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Marchmentand Gill Crime Sci (2021) 10:12
https://doi.org/10.1186/s40163-021-00149-6
SYSTEMATIC REVIEW
Systematic review andmeta-analysis ofrisk
terrain modelling (RTM) asaspatial forecasting
method
Zoe Marchment* and Paul Gill
Abstract
Background: Several studies have tested the reliability of Risk Terrain Modelling (RTM) by focusing on different geo-
graphical contexts and types of crime or events. However, to date, there has been no attempt to systematically review
the evidence on whether RTM is effective at predicting areas at high risk of events. This paper reviews RTM’s efficacy
as a spatial forecasting method.
Methods: We conducted a systematic review and meta-analysis of the RTM literature. We aggregated the available
data from a sample of studies that measure predictive accuracy and conducted a proportion meta-analysis on studies
with appropriate data.
Results: In total, we found 25 studies meeting the inclusion criteria. The systematic review demonstrated that RTM
has been successful in identifying at risk places for acquisitive crimes, violent crimes, child maltreatment, terrorism,
drug related crimes and driving while intoxicated (DWI). The proportion meta-analysis indicated that almost half of
future cases in the studies analysed were captured in the top ten per cent of risk cells. This typically covers a very small
portion of the full study area.
Conclusions: The study demonstrates that RTM is an effective forecasting method that can be applied to identify
places at greatest risk of an event and can be a useful tool in guiding targeted responses to crime problems.
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Background
Research consistently demonstrates crime is spatially
concentrated. Urban crimes, such as burglary and rob-
bery, occur most often near common routine activity
nodes (Bowers, 2014) and in places known to a large
number of people (Davies & Johnson, 2015; Johnson
& Bowers, 2010). is has profound implications for
policing, as finite resources can be focused on identi-
fied micro-level places (Braga etal., 2014; Kennedy etal.,
2016). Multiple methods exist to identify crime hotspots
using retrospective analyses, including spatial and tem-
poral analysis of crime (STAC) (Block and Block 2004),
kernel density estimation (KDE) (Chainey et al., 2008),
and nearest neighborhood hierarchical (Nnh) clustering
(Levine, 2004). is paper synthesises the evidence base
on an alternate approach, risk terrain modelling (RTM)
(Caplan & Kennedy, 2010). is method builds upon tra-
ditional hotspot techniques by including measures that
reflect the study area’s physical and social environment.
Building on the foundations of environmental crimi-
nology, Caplan and Kennedy (2010) developed risk ter-
rain modelling. Whereas competing predictive models
rely solely on retrospective analyses, RTM additionally
incorporates theoretical foundations in the spatial analy-
sis of crime and identifies the spatial risks determined by
the features of a landscape (Caplan etal., 2011a, Caplan
etal., 2011b). e combination of multiple criminogenic
features at the same place contributes to a risk value that
Open Access
Crime Science
*Correspondence: zoe.marchment@ucl.ac.uk
Department of Security and Crime Science, UCL, London, England
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Page 2 of 11
Marchmentand Gill Crime Sci (2021) 10:12
indicates the likelihood of crime occurring in that area
and represents that area’s vulnerability to crime (Ken-
nedy et al., 2016). is value can be used to forecast
where crime will occur over a period of time.
RTM includes many concepts from crime pattern the-
ory and is capable of measuring Brantingham and Brant-
ingham’s (1993) concepts of crime generators and crime
attractors. e RTM process tests a variety of factors that
are thought to be geographically related to incidents. It
then identifies the features that are potentially correlated
with the presence or absence of future event(s) in a par-
ticular location. Because RTM includes contextual infor-
mation relevant to the social and physical environment it
can be used to identify areas within a city that have the
greatest estimated opportunity and therefore pose the
highest level of risk of future incidents. As well as identi-
fying places where events will persist, it can also identify
areas where places may emerge or displace, based on rel-
atively stable environmental and contextual risk factors
that go beyond incident-based data.
To improve the accessibility of RTM to practitioners,
Rutgers University developed software that automates
the process: the Risk Terrain Modeling Diagnostics
(RTMDx) Utility. is tool evaluates the relative influ-
ence and importance of risk factors using a bidirectional
stepwise regression process. e variables are examined
and the most problematic risk factors are selected, along
with their most appropriate spatial influence distance, to
build the overall best model. RTMDx allows for two types
of model: aggravating (to identify factors that increase
risk) and protective (to identify factors that decrease
risk).1
Spatial influence considers the qualities of features on
locations of crimes, i.e., it “describes the way in which
features of a landscape affect places throughout the land-
scape” (Caplan, 2011: 532). Certain places within the
spatial influence of criminogenic features may be more
vulnerable to crime than those not within this spatial
influence and can therefore be considered riskier. Two
parameters for spatial influence of each variable can be
assessed in RTMDx, based on proximity or density. Spa-
tial influence for proximity is operationalised as the pres-
ence of a physical feature within the defined distance
from the event. Spatial influence for density is operation-
alised as a high concentration of a physical feature within
the defined distance from the event.
