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Risk Terrain Modeling: Seasonality and Predictive Validity

Justice Quarterly (2019). https://doi.org/10.1080/07418825.2019.1630472

Published onJun 26, 2019
Risk Terrain Modeling: Seasonality and Predictive Validity
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Abstract:

This study focuses on crimes involving firearms in Baltimore, Maryland to answer three research questions concerning the effect of seasonality: 1) Do changes in the seasons affect which spatial factors are significantly related to crime?; 2) Does Risk Terrain Modeling have predictive validity on a short-term basis?; and 3) Are the same areas high-risk throughout the year? To accomplish this, the authors ran twelve monthly risk terrain models and one yearly risk terrain model. The study found that risk factors vary by month and that monthly and yearly spatial risk factors do not necessarily overlap. The study also found that risk terrain models retain their predictive validity on a short-term basis. The results are further discussed in relation to whether the same areas are high-risk throughout the course of the year.

Keywords:

Risk-Terrain Modeling, Seasonality, Crime Forecasting

Citation:

Szkola, J., Piza, E. and Drawve, G. (2019). Risk Terrain Modeling: Seasonality and Predictive Validity. Justice Quarterly. https://doi.org/10.1080/07418825.2019.1630472

Introduction

Police have a strong need to understand where crime is most likely to occur so that they can direct their limited resources to the most at-risk locations, potentially having the largest impact. There is a growth in police departments, both in the United States and internationally, employing crime analysts to help understand the spatio-temporal patterns of crime to best allocate resources to reduce crime. This level of analysis has led to the ability to forecast where future crime is most likely to occur, based upon historical data and other factors. This practice has its origins in the pin maps that existed in police departments prior to the advent of geographical information system (GIS) technology. In short, decades of research has supported the notion of, “place matters” when examining crime (P. J. Brantingham and Brantingham, 1981; Haberman, 2017; Hirschfield and Bowers, 1997; LeBeau and Leitner, 2011; Ratcliffe, 2004)

Commonly, hotspot mapping is used to identify places with high densities of past crime (Sherman, Gartin, & Buerger, 1989). This information is used to direct resources to areas where crime events are highly clustered (Telep and Weisburd, 2015) in hopes to prevent and reduce crime by hedging on the idea that crime is likely to occur in the future at those clusters. Hotspot mapping is a mainstream technique used throughout the world to identify crime clusters across law enforcement jurisdictions; however, hotspots policing centers on where crime occurs, and hotspot identification does not offer any insights into why crime might be occurring in these locations (Caplan, Kennedy, & Miller, 2011). With that, we know where crime clusters but what needs greater understanding is what contributes to crime occurring at these locations.

Building from hotspot methodology and the larger Environmental Criminology literature, Risk Terrain Modeling (RTM) was developed as a spatial diagnostic tool to understand what elements of the environment are contributing to crime occurrence (Caplan and Kennedy, 2011). RTM differs from traditional hotspot techniques by not only including historical crime data, but also bringing in underlying spatial correlates of crime from criminological theory (Caplan, et al., 2011). Incorporating the spatial risk factors (i.e. crime generators/attractors) known to be associated with crime enables practitioners to construct specific interventions to crime in the area based on the risk factors present. RTM has been used with police departments to gain an understanding of where risk is greatest for future crime, allowing for place-based policing efforts, but also identifying what factors are linked with specific crime types (Kennedy, Caplan, & Piza, 2011; Piza, Kennedy, & Caplan, 2018).

