finds areas of elevated
risk from initial crimes in the range of 150–1,200 feet.
This paper experiments with three alternative square grid systems with cells of sizes 500
feet on a side (approximately four blocks in area), 750 feet on a side (nine blocks), and
1,000 feet on a side (16 blocks). We expected that there would be many cases where two or
more adjacent cells are temporary hot spots, especially for the smaller cell sizes. If we had
chosen to use buffers of initial or flare-up crimes instead of fixed grid cells, we would have
chosen a size less than 500 feet for the smallest grid size. To increase the chance of
capturing an entire or most of a near-repeat cluster with a grid cell, it is necessary to have
grid cells larger than the clusters.
Monthly Data
Another simplification of this paper is to use monthly time series data instead of real-time
occurrences of crimes. A hot spot is ‘‘on’’ after detection if it has one or more P1V crimes
within a month and ‘‘off’’ if none occurred. Below in this section we reason that monthly
data biases the percentage of crimes exposed to prevention measures on the low side but
does not bias workload estimates on the average. Otherwise there are no considerable
errors in using monthly data. Nevertheless, future work should consider weekly and realtime time series data with the potential of improving crime-prevention efficiency.
Stopping Rule
Gorr and Lee (2012) also used monthly data but for custom hot spot boundaries estimated
via KDS, rather than fixed cells, to study temporary hot spots. Their results showed that
temporary hot spots exist for only 1 or 2 months if no time gaps are permitted with ‘‘off’’
months in between ‘‘on’’ months. Further exploration of 1990–1999 P1V crime data in
Pittsburgh suggested that it is common to have a gap of one or more months but then
crimes resume in the area before going ‘‘off’’ for long periods of time. It therefore seemed
worthwhile to allow gaps and to experiment with their size.
As a result, this paper allows time gaps of ‘‘off’’ months with stopping-rule alternatives
of 1, 2, and 3 months in a hot spot cell. For example, suppose that after detection of a hot
spot cell and prevention resources are deployed, a gap of one month allows a temporary hot
spot to continue. Then the stopping rule is 2 months: workload continues until there are
2 months in a row that are off with no additional P1V crimes. For a specific example,
suppose that ‘‘1’’ stands for an ‘‘on’’ month, ‘‘0’’ stands for an ‘‘off’’ month, and subscripts
are month sequence numbers in the following example for a cell:
01 02 13 14 05 16 07 18 09 010
Suppose that rules declare the third month to be the start of a temporary hot spot. The
hot spot exists for 6 months (3–8), prevention work starts in month 4 and stops after month
10. The workload length is 7 months (4–10), and 3 months have their crimes exposed to
prevention measures (months 4, 6, and 8). If month 4 had one crime, month 6 two crimes,
and month 8 one crime, there are four crimes exposed to prevention. The flare-up or
123
J Quant Criminol
initiation crimes of month 3 are not exposed to prevention. In a real-time system, prevention could start immediately after the first crime detected, so if there were two crimes in
the detection month, 3, the second crime could be exposed to prevention. Computational
experiments in this paper, however, assume that prevention does not start until month 4 for
the example and thus bias then number of crimes exposed to prevention on the low side.
Estimates show this bias to be on the order of 10 % low.
The simplification of using monthly data instead of real-time occurrences of crime to
trigger decisions does not bias workload estimates in regard to a real-time system. While
monthly data delays the start of workload by a half month on the average, it also delays
stopping by a half month on the average, cancelling out errors in aggregate statistics.
Detection Rule
While several time series monitoring methods exist to signal changes in time series data (e.g.,
Brown 1959, 1963; Trigg 1964), this paper uses a simple rule with thresholds based on P1V
crime count within a month for each cell. At first, thresholds of 1, 2, 3, etc. were considered,
but monthly crime counts of 2 or higher are infrequent (occurring only 14 % of the time) in
micro-scale locations such as the cells used in this paper. Therefore while we initially considered a flare up to be two or more crimes within close distance and short period, we use a
threshold of one. This decision is justified based on near-repeat crime theory.