In the software it is also necessary to define the grid cell
size for the outputs. Caplan and Kennedy suggest that
using the average street length with a cell raster size of
half a street length is appropriate to create the cells. Tay-
lor and Harrell (1996) propose that places prone to crime
consist of a few streets, and this measure is a realistic
area to use for the guidance of future policing measures.
In RTMDx, the testing process begins by building an
elastic net penalised regression model assuming a Pois-
son distribution of events. e process then selects
variables that may be potentially useful through cross
validation, which are then utilised in a bidirectional step-
wise regression process (starting with a null model),
to build the optimal model by optimising the Bayesian
Information Criteria (BIC). is score is a balance of
complexity of the model and fit of the data. e models
also include two intercept terms that represent the back-
ground rate of events and overdispersion of the event
counts. Exponentiated coefficient values are used to pro-
duce the relative risk values, which can be interpreted as
the weights of the risk factor (Caplan etal., 2013b). ese
can be used to understand the riskiness of each factor rel-
ative to one another.
Several studies tested RTM’s reliability by focusing on
different geographical contexts and types of crime or
events. However, to date, there has been no attempt to
systematically review the evidence on whether RTM is
effective at predicting areas at high risk of events. is
paper reviews RTM’s efficacy as a spatial diagnostic and
forecasting method. We conducted a systematic review
and meta-analysis of the RTM literature. We answered
this by aggregating the available data from a sample of
studies that measure predictive accuracy and conducting
a proportion meta-analysis on studies with appropriate
data. In the following sections, we first discuss the meth-
odology, followed by the synthesized results. We con-
clude with a discussion of the implications of our findings
for future research. Our results reinforce earlier recogni-
tions of RTM as an effective forecasting method.
Methodology
Identifying studies: databases andinformation sources
Studies were identified using the following search
methods:
(a) A keyword search of relevant electronic databases
(b) Forward and backward citation searches of candi-
date studies.
We searched two electronic databases (Web of Sci-
ence and ProQuest Central). Full text versions of identi-
fied studies were obtained through one of the following
means (in order of preference): electronic copies via
the university’s e-journals service, electronic copies of
studies available from elsewhere on the internet, paper
1 See Hefner, J. (2013). Statistics of the RTMDx Utility. In J. Caplan, L. Ken-
nedy, and E. Piza, Risk Terrain Modeling Diagnostics Utility User Manual
(Version 1.0). Newark, NJ: Rutgers Center on Public Security.
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Page 3 of 11
Marchmentand Gill Crime Sci (2021) 10:12
copies, electronic/paper copies requested through the
inter-library loan system (which sources most materi-
als from the British Library) and electronic/paper copies
requested from the authors themselves.
We used the following inclusion criteria:
(a) e study must have used RTM to identify risk fac-
tors for one or more crime types in a defined geo-
graphical area
(b) e study must have reported at least one meas-
ure of predictive accuracy, e.g. percentage of future
events captured in high risk areas, logistic regres-
sion, predictive accuracy index, recapture rate
index. A predictive tool can be considered accurate
when its results are useful for forecasting a large
number of future events.
e review considered peer reviewed studies that were
published in print or available online from January 2010
to March 2020. We chose to only include peer reviewed
studies to avoid the inclusion of non-peer reviewed
studies that may have affected the outcome of the meta-
analysis. Studies were limited to English because of the
language skills existing in the team. e search strategy
for the systematic review is based on the Campbell Col-
laboration method Campbell Collaboration (2017).
Search terms
In order to discover relevant items for the systematic
review, a number of search terms were used in the above
electronic databases:
– Risk AND terrain AND model*
– Risk-terrain AND model*
– Place-based AND correlate*
– Place AND based AND correlate*
– Place-based AND risk AND factor*
– Spatial AND correlate*
– Spatial AND risk AND factor*
ese search terms resulted in 5067 unique studies
(once duplicates were removed) which required screen-
ing. e first level of screening involved the review team
(Marchment and Gill) examining the title and abstract of
those studies returned following our electronic and bib-
liographic searches.
Next, the studies were read in their entirety in order to
rigorously judge whether they should be included in the
full systematic review and meta-analysis. Of those stud-
ies brought forward to the final phase of the systematic
review, backwards and forwards citation searches were
performed to pursue further candidate studies. is
involved reviewing the titles of each study cited within
the initially included study (e.g. backwards) and also the
subsequent citations that each candidate study accrued
up to and including the end of April 2020 according to
Google Scholar (e.g. forwards). e forwards citation
search was conducted first. A forward and backward cita-
tion search was also conducted on studies found in these
initial citation searches and this continued until all lines
of inquiry were complete.
In total, we found 25 studies meeting the inclusion
criteria (see Table1). All items and variables measured
in these studies were then extracted from the original
papers, synthesised and outlined in the below sections.