RTM has been utilized and validated across multiple crime types such as shootings (Caplan, et al., 2011; Kennedy, et al., 2011; Piza and Gilchrist, 2018), robbery (Barnum, Caplan, Kennedy, & Piza, 2017; Connealy & Piza, 2019), carjacking (Lersch, 2017), aggravated assault (Kennedy, Caplan, Piza, & Buccine-Schraeder, 2016), motor vehicle theft and recovery (Piza, Feng, Kennedy, & Caplan, 2016), is utilized in multiple jurisdictions throughout the United States (Piza, et al., 2018), and has been extended to multidisciplinary studies. RTM is not, and was never intended to be, a purely academic tool. The studies have been used to inform police strategy, but due to the time horizon of the forecasts, RTM has not yet been used to specifically inform police tactics on a month-to-month basis. RTM forecasts typically use a minimum of six months of spatial data to predict the most at-risk places for specific crime types over the subsequent time period. This methodology is useful because the larger the sample, the more power the statistical method employed will have. However, this also limits the utility of the tool to longer-term strategic decisions, versus shorter-term (monthly) tactical decisions regarding the utilization of police resources. Police departments, especially at an individual precinct level, often work on this smaller tactical horizon and internal crime analysts typically work on 7- or 28-day time periods. With police departments using smaller time-horizons to make decisions and target specific interventions it is necessary to gain an understanding of whether the RTM is usable on across smaller time frames.

Literature Review

Seasonality

The idea of seasonality as an influencer of crime dates as far back as the 1800s. In what was widely acknowledged as the first spatial analysis of crime patterns, Quetelet (1842) observed that violent crimes were highest in the summer and that crimes against property were highest in the winter months throughout France. Quetelet believed the increased temperatures could be attributed to people being shorter tempered and that people being outside more could lead to more frequent interactions. Quetelet’s theoretical musings for this occurring can be traced forward to two future theories: routine activities theory (RAT) and temperature and aggression theory.

Routine Activities Theory

RAT (Cohen and Felson, 1979) explains the importance of considering people’s routine activities in understanding where crime occurs in space. RAT postulates that crime results from the intersection of three elements in time and space: a suitable target, a motivated offender, and the absence of a capable guardian (Cohen and Felson, 1979). The routine activities of individuals, specifically their leisure activities, typically change with the seasons. For example, in the warmer times of the year both victims and offenders are outside more often and, thus, more likely to interact. This increases the likelihood of occurrence of crime in these spatial contexts, particularly if a capable guardian is absent. This work was expanded on by Brantingham and Brantingham (1993) who developed the idea of paths, nodes, and edges, which brings the idea of travel paths and major areas where people converge, or nodes, into the idea of routine activities theory. It moves the theoretical discussion into more of a micro-temporal frame where the daily actions of both the offender and victim are accounted for. Their idea focused on the selection of targets by offenders, but its main ideas have large implications for routine activities theory, especially when considered in light of how people’s routine daily activities change as the larger physical environment changes on a monthly and daily basis. Given that people’s daily activities change across seasons, we would expect the spatial distribution of crime patterns to behave similarly.

While not the explicit focus of routine activities, temperature does play a role in a RAT explanation. The routine activities explanation of why crime varies by season can be boiled down to the simple idea that people do different routine activities during different parts of the year. People spend more time outdoors in public spaces (e.g. walking on sidewalks, at public beaches, in parks, etc.) during the warmer times of the year increasing the number of possible convergences since both motivated offenders and suitable targets will be more prevalent. Under a RAT approach, temperature would be but one of many factors that influenced peoples’ routines with other factors combining with temperature to affect their daily activities. Due to this, few RAT tests have directly addressed temperature variations (Hipp, Curran, Bollen, & Bauer, 2004). The tests, when conducted, have not been direct. One study conducted in England and Wales found warmer temperatures were associated with higher rates of a wide variety of crimes, while neither the amount of sunshine or rain effected crime levels (Field, 1992). Field (1992) advanced a RAT explanation of this effect based on the premise that during warmer periods, people spend more time outside of their homes, thus increasing the opportunity for crime. Others have also incorporated RAT into explanations of seasonal variations but without explicit reference to temperatures (Landau and Fridman, 1993; Van Koppen and Jansen, 1999). RAT presents a compelling explanation for the seasonal variations in crime primarily because people’s routine activities change based on the season – resulting in changes in the interaction of the three main components of RAT.