Prediction Rule
While the detection rule has the advantage of being highly reactive, by itself it produces
too many false positives. It makes sense to deploy prevention resources only if additional
crimes are expected to occur within the cell in the near term so that they can be exposed to
prevention measures. Hence we add a rule predicting persistence of a flare up to become a
temporary hot spot with additional crimes. A simple rule is to use the history of P1V crime
occurrence within the cell, so we use the number of months with one or more P1V crimes
within the preceding 12 months and thresholds of 1, 2,…, 5 months. There are many
additional and more sophisticated methods for predicting persistence; for example, using
univariate time series methods, multivariate forecasts based on leading indicator crimes
(Cohen et al. 2007; Gorr 2009), near-repeat forecasts (Bowers et al. 2004; Mohler et al.
2011), or a spatial scan statistic (Neill 2009).
Resource Deployment Rule
If both the detection and prediction/persistence rules ‘‘fire’’ or attain thresholds, then police
are deployed for prevention work in the cell. If a particular police zone or precinct does not
have sufficient resources for deployment in all hot spot cells for consideration, the prediction rule magnitudes (number of ‘‘on’’ months in the previous 12 months) can serve as a
score for ranking cells and resource allocation decisions.
Performance Measures
Over a period of computational experiments across the police jurisdiction, the benefit of a
hot spot management system is represented by percentage of total P1V crimes exposed to
prevention measures while cost is the average percentage area of a police jurisdiction under
123
J Quant Criminol
workload. Also considered is the make-up of hot spots, in regard to commercial and
residential land uses. While crime concentrations are highest in large commercial areas, it
is beneficial to provide crime prevention services in widely-scattered residential and small
commercial areas as well to build police/citizenship relations and reduce fear of crime.
Summary of Experiment
We used all Pittsburgh P1V crime data from 2000 through October 2010, plus 1997
through 1999 data for initial chronic hot spot boundary forecasts, to evaluate coordinated
chronic and temporary hot spot programs.
We estimate chronic hot spots with a set of threshold crime concentrations leading to a
tradeoff curve for hot spot sizes over the range from 0 to 5 % of Pittsburgh. We use the
KDS method of Gorr and Lee (2012) for chronic hot spots that estimates a crime density
surface with search radius of 250 feet corresponding for Pittsburgh to the street-segment
scale of Weisburd et al. (2004). Given the economic redevelopment of some of Pittsburgh’s most crime-ridden areas in the latter part of the 1990’s and early 2000’s, it is not
sensible to use all available data (starting in 1990) to estimate current chronic hot spots.
Therefore, we estimate chronic hot spots using 3 years’ historical data. For example, for
year 2000 chronic hot spots we make a KDS estimate using 1997–1999 data, select a
threshold density which if exceeded defines a hot spot, and then forecast that the resulting
hot spots persist throughout 2000. For 2001, we advance the time window one year and
repeat the process, etc. Three years’ data in a moving time window proved sufficiently long
for estimating chronic hot spots while also being somewhat responsive to underlying
changes in crime patterns.
We estimate temporary hot spots over the same range of areas, 0–5 %, using alternative
grid sizes and rule thresholds in all possible combinations for EWS. Grid sizes were 500,
750, and 1,000 feet on a side. Thresholds were as follows: detection rule threshold = 1
P1V crime; prediction rule thresholds = 1, 2, 3, 4, and 5 months; and stopping rule
thresholds = 1, 2, and 3 months. The frontier of experimental points plotted as percentage
P1V crime exposed to prevention versus percentage of Pittsburgh under prevention
workload is the optimal tradeoff curve. For the combination hot spot program, we estimate
chronic hot spots covering one percent of Pittsburgh’s area and then apply the rule-based
EWS to remaining crimes outside of chronic hot spots, using the same experimental
variations as in the previous paragraph. We assume that prevention resources are constantly allocated to those chronic areas, but that resources are dynamically allocated to
temporary hot spots according to EWS rules.
Results
From the computational experiments described in the previous section, we first provide
estimates of the maximum-size hot spot programs feasible in Pittsburgh given current
resources. Then we present tradeoff curves for the three hot spot programs considered.
Finally we present sample maps of hot spots along with some resulting statistics.
Estimates of Feasible Workload Area
Using a simple Excel spread sheet model, we estimate that currently the Pittsburgh Police
could have a hot spot program of 12–16 random patrols per day per hot spot (chronic and/
123
J Quant Criminol
or EWS) in the range of about 2–3 % of Pittsburgh’s area (workload). While these are at
best rough estimates, using the most favorable end points of parameter ranges, we find that
5 % workload is infeasible.