Proportion meta‑analysis
As the results of the studies were typically reported as
non-comparative outcomes, a proportion meta-analysis
was appropriate, and conducted to estimate the pooled
proportion and 95% confidence intervals of cases accu-
rately predicted by RTM in the top 10% of risk cells.
When data permitted, proportions of interest were calcu-
lated from the relevant numerator and denominator.
Results
Study characteristics
In this section, we discuss the general characteristics of
the papers selected for inclusion. More than half of all
studies were published since 2017, indicating a rapid
growth of knowledge in this area in a relatively short
period. is may be due to the availability of the RTMDx
software as a free download during this time. e major-
ity of the studies were conducted in the US (n = 14).
Other studies were conducted in Italy (n = 3), Colombia
(n = 2), Canada (n = 1), Spain (n = 1), Austria (n = 1),
Northern Ireland (n = 1), Turkey (n = 1), and Japan
(n = 1).
Crime types included burglary, robbery, theft, homi-
cide, assault, gang violence, shootings, terrorism, auto
theft, thefts from vehicles, alcohol related traffic crashes,
and child maltreatment. In terms of data, this was usu-
ally gained from the relevant police department for crime
studies.
Evaluation metrics
is section looks at measures of forecasting perfor-
mance. e most commonly used evaluation metrics
were (in the following order): hit rates, predictive accu-
racy index (PAI), logistic regressions, and incidence rate
ratio (IRR). e two main measures used were hit rates
and PAI, which are detailed below.
Hit rates capture the percentage of events occurring
in defined risk areas (e.g. high to very high risk cells) in
a post study time period. Our review found 27 differ-
ent hit rate measures (see Table 2). Results varied from
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Marchmentand Gill Crime Sci (2021) 10:12
23 to 85%, with an average of 43.6%. Given the relatively
small geographic spaces identified as high or very high
risk within these studies (see below), this result confirms
RTM’s predictive capabilities. However, given the vari-
ance between studies, further research should investigate
the reasons for the differences between high performance
and lower performance studies.
Hit rates have limitations, as they do not take into
account the size of the area where crimes are predicted
to occur, necessitating the need for the PAI as a compara-
ble metric. PAI standardizes predictions by the size of the
geographic area determined to be problematic, defined
by the percent of crime divided by the percent of the area
forecasted to be a hotspot (Chainey etal., 2008). Higher
PAI values indicate better performance, or more accurate
predictions. Greater prediction accuracy reflects a higher
hit rate over a small geographic area. Our review identi-
fied 13 different PAI values ranging from 1.71 (auto theft;
Kocher & Leitner, 2015) to 41.04 (robbery; Drawve, 2016)
(see Table3). e median PAI value was 7.42. Although
the average across these studies is 12.98, it is highly
skewed by five high performing RTM’s reported in three
separate analyses.
Crime types
Acquisitive crimes
8 studies applied RTM to acquisitive crimes. 3 stud-
ies generated PAI values for five crime types. PAI values
ranged from 1.71 (auto theft; Kocher & Leitner, 2015) to
18.46 (robbery, Kocher & Leitner, 2015). e other three
PAI values were closer to the lower end of the range and
included 1.87 (vehicle theft; Ohyama & Amemiya, 2018),
3.61 (robbery; Caplan et al., 2020) and 4.46 (burglary,
Kocher & Leitner, 2015). Hit rate values ranged from 25%
(burglary; Kocher & Leitner, 2015) to 53.4% (burglary;
Dugato etal., 2018).
Caplan et al., (2020) examined robberies in Brook-
lyn, New York, using RTM. e average hit rate for one
Table 1 Included studies
Authors Crime type City studied Outcome measure
Anyinam (2015) Violent crime New Haven, Connecticut Hit rate
Caplan (2011) Shootings Irvington, New Jersey Hit rate
Caplan et al., (2013a, 2013b) Violent crime Irvington, New Jersey Hit rate
Caplan et al., (2020) Robbery Brooklyn, New York PAI
Caplan et al., (2011a, .2011b) Shootings Irvington, New Jersey IRR
Daley et al., (2016) Child maltreatment Fort Worth, Texas Hit rate
Drawve (2016) Robbery Little Rock, Arkansas PAI
Drawve et al., (2016) Gun crime Little Rock, Arkansas Hit rate
Odds ratio
PAI
Dugato et al., (2017) Mafia homicide Naples, Italy Hit rate
Dugato et al., (2018) Residential burglaries Milan, Italy Hit rate
Dugato (2013) Robberies Milan, Italy Hit rate
Escudero and Ramírez (2018) Illicit drug markets Bogotá, Colombia Hit rate
Garnier et al., (2018) Robberies Newark, New Jersey Hit rate
Giménez-Santana et al., (2018a) Alcohol related traffic crashes Cádiz, Spain Hit rate
PAI
Giménez-Santana et al., (2018b) Violent crime Bogotá, Colombia Hit rate
Kennedy et al., (2011) Shootings Newark, New Jersey Hit rate
Odds ratio
Kennedy et al., (2016) Aggravated assault Chicago, Illinois IRR
Kocher and Leitner (2015) Assault, auto theft, burglary and robbery Salzburg, Austria Hit rate
Marchment et al., (2019) Bombings and bomb hoaxes Belfast, Northern Ireland Hit rate
Ohyama and Amemiya (2018) Thefts from vehicles Fukuoka, Japan Hit rate
PAI
Onat and Gul (2018) Terrorist acts Istanbul, Turkey Hit rate
Onat et al., (2018) Drug Ontario, Canada Hit rate
Valasik (2018) Gang violence Los Angeles, CA Hit rate
Valasik et al., (2019) Lethal violence Baton Rouge, Louisiana Hit rate
Yerxa (2013) Residential burglary Pacific Northwest Odds ratio
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Marchmentand Gill Crime Sci (2021) 10:12
month was 8.41, meaning an average of 8.41% of rob-
beries were predicted in the high-risk cells. e average
PAI value for RTM across all months was 3.61. Anyinam
(2015) examined robberies in New Haven, Connecticut.