Temperature and Aggression Hypothesis

The temperature and aggression hypothesis was first put forth by Quetelet and later tested by many scholars (Anderson, 1987, 1989; Anderson and Anderson, 1984; Bushman, Wang, & Anderson, 2005; Cohn and Rotton, 2005; Rotton and Cohn, 2000). Temperature aggression theory mainly postulates that when temperatures reach points where they are uncomfortably hot for humans, aggression increases and rationality wanes (Anderson, 1989). This theory was tested multiple times and support was found for a linear relationship between temperature and violent crimes (Anderson, 1987; Anderson and Anderson, 1984; Bushman, et al., 2005). The linear relationship between temperature and aggression is not universally accepted with some scholars arguing that the relationship is curvilinear, meaning that past a certain high temperature as the temperature continues to increase the number of violent crimes decrease (Cohn and Rotton, 2005; Rotton and Cohn, 2000).

Spatial Variations

While which theory better explains the variation of crime by season has not been decided, that crime does vary by season has been extensively researched (Baumer and Wright, 1996; Cohn, 1990). Seasonal patterns of crime have been observed across multiple locations and large study areas (McDowall, Loftin, & Pate, 2012). McDowall et al. (2012) used data from 88 US cities over a 24-year period to show that all major crimes undergo seasonal changes and that for the most part they follow similar cycles regardless of the geographic area. However, the difference in the peaks and the troughs of the crime rates across seasons were flatter in warmer climates and more extreme in colder climates (McDowall, et al., 2012). This study identified seasonal changes in time were not solely a product of temperature changes, but there was also a social component influencing the seasonal changes in crime.

Andreson and Malleson (2013) took a more detailed look at seasonality by measuring how the distribution of various crimes shifts throughout the year within the same city. Their work demonstrated that in addition to varying in frequency by season, crimes also varied in locations across the city by season, demonstrating different spatial patterns than those observed from the yearly aggregate (Andresen and Malleson, 2013). Their research indicated that looking at spatial crime patterns on an aggregated yearly basis could lead to missing important spatial patterns that are only evident on a seasonal basis.

This has the further consequence of perhaps missing effects of important crime reduction initiatives if crime is only analyzed in aggregated terms on a yearly basis. Regarding place-based policing, some interventions may only be appropriate for specific seasonal periods throughout the year given the observed spatial crime patterns. This finding also has important theoretical implications due to many tests of theories utilizing aggregated data that smooths out monthly variations in crime.

Risk Terrain Modeling

RTM is a spatial diagnostic technique that enhances the understanding of the spatial distribution of crime by incorporating place-based criminological theory (Caplan, et al., 2011). The focus on places has led to the categorization of both crime generators and crime attractors. Crime generators are locations that attract large number of people for reasons unrelated to criminal motivation such as malls, tourist attractions, or business districts (P. L. Brantingham and Brantingham, 1995). Crime attractors are locations that create known opportunities for crime to occur and attract motivated offenders because of these opportunities, such as bars, drug markets, or poorly lit commercial areas (P. L. Brantingham and Brantingham, 1995). The largest difference between the two is that offenders purposively seek out crime attractors because of the known criminal opportunities and go to these areas to commit crime, while generators are associated with crime simply because of the larger volume of people. RTM applies these concepts to go beyond identifying where crime has been concentrated in the past and associates it with specific crime attractors or generators. The technique’s aim is to understand what spatial risk factors are related to the crime clustering and then identifying areas that are most at risk for specific crime to occur in the future based on the spatial risk factors present.

RTM forecasts risk for specific locations by operationalizing spatial risk factors (i.e. crime generators and attractors) for specific crime types across a common raster map. RTM operationalizes each risk factor on a distinct raster map (i.e. layer) and assigns it a value (risk score). Once each factor has been operationalized as separate layers, the layers are combined into one composite map, indicating an overall risk assessment of the study area (Caplan, et al., 2011). Incorporating spatial risk factors, and identifying which risk factors are significantly associated with certain crime types, enables law enforcement to design interventions specifically targeting risk factors of crime in the locations.