The model incorporates the number of patrol units (36–42); average time per shift
available for patrolling hot spots (only a half hour to one hour due to reduced numbers of
sworn officers in Pittsburgh due to budget limitations and resulting high 911 call loads per
officer2); average patrol speed including stops for traffic signals (5–15 miles per hour); size
and shape of temporary hot spots made up of 500 foot cells (isolated, linear, and compact
multiple-cell areas); and efficient looping drive patterns in square, equal-size blocks with
two-way streets that first loop consecutively through north–south streets or east–west
streets and then loop through the remaining streets in the other orientation. In addition,
according to Pittsburgh Police policy, patrols must ‘‘park and walk’’ at least a half hour per
shift and this resource would also be available for hot spots.
Tradeoff Curves
Figure 1 shows the three tradeoff curves for the chronic, EWS, and combined chronic and
EWS programs. All three programs have decreasing marginal benefits as expected, and the
combination program has the best overall efficiency, equaling that of the chronic curve up
to 1 % workload and then exceeding both the chronic and EWS curves thereafter. Figure 1
estimates that the combination program could provide 27 % exposure of total P1V crimes
in Pittsburgh to prevention for 2 % workload and 33 % exposure for 3 % workload. A
chronic hot spot program would be close, with 26 % exposure at 2 % workload and 31 %
exposure at 3 %, and the EWS would be somewhat worse at 23 % exposure at 2 %
workload and 29 % at 3 %. As noted in the data section of this paper, these estimates of
prevention exposure are in addition to the good policing practices already used by the
Pittsburgh Police Bureau.
To use a tradeoff curve for implementation, one must tabulate a ‘‘reverse function’’
when building the curve for looking up the threshold crime density corresponding to a
point on the curve. For EWS hot spots one must be able to look up the optimal grid size and
decision rule thresholds. Of note is the EWS reverse function. Table 2 has a sample of
points for the combination program’s EWS. For 2 % total workload (1 % chronic and 1 %
EWS), the optimal grid size is 500 feet on a side, 3 of the previous 12 months of a cell have
to have at least 1 P1V crime each, and workload persists until a gap of more than 2 months
occurs before stopping. For 2.7 % total workload, the only change is the more liberal
persistence rule of 2 instead of 3 months with 1 or more P1V crimes. The grid size of 750
feet does not enter until 7.6 % workload and 1,000 feet does not enter 10 % for the tradeoff
curve.
Hot Spot Maps
Figures 2 and 3 are maps of P1V crime hot spots. Figure 2 compares two hot spot programs, chronic and EWS, each covering 3 % of Pittsburgh’s area for 2009 (the last full
year of data available). The chronic hot spot areas are constant throughout 2009 while the
2
This estimate was provided by Commander Brackney of the Pittsburgh Police Bureau through personal
communication. In contrast, one estimate in the literature (Famega et al. 2005) is that up to 75 % of patrol
officers’ time is not spent answering calls, so other cities may have higher average times available for hot
spot patrol than Pittsburgh.
123
J Quant Criminol
Fig. 1 Tradeoff curves for chronic, EWS, and combination program hot spots: 2000–2010
Table 2 Optimal grid sizes
and rule thresholds for the
EWS of the combination hot
spot program: 2000–2010
Prediction rule
(months)
Stopping
rule
(months)
Workload
(percentage area
of Pittsburgh)
Grid size
(length of
side, feet)
1.0
Substituted by chronic hot spots system
1.3
500
4
1
1.6
500
4
2
1.8
500
4
3
2.0
500
3
2
2.4
500
3
3
2.7
500
2
2
3.4
500
2
3
5.0
500
1
3
7.6
750
2
3
10.3
750
1
3
EWS hot spots change each month. Shown are July 2009 EWS hot spots. All cells in
Pittsburgh with one or more P1V crimes in July 2009 are shown as solid circles (these are
positives). A cell that had prevention workload in July 2009 (and perhaps could have been
prevented) is shown as a solid circle with the square boundary of the cell (true positives). A
solid circle without a square boundary around it is a false negative. Cells without solid
circles but square boundary shown had workload but no P1V crimes (false positives). Also
shown on the map are separate boundaries of commercial and poverty areas of Pittsburgh.
Note that because of the computational experiments behind these figures in which there
123
J Quant Criminol
Fig. 2 Map comparing 3 % area chronic hot spots (2009) with 3 % EWS hot spots (July 2009): part 1
violent crimes
was no hot spot policing in effect, it is possible to identify all the cases listed above. In
practice with hot spot policing, however, crimes that occurred as true positives may be
prevented and then show up incorrectly as false positives.