In the test period, 39% of robberies occurred in high or
very high-risk cells, which made up only 6.09% of the
city. Dugato (2013) looked at robberies in Milan, Italy,
between 2007 and 2010. 36% of the robberies commit-
ted during the test period occurred in 6.8% of the riski-
est areas identified using RTM. 43% of events occurred
within high or very high-risk cells (the top 10% of total
cells).
Dugato etal., (2018) also examined residential bur-
glaries in Milan, Italy. Burglaries that occurred in 2014
were used to evaluate the effectiveness of the final
risk map. More than half (53.37%) occurred in areas
defined as high or very high risk. Yerxa (2013) analysed
burglary in a city in the Pacific Northwest using RTM.
The odds ratio from their logistic regression suggested
that with every increased unit of risk, the likelihood of
a residential burglary increased by approximately 59%.
Kocher and Leitner (2015) used RTM to look at sev-
eral crime types in Salzburg Austria, including burglary,
robbery and auto theft. eir RTMs correctly predicted
25% of burglaries, and 43.5% of robberies. e PAI
value for robberies was 18.46. In contrast, the predic-
tions for burglaries and auto thefts performed rather
poorly, with PAI values of 4.46 and 1.71, respectively.
Ohyama and Amemiya (2018) examined thefts from
vehicles in Fukuoka, Japan. ey found that 40.9% of
thefts from vehicles occurred in high or very high-risk
cells. e PAI was 1.87. Giménez-Santana etal., (2018a,
2018b) used RTM to look at theft in Bogotá, Colombia.
e top 10% of cells with the highest risk predicted 40%
of all theft incidents occurring during 2013 in the city.
Table 2 Performance of RTM using hit rate as the forecasting performance measure
Study Crime type Hit rate (high‑
very high risk
cells)
Valasik et al., (2019) Lethal violence 23%
Kocher and Leitner (2015) Burglary 25%
Kocher and Leitner (2015) Auto theft 25.7%
Giménez-Santana et al., (2018a, 2018b) Assault 29%
Giménez-Santana et al., (2018a, 2018b) Homicide 32%
Valasik (2018) Gang violence 33%
Dugato et al., (2018) Burglary 35.7%
Kocher and Leitner (2015) Assault (spring) 37%
Anyinam (2015) Robbery 39%
Giménez-Santana et al., (2018a, 2018b) Theft 40%
Ohyama and Amemiya (2018) Thefts from vehicles 40.9%
Anyinam (2015) Non-fatal shootings 41%
Giménez-Santana et al., (2018a, 2018b) Alcohol related traffic crashes 41%
Caplan (2011) Shootings 42%
Dugato (2013) Robbery 43%
Onat and Gul (2018) Terrorist acts 43%
Kocher and Leitner (2015) Robbery 43.5%
Kocher and Leitner (2015) Assault (summer) 44.4%
Caplan et al., (2013a, 2013b) Violent crime 45%
Drawve et al., (2016) Gun crime 48%
Marchment et al., (2019) Bombings 50%
Marchment et al., (2019) Bomb hoaxes 50%
Daley et al., (2016) Child maltreatment 52%
Anyinam (2015) Homicide 57%
Escuerdo & Ramírez (2018) Illicit drug markets 64%
Dugato et al., (2017) Mafia homicide 85%
Onat et al., (2018) Drug crime 85%
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Marchmentand Gill Crime Sci (2021) 10:12
Violent crimes
Twelve studies identified risk factors for violent crimes
using RTM. 2 studies generated PAI values for 3 crime
types. ey were 3.53 (homicide; Giménez-Santana etal.,
2018a, 2018b), 3.56 (assault; Giménez-Santana et al.,
2018a, 2018b) and 19.246 (gun crime; Drawve et al.,
2016). Hit rates ranged from 18% (homicide; Giménez-
Santana et al., 2018a, 2018b) to 85% (mafia homicide;
Dugato etal., 2017).