When RTM has been used in the past, it has been used with historical datasets of crime of at least six months (e.g. Caplan, et al., 2011; Connealy and Piza, 2019; Drawve, 2016; Kennedy, et al., 2011). These risk maps were then often validated across the same sized time period, with the notable exception of Drawve (2014) who looked at the accuracy of RTM across multiple temporal horizons ranging from two days to up to three years. When RTM studies were conducted with law enforcement agencies, such as the work done by Kennedy, Caplan, and Piza (2018), the information was used to inform specific intervention approaches to address specific crime problems. Kennedy et al. (2018) worked with police departments in Kansas City, Newark, Colorado Springs, and Glendale to use RTM to identify the significant risk factors associated with specific crime problems in each city, and then assess the interventions implemented to address the risk factors. Each intervention designed by the study targeted not only the high-risk micro locations, but also the spatial risk factors identified as contributing to crime in these locations. (Kennedy, et al., 2018).

In all of the cities included in Kennedy et al.’s (2018) project, RTM models identified risk factors and target areas for subsequent police interventions. Each police agency designed their intervention in a manner that directly targeted prominent risk factors in the targeted areas. In the evaluation of the effectiveness of the interventions (which found noteworthy crime reductions in target areas as compared to statistically matched control areas), the authors controlled for seasonality by comparing the same time periods in each year. However, in each city the authors used a full year of data to create the RTM, but the targeted intervention lasted only approximately 90 days. By using data aggregated to the yearly level, it is possible that the police interventions focused of spatial risk factors that were significant in the year-wide model, but that did not pose any public safety concerns during the months that the intervention actually took place. While Kennedy et al.’s study controlled for seasonality in the empirical evaluation of the interventions, peoples’ interactions with spatial features were implicitly assumed to be roughly the same throughout the year. To date this has been the common methodology applied.

Current Study

The current study acknowledges that RTM has yet to forecast risky places across smaller temporal time frames that can better address seasonal variations in spatial risk factors. At best, prior RTM research has considered seasonality by controlling for the intervention time period in the statistical evaluation (Kennedy et al., 2018). The potential effect of seasonality on what risk factors are significantly associated with the outcome events of interest has not been considered. This is an important area because people do interact differently with spatial features throughout the year.

In recognition of such issues in the prior literature, we conduct month-to-month forecasts looking at specific types of crime to control for a larger number of factors than longer-term models. This approach acknowledges that a number of variables that change on a monthly basis may not change on a yearly basis. Among the factors that must be considered when making month-to-month forecasts are seasonal changes in environmental conditions that may affect crime patterns such as temperature and precipitation (McDowall, et al., 2012). Specifically, for short-term RTM forecasts, we must consider how temperature and precipitation may change how individuals interact with specific spatial features in the environment. If individuals’ interactions with the spatial features change due to environmental conditions then this could affect which factors are significantly associated with specific crime types. Six month, or yearly, forecasts generally smooth out monthly, or seasonal, variations that are observed on a monthly basis due to the larger amount of data available. This information is critical to police departments who want to know with as much precision as possible how to respond to crime so that they can ensure they are responding to the appropriate areas and with the appropriate interventions if the spatial risk factors change. As demonstrated by Kennedy et al.’s (2018) work, designing interventions on what risk factors are significant over the course of a year can be effective, but it might not be the most efficient approach. Using monthly RTM models can lead to more tailored interventions and a more nuanced allocation of resources allowing police departments to be more efficient and effective overall. Using yearly or six-month models can lead to an allocation of resources and specific intervention strategies based on data that may apply to the year overall, but not to a specific time period within that year.