There are several observations from this map. First, there are clear overlaps of chronic
hot spots and EWS workload cells and there are numerous workload cells outside of
chronic hot spots. Second, chronic hot spots tend to have one or more positive cells, but
many areas (represented as cells) in chronic hot spots did not have crimes (perhaps due to
‘‘cops on the dots’’ already preventing crimes). Third, chronic hot spots tend to be in large
commercial areas and/or poverty areas. Fourth, EWS workload areas outside of chronic hot
spots are widely-scattered and tend to be in small commercial or non-commercial areas
(another map, not included in this paper, shows the non-commercial areas to be largely
residential). Of course, maps of other months have some of the same and many different
workload cells due to the dynamics of the EWS.
Figure 3 is a map of the combination program with 1 % chronic hot spots supplemented
with 2 % EWS hot spots. Not shown are crimes within chronic hot spots, but only shown
are cells with one or more P1V crimes outside of chronic hot spots. In comparing this map
to that of Fig. 2 with 3 % chronic hot spots, one can see that some chronic hot spots have
disappeared and all are smaller in size, shedding lower crime density areas. In the place of
removed chronic hot spot area are EWS workload cells. Also there are a great many EWS
workload cells scattered throughout the city.
123
J Quant Criminol
Fig. 3 Map for the combination hot spot program with total 3 % area workload (1 % chronic with 2 %
EWS): part 1 violent crimes
Table 3 Commercial and
residential land uses for
alternative hot spot programs
with 3 % area workload:
2000–2010
Hot spots
combination
Residential
(%)
Chronic
49
36
15
EWS
56
22
22
Combination
56
24
20
Commercial
(%)
Balance
(%)
Lastly, Table 3 has the 3 % total workload areas of each hot spot program broken out by
residential, commercial, and balance of Pittsburgh areas. Here you can see that chronic hot
spots have the largest share of commercial areas (36 vs 22 and 24 % for the EWS and
combination programs) while the EWS and combination programs have the largest residential share (56 vs 49 % for chronic hot spots). Overall the EWS has 22 % more residential and non-commercial hot spots than do chronic hot spots, and combination hot spots
have 19 % more residential and non-commercial hot spots.
Discussion
One implication of this paper’s findings is that hot-spot size potentially could have dramatic impacts on performance in hot-spot field experiments. As noted earlier in this paper,
123
J Quant Criminol
Pittsburgh’s chronic hot spots, estimated via KDS, are steeply peaked so that after hot spots
covering the 1 % hottest areas, crime density falls off exponentially with additional
chronic hot spot area. Perhaps studies such as reported in Braga et al. (2012) had a variety
of hot spot sizes so that corresponding crime densities could account for a significant
variation in crime reduction.
The EWS has the needed components for dynamic decision making on crime hot spots,
and its underlying methods are simple and easy to implement. There are, however, more
sophisticated detection and prediction methods available than those used in this paper. For
example, detection can use time series monitoring methods instead of occurrence of a
crime as used in this paper. The spatial scan statistic, based on city blocks, is a prime
candidate for making improvements in detection. Perhaps LISA and Gi* statistics of spatial
association could improve identification of spatial clusters. Also, additional data about the
nature of detected crimes (e.g., has gang involvement, involved illegal drug dealing) might
better predict persistence of a temporary hot spot than the rule used in the paper based only
on historical frequency of ‘‘on’’ months in a cell. Additional computational experiments,
before field research, may improve efficiency of the EWS.
The existing literature has field research results for chronic hot spots. The first step for
empirical research on the EWS is to estimate effect size of crime prevention for temporary
hot spots. It would be straightforward to design and run a controlled experiment for this
purpose because the relatively wide separation of temporary hot spots allows for treatments
that do not contaminate controls.
Summary
This paper developed and conducted preliminary computational experiments on an EWS
for crime prevention at temporary hot spots as a supplement to chronic hot spots using part
1 violent (P1V) crime data from Pittsburgh, Pennsylvania (2000–2010). Chronic hot spots
have high crime densities continuously over long periods, years, and merit constant police
resource allocations for crime prevention. Temporary hot spots also have high crime
densities but only for durations of time on the order of months and generally over smaller
areas than chronic hot spots. While chronic hot spots are relatively simple to identify and
manage, temporary hot spots require a dynamic decision-making system, an EWS, for
early detection of crime flare-ups, predicting persistence of crimes after detection,
deploying prevention resources, and stopping deployments after a temporary hot spot is
extinguished. This paper provided a simple rule-based EWS.