Anyinam (2015) showed that 41% of non-fatal shoot-
ings and 57% of murders occurred in areas deemed to be
high or very high-risk, which made up only 6.09% of the
study area (the city of New Haven).
Caplan et al., (2011a, 2011b) studied shootings in
Irvington, New Jersey using RTM. ey used two six-
month periods to test the predictive validity of the risk
terrains. e odds ratios for period 2 suggested that for
every increased unit of risk, the likelihood of a shooting
significantly increased by at least 56%. e odds ratio for
period 1 suggested a shooting likelihood of 69%.
Caplan (2011) found that 42% of all shooting incidents
occurred in the top 10 percent of the highest risk places
during their post study period of the calendar year 2007.
e logistic regression suggested that for every increased
unit of risk, the likelihood of a shooting more than
doubled.
Caplan et al., (2013a, 2013b) studied violent crime
incidents in Irvington, New Jersey. ey found that for
every unit increase of a 100 ft × 100 ft cell’s risk value, the
likelihood of a violent crime occurring there during the
6-month test period increased by 92%. 45% of all violent
crimes in 2008 happened at places with risk values of 3 or
more, which comprised 10% of the study area.
As well as burglary, robbery and auto theft, Kocher
and Leitner (2015) examined assault in Salzburg Austria,
2013. e PAI value for spring was 31 and the PAI for
summer was 23.
Kennedy etal., (2016) identified risk factors for aggra-
vated assault in Chicago using RTM. e IRR from the
negative binomial regression suggested that the aggra-
vated assault count increased 2% (IRR = 1.02) for every
unit increase of risk.
Giménez-Santana etal., (2018a, 2018b) looked at vio-
lent crime in Bogotá, Colombia using RTM. e top 10%
cells with the highest risk for homicide incidents wit-
nessed 32% of all homicide events. For assault, 20% of all
events that occurred during 2013 were located in the top
5% cells posing the highest risk.
Valasik (2018) used RTM to study gang homicides in
Los Angeles, California. 8% of gang homicides commit-
ted in 2012 occurred in very high risk cells, while about
42% of gang homicides took place in medium risk cells.
e remaining half occurred in low risk cells.
Valasik etal., (2019) used RTM to forecast homicide in
Baton Rouge, Louisiana. Very high risk cells were signifi-
cantly more likely (23 × higher) to experience a homicide
when compared to low risk cells. e incidence rate ratio
for very high risk cells was 22.9.
Drawve (2016) found that the odds of a gun crime
occurring in an area identified as having very high
risk experienced over 55 times the odds of gun crime
relative to areas with a spatial risk value of zero (odds
ratio = 55.05). e PAI prediction value for the RTM was
19.246. e RRI for the RTM was 1.18.
Kennedy etal., (2011) found that the top 40% of high-
risk cells in the risk terrain map correctly predicted the
locations of 84% of the shootings during the next period.
RTM has also been applied to the study of organised
crime related homicide. Dugato etal., (2017) examined
both attempted and completed mafia homicides com-
mitted by the Camorra in Naples, Italy, during 2012 (data
obtained from Italian government). 85% of the mafia
homicides committed in 2012 were located within cells at
high or very high risk. e regression suggested that the
few cells with very high or high risk had a significantly
higher probability of experiencing a mafia homicide in
comparison with those categorized as being at very low
risk. e incidence rate ratio for very high risk cells was
47.99 and for high risk was 37.92.
Drug related crime
Two studies have used RTM to study drug related crimes.
Escudero and Ramírez (2018) looked at the locations
of illicit drugs sale points in Bogotá, Colombia. e
Table 3 Performance of RTM Using PAI as the Forecasting
Performance Measure
Study Crime type PA I
Kocher and Leitner (2015) Auto theft 1.71
Ohyama and Amemiya (2018) Thefts from vehicles 1.87
Giménez-Santana et al., (2018a,
2018b)Homicide 3.53
Giménez-Santana et al., (2018a,
2018b)Assault 3.57
Caplan et al., (2020) Robbery 3.61
Kocher and Leitner (2015) Burglary 4.46
Giménez-Santana et al., (2018a,
2018b)Theft 7.42
Giménez-Santana et al., (2018a,
2018b)Alcohol related traffic crashes 9.1
Kocher and Leitner (2015) Robbery 18.46
Drawve et al., (2019) Gun crime 19.25
Kocher and Leitner (2015) Assault (summer) 23.40
Kocher and Leitner (2015) Assault (spring) 31.37
Drawve (2016) Robbery 41.04
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Marchmentand Gill Crime Sci (2021) 10:12
approximate accuracy for high and very high risk was
64%. Onat etal., (2018) looked at illicit drug activities in
the Durham Region in Ontario, Canada. ey found that
nearly 85% of all places with illicit drugs arrests in 2012
and 2013 overlapped with places they had identified as
high-risk places of 2011 and 2012, respectively.