The study reported in this paper fills the gap in the literature regarding the short-term predictive validity of RTM, building upon prior RTM studies on gun crime (Caplan, et al., 2011; Drawve, 2016; Kennedy, et al., 2011; Piza and Gilchrist, 2018). We also seek to contribute to the well-developed literature on the effect seasonality has on crime patterns. Andreson’s and Malleson’s (2013) work demonstrated that spatial patterns of crime are also subjected to seasonal variation, but to date there has been no research into whether spatial risk factors are stable over time, or if they too will be subjected to seasonal variations. This area has gone unexamined due to the larger time frame of data used to build RTMs, which likely smooths over seasonal variations. We examine the effectiveness of RTM in predicting crimes involving fire arms on a month-to-month basis. We aim to assess three research questions:

RQ1: Do changes in the seasons affect which spatial factors are significantly related to crime?

RQ2: Does RTM have predictive validity on a short-term basis?

RQ3: Are the same areas high-risk throughout the year?

Methodology

Study Location

The current study focuses on Baltimore, Maryland. Baltimore is the largest city in Maryland at 92.28 square miles and has a population of 623,280 people. Baltimore has a temperate climate with average temperatures ranging from a low of 43 degrees in January to a high of 89 degrees in July. Through 2013, Baltimore experienced a steady increase in gun crime, reaching a four-year high. Gun crime declined in 2014, but rebounded in 2015 and 2016 to remain at all-time high levels. In 2017, Baltimore earned the unwanted distinction as the deadliest big city in the nation with a murder rate of 55.8 per 100,000 residents (Madhani, 2018), with 88% of these individuals being killed with a firearm (Rector, 2018).

Outcome Event

The dependent variable consisted of any crime that involved the use of a firearm for calendar year 2013 and calendar year 2014 broken down by month throughout Baltimore. Figure 1 shows the gun crimes in 2013 by month. The figure shows the rough seasonal fluctuation that occurs in gun crimes. Shooting incidents are relatively rare events compared to other crime types; however, any crime that involves the use of a firearm has the potential to escalate into a shooting scenario often with devastating results. Gun Crimes were chosen due to the seriousness of the crime, particularly in Baltimore, and the robust history of looking at shooting incidents in the RTM literature (Caplan, et al., 2011; Kennedy, et al., 2011; Piza and Gilchrist, 2018). Additionally, by broadening the outcome event to include all firearm related crimes, this allowed the sample size to increase, moving away from small counts per month.

Figure 1


Potential Risk Factors

The risk factor data for this study came from several different sources. Based on prior research 10 potential risk factors were included in the RTM: schools, bus stops, bars, carryout restaurants, check cashing establishments, consignment shops, convenience stores, off site alcohol establishments, pawn brokers, and restaurants (Caplan and Kennedy, 2011; Drawve, 2016; Gerell, 2018; Kennedy, et al., 2016; Xu, Kennedy, & Caplan, 2010). While more potential risk factors were initially identified, the factors chosen to be included in the model were based upon a discussion of Baltimore’s specific characteristics and decisions to limit the total risk factors to avoid over complicating the model.1 The data for bars, carryout restaurants, check cashing establishments, consignment shops, convenience stores, off-site alcohol establishments, pawn brokers, and restaurants was obtained from InfoGroup2 in line with previous RTM research (e.g. Barnum, et al., 2017) and general criminology research (e.g. Hipp, Kim, & Kane, 2018; Williams and Hipp, 2019). The data for school locations and bus stops were obtained from Baltimore’s Open Data Portal.

Weather Data

Data concerning the weather for 2013 consisted of both average monthly temperature and the total amount of monthly precipitation. The average monthly temperature data was calculated using hourly temperature readings. Figure 2 displays the average temperature by month in 2013 alongside the count of crimes that involved firearms by month. The monthly precipitation data was calculated by using hourly precipitation totals. Figure 3 displays the total precipitation by month in 2013 alongside the count of crimes that involved firearms by month. All weather data was obtained from the history archives of the Weather Underground website (www.wunderground.com/history).