The Pittsburgh Police Bureau has used crime mapping (putting ‘‘cops on the dots’’),
CrimeStat management, and other modern policing practices, such as ‘‘park and walk,’’
since the early 2000s but has not conducted centralized or sustained hot spot programs
during the study period. Thus Pittsburgh provided an ideal test bed for estimating the
effectiveness of hot spot programs for additional crime prevention above that provided by
modern policing practices.
The empirical study compared the efficiency of chronic, EWS, and combination chronic
and EWS programs via tradeoff curves of benefits versus costs represented by percentage
of P1V crime that could have been exposed to prevention efforts and percentage area of
Pittsburgh under prevention workload by police. A second criterion, assessed by GIS
analysis, is the distribution of hot spots and allocation of police prevention resources across
the city. A program that allocates resources equitably and responsively to prevent crimes
and reduce fear of crime is desirable.
123
J Quant Criminol
We forecasted chronic hot spot boundaries one year ahead using kernel density
smoothing (KDS) applied to a three-year moving window of data and obtained a chronic
hot spot tradeoff curve by varying the threshold concentration defining hot spot boundaries.
We defined temporary hot spots using grid cells of alternate sizes and varied decision rule
thresholds for predicting hot spot persistence and stopping. The frontier of all experimental
points, plotted as benefits versus costs, provided the EWS tradeoff curve. The combined
hot spot program uses chronic hot spots up to 1 % area of Pittsburgh under prevention
workload and then adds temporary hot spots for areas outside of chronic hot spots, again
producing a tradeoff curve. The rationale for this program was that crime density declines
exponentially as percentage area workload increases for chronic hot spots so that additional
area after about 1 % has behavior closer to temporary hot spots. Also, feasible areas for
chronic hot spots are a subset of feasible areas for temporary hot spots so that after the
hottest areas are assigned to chronic hot spots, there may exist better or simply more of the
best temporary hot spots such as adjacent to the hottest chronic hot spots.
The research included a simple spreadsheet simulation to roughly estimate the maximum percentage area of Pittsburgh that the Pittsburgh Police Bureau could cover with
12–16 random patrols per day with existing resources. Varying the many parameters, we
concluded that the range is from about 2–3 % but certainly not as high as 5 %. We thus
provided tradeoff curves over the range from 0 to 5 % area. They show the combination
hot spot program to be the most efficient, exposing 33 % of Pittsburgh’s P1V crimes to
prevention at 3 % area, but not by a great deal over the chronic hot spot program. The
EWS program is dominated by the other two programs, but again, not by much.
Chronic hot spots tend to exist in large commercial areas, or in residential areas adjacent
to large commercial areas, and in poverty areas. Of course, they are fixed in location over
long periods of time. Temporary hot spots change from month to month and are widely
scattered across the city, including smaller commercial areas and more residential areas.
Hence temporary hot spots managed via the EWS are more equitable and responsive to
changing crime patterns than chronic hot spots. Indeed the EWS can be the basis of a
positive relationship between police and neighborhoods to prevent and reduce fear of
crime. The combination hot spot program has the best of both chronic and temporary hot
spots, with the highest-efficiency crime prevention overall plus dynamic and widespread
crime prevention across a city, providing more responsive and equitable allocations of
police prevention resources than a solely-chronic hot spot program.
Acknowledgments We are grateful to Professors Al Blumstein, John Eck, Daniel Neill, Jerry Ratcliffe,
and David Weisburd for their suggestions on our earlier research leading to the current paper. We also wish
to thank Acting Chief Regina McDonald, Commander RaShall Brackney, and Detective Deborah Gilkey of
the Pittsburgh Bureau of Police for assistance with the crime data used in this paper and their insights into
crime patterns in Pittsburgh. Finally, we owe our gratitude to the referees and editors for their many
insightful suggestions.