Child maltreatment
One study, Daley (2016), looked at maltreatment of chil-
dren, who were either physically, sexually, or psycho-
logically abused, neglected, or abandoned in Fort Worth,
Texas. ey used data from the year 2013, obtained from
the Department of Family and Protective Services (DFPS)
and Fort Worth Police Department (FWP). In the fol-
lowing year, 2014, 52% of all cases of child maltreatment
were accurately predicted in the 10% of highest risk cells
determined by the RTM. Further, almost all observed
incidents were located in cells that were predicted to
have an elevated risk. e highest risk stratum (10% of
the study area) included 52% of all future cases; the sec-
ond risk stratum (20% of the study area) contained over
80%; and the third risk stratum (30% of the study area)
predicted over 90% of 2014 cases. Only 133 of the 5391 or
2% of all instances occurred in areas that were not identi-
fied as having an elevated risk.
Driving whileintoxicated
Giménez-Santana et al., (2018a, 2018b) used RTM to
identify correlates of alcohol-related traffic crashes in the
Spanish province of Cádiz. RTM was able to predict 41%
of all alcohol related crashes that occurred in places iden-
tified as posing a higher risk for future traffic accidents.
e PAI value was 9.1.
Terrorism
Two studies have used RTM to examine predictive accu-
racy for terrorist events. Both had promising results, with
hit rates of 43% (Onat & Gul, 2018) and 50% (March-
ment etal., (2019). Onat and Gul (2018) used RTM to
identify correlates of terrorist incidents in Turkey, using
data acquired from Istanbul Police Department between
2008 and 2012. More than 43% of all places with terror-
ist incidents in the second period overlapped with the
top 10% highest risk-places of the first period. Logistic
regression results suggested that for every increased unit
of risk, the likelihood of a violent terrorist incident hap-
pening at a particular place increased by 2.2%. March-
ment et al., (2019) used RTM to identify correlates of
dissident Republican incidents in Belfast, Northern Ire-
land. ey compared two incident types, bombings and
bomb hoaxes. Logistic regression or other methods of
testing predictive accuracy were not possible due to the
size of data. During the post-study period, 28 bombings
occurred. Seven bombings occurred in the cells that were
inferred as being at very high risk. Seven occurred in
high risk cells. 2 bombings occurred in medium risk cells
and 12 bombings occurred in areas deemed to be at low
risk. Eight hoaxes occurred post-2013. Four occurred in
medium risk areas, two in high risk areas and two in very
high-risk areas. No hoaxes occurred in areas deemed to
be at low risk.
Comparisons toother methods andintegrated approaches
is section discusses the papers identified in the search
that examined the accuracy of RTM in comparison to
other approaches or used RTM in combination with
other spatial analyses.
Ohyama and Amemiya (2018) compared five meth-
ods (RTM, KDE, ProMap, SEPP and ST-GAM) and con-
cluded that RTM yielded the best results. e hit rate
and PAI for RTM were almost twice as high as those for
KDE, ProMap, and SEPP. 40.9% of thefts from vehicles
occurred in high or very high risk cells, with a PAI of
1.87. Both hit rate (40.9%) and PAI (1.87) were the high-
est for RTM.
Marchment (2019)2 compared RTM to KDE in her
study of dissident Republican activity in Northern Ire-
land. For KDE, only three bombings (out of 28) occurred
in high or very high-density areas during the test period
of two years. However, most hoaxes occurred in high or
medium density areas. For RTM, 50% of bombings and
50% of bomb hoaxes occurred in high or very high risk.
Seeing as only a small proportion of the city was deemed
to be at the high or very high levels of risk, this is impres-
sive. However, some caution should be taken in interpret-
ing these results due to the small amount of data used,
and a large proportion (43%) of bombings did occur in
low risk cells.
Daley (2016) found the highest risk stratum of their
RTM (10% of the study area) included 52% of all future
cases, which was almost 10% more than the hotspot
model, which included 43% of cases. e second risk
stratum (20% of the study area) contained over 80% of
cases, compared with 66% for the hotspot model, and the
third risk stratum (30% of the study area) predicted over
90% of 2014 cases, compared with 81% for the hotspot
model.
However, KDE outperformed RTM in Dugato’s (2013)
study of robberies in Milan. e hot spots for each
method were identified using 6.8% of the cells with the
highest level of risk value for RTM and density value for
KDE. Although KDE was more accurate, RTM was more
2 is information regarding KDE was taken from Marchment’s doctoral the-
sis, which uses the same data as Marchment etal., (2019).
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 8 of 11
Marchmentand Gill Crime Sci (2021) 10:12
reliable and its predictive power remained more stable
over time. is was measured using the Recapture Rate
Index (RRI), which measure of the reliability of the fore-
casting power over time. Drawve (2016) compared RTM
to Spatial and Temporal Analysis of Crime, KDE, near-
est neighbour hierarchical. He also found that KDE was
the most accurate, but it had the second lowest average
reliability value/ RTM was the most reliable and precise,
with the highest RRI, as well as having the second highest
PAI. ese results suggest that although RTM may be less
likely to forecast rapid changes in the short term, it can
produce consistent results in the long term.