Figure 2


Figure 3


Analytic Strategy

The current study utilized RTMDx 1.5 software provided by Rutgers Center for Public Security. RTMDx automates many of the RTM steps by providing a web-based graphical user interface to enter all relevant variables. The software then operationalizes each of the variables to the common raster map and runs a negative binomial regression and a Poisson regression that selects the model with the lowest Bayesian Information Criterion (BIC) score to determine which variables are spatially related to the crime under study. RTMDx also includes a penalized regression process that iteratively runs the model by individually including risk factors until the most parsimonious model is achieved. For each factor that is significant, a relative risk value is calculated based on the exponential of the regression coefficient. This risk value expresses the riskiness associated with each individual spatial feature. The program then builds a composite raster map by combining the map layers of each of the variables that was significantly related to create a composite risk score. The risk score is reported in terms of the relative risk value (RRV), which is the sum of each of the individual relative risk scores associated with the crime type in a given cell on the map. RTM operationalizes the risk associated with each spatial feature inputted into the data set as either an influence by the proximity to the factor or the density of the factor. From that operationalization, RTM produces an RRV, which is the risk associated with that spatial feature compared to areas that do not contain that feature. RTM also calculates the spatial influence, which is the distance to which a specific environmental feature will affect behavior (Kennedy, et al., 2018). The relative risk value provides a situational indicator for each cell in the map with higher values representing cells that have a higher risk of shootings relative to other areas in the city without significant risk factors.

The study in total ran twelve separate monthly models, one for every month in calendar year 2013 and an additional model for the full year. Each raster map contained equally sized 165’ x 165’ foot cells, representing half the size of an average block as measured within the ArcGIS 10.4.1 software package. The raster map contained 92,054 cells. Each risk factor was operationalized for both proximity and density in order to measure its relationship with the crime locations by both how close it was to a crime, and the concentration of the feature in a given area. The spatial factors that were significant in each model were recorded in a matrix. These factors were compared to determine whether there was any pattern by month for which factors were significant.

To examine the effect of seasonal variation on the validity of short-term RTM’s two longitudinal logistic regression models were utilized. One model looks at the ability of Month 1 to predict Month 2 (e.g. Does January predict February’s riskiest areas?) and the other model looks at how well January 2013 predicts January 2014’s riskiest areas. This methodology was used to stay in line with prior research. In prior RTM research the models’ predictive validity was tested in two ways (Caplan, et al., 2011; Kennedy, et al., 2011; Kennedy, et al., 2016). Some research tested it with models from time one predicting time two, e.g. does a model using data from the first six months of the year correctly identify the areas most at risk for the next six months. Other research tested whether year one correctly predicted the areas most at risk in the following year. In order to stay true to prior methods, the output from the models was tested against the crimes from the subsequent month and the same month in the subsequent year utilizing longitudinal logistic regression.3

The models all controlled for the number of days in the month, linear trends, spatial lag, average monthly temperature, and monthly precipitation totals. Both of these models were tested with the individual relative risk value and for areas identified as high-risk by having risk scores above two standard deviations from the mean. Due to the wide range of risk scores that are present in RTMs it is common practice to identify the highest risk areas. Using a binary indicator of areas that are the highest risk in the logistic regression models provides an easier to understand metric for understanding the predictive power of the model. It eliminates the need to understand the range of risk scores present across the map and allows for a truer picture of whether areas identified as having high-risk scores are more likely to have increase crimes that involve firearms.

To answer the third research question a conjunctive analysis of case configurations (CACC) was used to observe whether high-risk areas remain the same from month to month. CACC is an approach that establishes a matrix of all possible combinations of categorical data and calculates what percentage of each combination is associated with an outcome of interest (Miethe, Hart, & Regoeczi, 2008). CACC has been used with RTM in the past to identify specific configurations of areas that are at risk for multiple types of robbery (Connealy and Piza, 2019) and to explore configurations of cases that are associated with high levels of traffic incidents (Drawve, Grubb, Steinman, & Belongie, 2018) and street robbery (Caplan, Kennedy, Barnum, & Piza, 2017). This study uses CACC in a slightly different way to examine whether the same areas of Baltimore remain high-risk throughout the year.