References
Block CR (1995) STAC hot-spot areas: a statistical tool for law enforcement decisions. In: Crime analysis
through computer mapping. Police Executive Research Forum, Washington, pp 15–32
Blumstein A, Cohen J, Das S, Moitra SD (1988) Specialization and seriousness during adult criminal
careers. J Quant Criminol 4:303–345
Bowers KJ, Johnson SD, Pease K (2004) Prospective hot-spotting the future of crime mapping? Br J
Criminol 44:641–658
Box S, Hale C, Andrews G (1988) Explaining fear of crime. Br J Criminol 28:340–356
123
J Quant Criminol
Brackney, Commander R (2/14/2013) Pittsburgh Bureau of Police, private communication
Braga AA, Weisburd DL (2010) Policing problem places: crime hot spots and effective prevention. Oxford
University Press, USA
Braga AA, Weisburd DL, Waring EJ, Mazerolle LG, Spelman W, Gajewski F (1999) Problem-oriented
policing in violent crime places: a randomized controlled experiment. Criminology 37:541–580
Braga AA, Papachristos AV, Hureau DM (2010) The concentration and stability of gun violence at micro
places in Boston, 1980–2008. J Quant Criminol 26:33–53
Braga AA, Hureau DM, Papachristos AV (2011) The relevance of micro places to citywide robbery trends: a
longitudinal analysis of robbery incidents at street corners and block faces in Boston. J Res Crime
Delinquency 48:7–32
Braga AA, Papachristos AV, Hureau DM (2012) The effects of hot spots policing on crime: an updated
systematic review and meta-analysis. Justice Q 29:1–31
Brown RG (1959) Statistical forecasting for inventory control. McGraw-Hill, New York
Brown RG (1963) Smoothing, forecasting and prediction of discrete time series. Prentice-Hall, Englewood
Cliffs
Chainey S, Ratcliffe J (2005) GIS and crime mapping. Wiley, New York
Chainey S, Reid S, Stuart N (2002) When is a hotspot a hotspot? A procedure for creating statistically robust
hotspot maps of crime. Taylor and Francis, London, pp 21–36
Chainey S, Tompson L, Uhlig S (2008) The utility of hotspot mapping for predicting spatial patterns of
crime. Secur J 21:4–28
Clarke RV, Weisburd DL (1994) Diffusion of crime control benefits: observations on the reverse of displacement. In: Clarke RV (ed) Crime prevention studies. Criminal Justice Press, New York
Cohen LE, Felson M (1979) Social change and crime rate trends: a routine activity approach. Am Sociol
Rev 44:588–605
Cohen J, Tita G (1999) Spatial diffusion in homicide: exploring a general method of detecting spatial
diffusion processes. J Quant Criminol 15:451–493
Cohen J, Gorr W, Singh P (2003) Estimating intervention effects in varying risk settings: do police raids
reduce illegal drug dealing at nuisance bars. Criminology 41:257–292
Cohen J, Gorr WL, Olligschlaeger AM (2007) Leading indicators and spatial interactions: a crime-forecasting model for proactive police deployment. Geogr Anal 39:105–127
Cohen J, Garman S, Gorr W (2009) Empirical calibration of time series monitoring methods using receiver
operating characteristic curves. Int J Forecast 25:484–497
Corcoran JJ, Wilson ID, Ware JA (2003) Predicting the geo-temporal variations of crime and disorder. Int J
Forecast 19:623–634
Craglia M, Haining R, Wiles P (2000) A comparative evaluation of approaches to urban crime pattern
analysis. Urban Stud 37:711–729
Croston JD (1972) Forecasting and stock control for intermittent demands. J Oper Res Soc 23:289–303
DeLisi M (2001) Extreme career criminals. Am J Crim Justice 25:239–252
Doran BJ, Burgess MB (2012) Putting fear of crime on the map. Springer, New York
Eck JE (1994) Drug markets and drug places: a case-control study of the spatial structure of illicit drug
dealing. Doctoral dissertation, University of Maryland, Faculty of the Graduate School
Eck JE (1997) Preventing crime at places. In: Sherman LW, Gottfredson D, MacKenzie D, Eck J, Reuter P,
Bushway S (eds) Preventing crime: what works, what doesn’t, what’s promising—a report to the
attorney general of the United States, Chap. 7. United States Department of Justice, Office of Justice
Programs, Washington
Famega CN, Frank J, Mazerolle L (2005) Managing police patrol time: the role of supervisor directives.