Giménez-Santana et al., (2018a, 2018b) compared
RTM and KDE for alcohol related vehicle incidents. ey
found PAI values of 3.3 for KDE, 9.1 for RTM, and 13.3
for all places where high vulnerability (spatial risk values)
and exposure (recent incidences) to past crashes inter-
sected. ese results indicate that RTM as a solo method
was overall more accurate in predicting the location of
future driving while intoxicated (DWI) crash accidents
when compared to KDE.
Giménez-Santana et al., (2018a, 2018b) found that
using a joint utility approach predicted 19% of all theft
incidents in Bogotá. eir RTM for assault resulted in
PAI values of 3.57 for high-risk places, compared to 4.76
for hotspots, and 5.85 for all places where high vulner-
ability and exposure to past crime intersected. e com-
bined effect of high-risk places and exposure to past
crime events increased the overall accuracy for pre-
dicting future assault incidents by 23%. For homicides,
the PAI values were 3.53 for high-risk places, 6.43 for
hotspots, and 6.47 for locations where high-risk places
overlapped with crime hotspots. Garnier et al., (2018)
found that a combined model of event-dependence and
environmental influences (RTM) performed significantly
better than RTM only in their study of robberies in New-
ark. e RTM only model also performed better than the
event dependence only model.
Drawve etal., (2019) found that their RTM and KDE
had very similar predictive accuracy to one another. ey
also used RTM and KDE jointly, restricting high-risk
(vulnerability) and hot spots (exposure) places to where
they overlapped. e predictive accuracy doubled using
this joint utility approach when compared to each tech-
nique on its own.
Caplan et al.’s (2020) RTM outperformed KDE in
terms of prediction accuracy, but only slightly. In 7 of the
11months, RTM produced a higher PAI value than KDE.
KDE resulted in a higher PAI value in 4 of the 11months.
e average PAI value for RTM across all months was
3.61 (SD = 1.16), and the average PAI value for KDE
across all months was 3.11 (SD = 0.69). However, the
results of an independent samples t-test suggest that the
differences were not statistically significant. PAI values
were highest when employing an approach that identified
locations that could be considered as both hotspots using
KDE, and risky using RTM. is integrated approach
produced the highest PAI values in 8 of the 11 time peri-
ods. e average PAI value for the integrated approach
across monthly periods was 7.18 (SD = 6.06), twice as
high as KDE or RTM alone.
Proportion meta‑analysis ofpredictive accuracy
Next, we performed a proportion meta-analysis on stud-
ies where the relevant data were available. Studies were
excluded when the data was not reported in a format to
calculate a proportion (e.g., a numerator and denomina-
tor were not reported, or the only outcome measure was
an odds ratio) leaving 16 studies. is was appropriate to
carry out a proportion meta-analysis. An I2 test for heter-
ogeneity indicated considerable inconsistency (I2 > 99%).
is statistic describes the percentage of variation that
is due to heterogeneity rather than chance. Heterogene-
ity was to be expected considering the different crime
types and settings across the included studies. erefore,
a random effects model was used in order to minimize
the effect of heterogeneity among studies. As a random
effects model was used it was appropriate for each study
to be weighted by the inverse of its variance (including
both the within studies variance plus the between stud-
ies variance). A forest plot was constructed showing the
individual study results and weights (demonstrating the
influence of each study on the weighted average) of the
individual studies, together with 95% CIs.
Fig. 1 Pooled proportion of cases accurately predicted by RTM in
the top 10% of risk cells. Each box represents the estimate of the
proportion within a study and its area is proportional to the weight
of the study. The horizontal solid lines represent 95% confidence
intervals
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 9 of 11
Marchmentand Gill Crime Sci (2021) 10:12
Figure 1 presents the meta-analytical proportion of
cases accurately predicted by RTM in the top 10% of risk
cells was 44.7%, 95% CI = [38.26, 51.1]. e proportions
ranged from 22.5 to 85.1%.
Discussion
To our knowledge, this is the first study that has system-
atically summarised the available evidence for the predic-
tive accuracy of RTM. We used a systematic literature
review and proportion meta-analysis approach to esti-
mate the proportion of future cases accurately predicted
by high risk cells. is study has demonstrated that RTM
is an effective spatial diagnostic and forecasting method
that can be applied to identify places at greatest risk of
an event and can be a useful tool in guiding targeted
responses to crime problems. RTM reliably identifies
problematic features that exacerbate the likelihood of
future crimes in a given geographic area. e detection
of these areas helps prioritise efficient police patrols and
other preventative and deterrent measures. In this way,
RTM guides efficient resource allocation. It not only
identifies potential hot-spots, but provides a reason-
ing for why they are ‘hot’ in the first place. Importantly
RTM, can also predict where crime may displace to,
based on relatively stable environmental and contextual
risk factors that go beyond incident-based data. RTM
can also be applied to a variety of crime types and has
been shown to be an effective forecasting method for a
range of acquisitive crimes, violent crimes, terrorist inci-
dents, child maltreatment, traffic incidents, drug related
crime and organised crime. e systematic review dem-
onstrated that RTM has been successful in identifying at
risk places for acquisitive crimes, violent crimes, child
maltreatment, terrorism, drug related crimes and DWI.
e proportion meta-analysis indicated that almost half
of future cases in the studies analysed were captured in
the top ten per cent of risk cells. is typically covers a
very small portion of the full study area.