Results

Seasonal Variation in Risk Factors

Table 1 displays the findings of the yearly RTM. Of the ten spatial risk factors tested, the yearly model included five significant risk factors. The strongest risk factor the models identified was the proximity to bus stops, which generated a RRV of 2.908 and had a spatial influence of 202 feet. The five factors identified as significant by the yearly model indicate the spatial risk factors in which gun crime is associated with on a yearly time frame – these would be the risk factors that any intervention would be built around to identify gun crime.

While the yearly model included five risk factors that were significant, the monthly models varied in how many risk factors were significant ranging from one to three. In the monthly models, four risk factors were significant in at least one month: bus stops, off-site alcohol, and pawn brokers. Of these, bus stops and off-site alcohol establishments were the most cited figures being significant, with each being significant in eight months of the year. Pawn brokers were the least cited risk factor and were only significant in September. Restaurants were significant risk factors for six months out of the year. Risk factors that were significant by month are shown in Table 2 with their RRVs.

Table 1: Significant Risk Factors for yearly Risk Terrain Model (2013)

Sig. Risk Factor

RRV

OP

SI

Bus Stops

2.908

Proximity

202

Off Site Alcohol

2.477

Proximity

303

Restaurants

1.421

Proximity

202

Convenience Stores

1.597

Density

303

Schools

1.491

Proximity

404

Table 2: Relative Risk Value by Month

Month

Bus Stops

Off Site Alcohol

Restaurants

Pawnbrokers

Conv. Stores

Schools

January

3.988

2.871

2.898

-

-

-

February

6.729

3.746

-

-

-

-

March

-

4.934

-

-

-

-

April

-

4.303

4.74

-

-

-

May

9.103

-

-

-

-

-

June

5.188

2.342

-

-

-

-

July

7.517

3.017

2.574

-

-

-

August

2.78

-

3.063

-

-

-

September

19.472

-

-

-

-

-

October

-

2.846

3.941

6.10

-

-

November

-

3.963

-

-

-

-

December

7.017

2.741

2.83

-

-

-

All of 2013

2.908

2.477

1.421

-

1.597

1.491

There was large variability of which risk factors were significant in each month, and there was no discernable seasonal pattern for which factors appeared in which months. There was also a wide range in the relative risk scores presented for each risk factor. Bus Stops demonstrated the highest range of relative riskiness, with a high of 19.47 in September, and a low of 2.78 in August. Restaurants and off-site alcohol establishments both had relatively stable risk scores with ranges around two.

Five factors were identified as significant in the yearly model. Three of those factors (bus stops, off-site alcohol, and restaurants) were also significant in the monthly models. Two of them, schools and convenience stores, never reached significance in the monthly models. Similarly, the monthly models identified four risk factors that were significant in at least one month, and one of those, pawnbrokers, never reached significance in the yearly model.

It is expected that some factors from the yearly models and monthly models would overlap, with some yearly factors being also found in many months and some common monthly factors being found in the yearly model. Some of these factors, such as bus stops, reflect the larger routines of individuals in the city. These features are used in a consistent way throughout the course of the year. The overlapping of some features should not overshadow the variability that is found in the factors in the yearly and monthly models. For example, restaurants, which were significant in the yearly model, were found to be significant as often as they were insignificant in the monthly models. Other factors, such as pawnbrokers, were only found in the monthly models. Pawnbrokers’ smaller temporal association with gun crimes is not detected in the yearly model, but for October it displays a relative high level of riskiness with an RRV of 6.10, making it the riskiest factor for that month. These findings indicate associations with spatial features that are shorter in temporal nature but intense in that period. The divergent findings in the yearly model indicate a temporal trend that is not particularly strong in any given month, but provides a steady undercurrent throughout the year. In short temporal frames, schools and convenience stores never have enough crimes involving firearms occur around them to become significant risk factors, but over the course of the year there are enough incidents around these two features to reach that critical level.