Justice Q 22:540–559
Felson M (1986) Linking criminal choices, routine activities, informal control, and criminal outcomes. The
reasoning criminal. Springer New York, pp 119–128
Felson M (1987) Routine activities and crime prevention in the developing metropolis. Criminology
25:911–931
Garland R (9/14/2012) Pittsburgh initiative to reduce crime. University of Pittsburgh, private
communication
Gorr WL (2009) Forecast accuracy measures for exception reporting using receiver operating characteristic
curves. Int J Forecast 25:48–61
Gorr WL, Lee YJ (2012) Longitudinal study of crime hot spots: dynamics and impact on part 1 violent
crime. In: Proceedings of the 32nd international symposium on forecasting, June 2012
Greene JA (1999) Zero tolerance: a case study of police policies and practices in New York City. Crime
Delinquency 45:171–187
123
J Quant Criminol
Grohe BR (2007) Perceptions of crime, fear of crime, and defensible space in Fort Worth neighborhoods.
Doctoral dissertation, University of Texas at Arlington
Grubesic TH (2006) On the application of fuzzy clustering for crime hot spot detection. J Quant Criminol
22:77–105
Haining R (2012) Ecological analysis of urban offence and offender data. In: The urban fabric of crime and
fear. Springer, Netherlands, pp 141–163
Harries K (1999) Mapping crime: principle and practice. No. NCJ 178919
Hesseling RBP (1995) Displacement: a review of the empirical literature. Crime prevention studies.
Criminal Justice Press, New York
Hinkle JC, Weisburd DL (2008) The irony of broken windows policing: a micro-place study of the relationship between disorder, focused police crackdowns and fear of crime. J Crim Justice 36:503–512
Jacobs BA, Topalli V, Wright R (2000) Managing retaliation: drug robbery and informal sanction threats.
Criminology 38:171–198
Jefferis E (1999) A multi-method exploration of crime hot spots: a summary of findings. US Department of
Justice, National Institute of Justice, Crime Mapping Research Center, Washington
Johnson SD, Bowers KJ (2004a) The burglary as clue to the future the beginnings of prospective hotspotting. Eur J Criminol 1:237–255
Johnson SD, Bowers KJ (2004b) The stability of space-time clusters of burglary. Br J Criminol 44:55–65
Keane C (1998) Evaluating the influence of fear of crime as an environmental mobility restrictor on
women’s routine activities. Environ Behav 30:60–74
Kling JR, Liebman JB, Katz LF (2007) Experimental analysis of neighborhood effects. Econometrica
75:83–119
Levine N (2013) CrimeStat IV: a spatial statistics program for the analysis of crime incident locations. Ned
Levine and Associates/National Institute of Justice, Houston/Washington
Makridakis S, Hibon M (2000) The M3 competition: results, conclusions and implications. Int J Forecast
16:451–476
Makridakis S, Andersen A, Carbone R, Fildes R, Hibon M, Lewandowski R, Newton J, Parzen E, Winkler R
(1982) The accuracy of extrapolation (time series) methods: results of a forecasting competition.
J Forecast 1:111–153
McClain JO (1988) Dominant time series monitoring methods. Int J Forecast 18:563–572
McGuire PG, Williamson D (1999) Mapping tools for management and accountability. In: Third international crime mapping research center conference, Orlando, pp 11–14
Miethe T (1991) Citizen-based crime control activity and victimization risks: an examination of displacement and free rider effects. Criminology 29:419–441
Mohler GO, Short MB, Brantingham PJ, Schoenberg FP, Tita GE (2011) Self-exciting point process
modeling of crime. J Am Stat Assoc 106:100–108
Moore MH, Trojanowicz RC (1988) Policing and the fear of crime. National Institute of Justice, Washington, pp 1–7
Morgan F (2001) Repeat burglary in a Perth suburb: indicator of short-term or long-term risk? Crime
Prevent Stud 12:83–118
Nagin DS (1999) Analyzing developmental trajectories: a semiparametric group-based approach. Psychol
Methods 4:139–157
Nasar JL, Fisher B, Grannis M (1993) Proximate physical cues to fear of crime. Landsc Urban Plann
26:161–178
Neill DB (2009) Expectation-based scan statistics for monitoring spatial time series data. Int J Forecast
25:498–517
Neill DB, Gorr WL (2007) Detecting and preventing emerging epidemics of crime. Adv Dis Surveill 4:13
Olligschlaeger AM in McEwen, T, Weisburd, D (ed) (1998) Crime mapping & crime prevention. Criminal
Justice Press, Monsey
Pease K (1998) Repeat victimisation: taking stock (Crime Detection and Prevention Series Paper 90). Home
Office Police Research Group, London
Piquero A (2000) Frequency, specialization, and violence in offending careers. J Res Crime Delinquency
37:392–418
Popkin SJ, Levy DK, Harris LE, Comey J, Cunningham MK, Buron L, Woodley W (2002) HOPE VI panel
study: Baseline report (http://www.urban.org/publications/410590.html)
Ratcliffe JH (2004) Geocoding crime and a first estimate of a minimum acceptable hit rate. Int J Geogr Inf
Sci 18:61–72
Ratcliffe JH (2012) The spatial extent of criminogenic places: a changepoint regression of violence around
bars. Geog Anal 44:302–320
Ratcliffe JH, Rengert GF (2008) Near-repeat patterns in Philadelphia shootings. Security J 21:58–76
123
J Quant Criminol
Ratcliffe J, Taniguchi T, Groff E, Wood J (2011) The Philadelphia foot patrol experiment: a randomized
controlled trial of police patrol effectiveness in violent crime hotspots. Criminology 49:795–831
Regattieri A, Gamberi M, Gamberini R, Manzini R (2005) Managing lumpy demand for aircraft spare parts.