RTM as an overall approach is relatively simple and
user-friendly, and the associated RTMDx software pro-
vides an opportunity for practitioners to readily utilize
the approach with minimal resources and time spent on
learning new processes. is means that it is within the
reach of many operational crime analysts in practical law
enforcement settings. Police often try to predict where
future crime will occur by looking at past crime locations,
and then determine the allocation of resources accord-
ingly. ese retrospective analyses, such as KDE, cannot
consider the influence of underlying social and physi-
cal factors. e additional characteristics determined
by RTM allow for more accurate predictions of future
crime locations and can improve the allocation of police
resources to designated areas with higher predicted levels
of criminal activity. As it is possible to identify the cor-
relates of the criminal events, due to the diagnostic
focus on the risk factors, targeted countermeasures can
be designed (Caplan & Kennedy, 2016). Further, crime
doesn’t have to be included as a risk factor to create an
RTM and can indicate risky areas based on crime genera-
tors and attractors.
A key limitation of RTM is that it does not address
temporal variations in crime locations (over the course
of day, duration of a week, over different seasons, etc.)
Another limitation of RTM in general is that it may iden-
tify areas as being risky where crime may never emerge.
It cannot be assumed that because a location is high in
risk according to identified risk factors, that crime will
always ensue—there can be numerous areas identified as
risky, but no crime may actually occur in these defined
risky areas. is is an avenue for future research. ere
is also a need to evaluate interventions put in place that
are based on areas that have been identified using RTM
as risky.
e findings from this systematic review reiterate Van
Patten etal., (2009), Kennedy etal., (2011), and Caplan,
Kennedy, and Piza (2013) who assert that RTM and KDE
should be used jointly. is review suggests that the pre-
dictive strength of RTM, and in turn the practical utility
of the method, may be enhanced when it is considered in
conjunction with other spatial analysis techniques, such
as KDE. Hotspots tend to change over time, so whilst the
presence of previous crime can be a reasonable predic-
tor of future crimes, it cannot forecast the spatial distri-
bution of where crime might emerge. It is important to
consider both the spatial distribution of past crime and to
identify correlates of events to most accurately forecast
where future crime incidents are likely to occur.
Whilst the synthesised results do point towards RTM’s
impressive predictive capabilities, some care should
be taken in interpretation, as with all crime and place
research. First, there is a great deal of variance across a
limited number of studies. Further investigation is war-
ranted to understand the study-level features which
might contribute toward greater model performance. For
the meta-analysis, only 16 studies had the data reported
in a format to calculate a proportion, meaning the results
of 9 studies were not included. e heterogeneity associ-
ated with the meta-analysis estimates was very high, indi-
cating that the summary estimates must be interpreted
with caution. RTM has been applied to a wide number
of crime types and the spatial features examined vary
from study to study. Further research is needed for each
to enable subgroup meta-analyses for the different crime
types.
Second, as the studies included in this paper were
selected carefully from peer-reviewed journals, there
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Page 10 of 11
Marchmentand Gill Crime Sci (2021) 10:12
might be a risk of publication bias. Studies that fail to
demonstrate impressive or meaningful results may be
less likely to get published and therefore fall out of our
rigorous search strategy. e field of psychology is under-
going an open science revolution on the back of similar
concerns regarding replicability and other associated
endemic problems. Criminology, and therefore RTM,
will not be immune to such problems. A greater cul-
tural emphasis on behaviours such as pre-registration of
analyses, provision of data and code would go some way
toward mitigating these problems. ird, RTM is still an
emerging method. Whilst 25 studies appears a lot, and
certainly sufficiently large for a systematic review, the
truth also remains that these 25 studies have looked at
12 different crime types. A lot more research is needed
before we can get specific about which crime types, and
contexts (e.g. urban vs. rural), RTM works best in.Addi-
tionally, our focus was on RTM’s predictive accuracy and
forecasting capabilities. RTM’s function goes beyond
prediction and includes diagnostic approaches to under-
standing crime occurrence in a given location. Future
systematic reviews and meta-analyses might seek to syn-
thesise this neighbouring evidence base.
Authors’ contributions
Both authors read and approved the final manuscript.
Funding
This work was funded by Newark Public Safety Collaborative.
Declarations
Competing interests
The authors declare that they have no competing interests.
Received: 10 September 2020 Accepted: 7 June 2021
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