J Air Transp Manag 11:426–431
Rengert GF, Piquero AR, Jones P (1999) Distance decay reexamined. Criminology 37:427–446
Reppetto T (1976) Crime prevention and the displacement phenomenon. Crime Delinquency 22:166–177
Rosenbaum DP (2006) The limits of hot spots policing. In: Weisburd D, Braga AA (eds) Police innovation:
contrasting perspectives. Cambridge University Press, New York, pp 245–263
Sanbonmatsu L, Ludwig J, Katz LF, Gennetian LA, Duncan GJ, Kessler RC, Adam E, McDade TW, Lindau
ST (2011) Moving to opportunity for fair housing demonstration program—final impacts evaluation
Scherdin MJ (1986) The halo effect: psychological deterrence of electronic security systems. Inf Technol
Libr 5:232–235
Sherman LW (1995) Hot spots of crime and criminal careers of places. Crime Place 4:35–52
Sherman L, Buerger M, Gartin P (1989a) Repeat call address policing: the Minneapolis RECAP experiment.
Crime Control Institute, Washington
Sherman LW, Gartin PR, Buerger ME (1989b) Hot spots of predatory crime: routine activities and the
criminology of place. Criminology 27:27–55
Skogan W (1986) Fear of crime and neighborhood change. Crime Justice 8:203–229
Skogan WG, Maxfield MG (1981) Coping with crime: individual and neighborhood reactions. Sage Publications, Beverly Hills, p 272
Spelman W (1995) Criminal careers of public places. In: Eck JE, Weisburd D (eds) Crime and places: crime
prevention studies 4. Willow Tree Press, New York
Taylor RB, Hale M (1986) Testing alternative models of fear of crime. J Crim Law Criminol 77:151–189
Tita G, Ridgeway G (2007) The impact of gang formation on local patterns of crime. J Res Crime
Delinquency 44:208–237
Tonry M (2011) Less imprisonment is no doubt a good thing. Criminol Public Policy 10:137–152
Townsley M, Homel R, Chaseling J (2003) Infectious burglaries: a test of the near repeat hypothesis. Br J
Criminol 43:615–633
Trigg DW (1964) Monitoring a forecasting system. Oper Res Q 15:271–274
Weisburd D, Braga AA (eds) (2006) Hot spots policing as a model for police innovation. Police innovation:
contrasting perspectives. Cambridge University Press, New York, pp 225–244
Weisburd DL, Bushway S, Lum C, Yang S (2004) Trajectories of crime at places: a longitudinal study of
street segments in the city of Seattle. Criminology 42:283–321
Weisburd DL, Wyckoff LA, Ready J, Eck JE, Hinkle JC, Gajewski F (2006) Does crime just move around
the corner? A controlled study of spatial displacement and diffusion of crime control benefits.
Criminology 44:549–592
Weisburd DL, Hinkle JC, Famega C, Ready J (2011) The possible ‘‘backfire’’ effects of hot spots policing:
an experimental assessment of impacts on legitimacy, fear and collective efficacy. J Exp Criminol
7:297–320
Weisburd DL, Groff ER, Yang SM (2012) The criminology of place: street segments and our understanding
of the crime problem. Oxford University Press, Oxford
Wilcox P, Eck JE (2011) Criminology of the unpopular. Criminol Public Policy 10:473–482
123