Predictive Validity of Models

The results from the two sets of longitudinal logistic regression models to test the predictive validity of RTM produced similar odds ratios and all models were significant (p < .001). The first set of models tested the validity of the model for month one predicting the location of crime at month two. Utilizing the raw relative risk score, the models for time one predicting time two indicated that for every one unit increase in the relative risk score there was a 1.7% increase in the odds of a crime involving a firearm occurring in that location in the following month. Over the twelve months relative risk scores ranged from a low of 1 to a high of 118.8. When the model was run using only areas identified as being the most at-risk (those cells with an RRS value over 2 standard deviations above the mean), the results indicate that these areas were 2.7 times as likely to have a crime involving a firearm occur than all other areas. In terms of the seasonal effect of temperature and precipitation, temperature was significant (p < .05) in the model utilizing the relative risk score, indicating that for every one degree increase in temperature there was a 0.5% increase in the odds of a crime involving a firearm occurring in that location in that month, while precipitation was not significant. Temperature however was not significant in the models using the highest risk only cells, while precipitation was significant (p < .05), indicating that there was a 3.8% decrease in the odds of a crime occurring in that location in that month for every one inch increase in the amount of precipitation that month. Full results are in Table 3.

Table 3: Longitudinal Logistic Regression Results for Time 1 Predicting Time 2

Model

OR

SE

P

Relative Risk Score

1.017

.0020

.000

Average Temp.

1.005

.0023

.020

Average Precipitation

1.032

.0186

.072

Spatial Lag

1.357

.0311

.000

Linearity

1.006

.0128

.623

Days in Month

1.047

.0000

.360

Highest Risk Only

2.702

.2141

.000

Average Temp.

1.003

.0022

.242

Average Precipitation

0.962

.0173

.031

Spatial Lag

1.334

.0305

.000

Linearity

1.007

.0121

.546

Days in Month

1.166

.0596

.003

The second set of models tested whether a model in year one predicted the location of crime for the same time period in year two. The models indicate that for every one unit increase in the relative risk score there was a 1.9% increase in the odds of a crime involving a firearm occurring in that location in the same month in the following year. When the model was run using only areas identified as being the most at-risk, above two standard deviations from the average risk score, the results indicate that these areas were 2.49 times as likely to have a crime involving a firearm occur than all other areas. In terms of the seasonal effect of temperature and precipitation, in the model using the relative risk scores, temperature was significant (p < .01), indicating a 0.7% increase in the odds of a crime involving a firearm occurring in that location that month for every one unit increase in temperature, while precipitation was not significant. Temperature remained significant (p < .01) in the model using the only the highest risk areas, indicating the same 0,7% increase in the odds of a crime involving a firearm occurring in that location that month for every one unit increase in temperature, while precipitation became significant (p < .05), indicating a 4.5% decrease in the odds of a crime involving a firearm occurring in that location that month for every one inch increase in precipitation. Full results are in Table 4.

Table 4: Longitudinal Logistic Regression Results for Year 1 predicting Year 2

OR

SE

p

Relative Risk Score

1.019

.0019

.000

Average Temp.

1.007

.0022

.003

Average Precipitation

0.985

.0202

.460

Spatial Lag

1.290

.0379

.000

Linearity

1.005

.0113

.616

Highest Risk Only

2.490

0.180

.000

Average Temp.

1.007

.0023

.002

Average Precipitation

0.955

.0205

.031

Spatial Lag

1.279

.0378

.000

Linearity

1.022

.0114

.046

Persistence of High-risk Areas

 Our analysis now turns to the question of the spatial stability of high-risk cells throughout the 12 months of our study period. We utilized the CACC approach (Miethe et al., 2008) to identify the places in the study area with an RRS greater than two standard deviations above the mean (i.e. high-risk cells) for each month in 2013. The CACC allows us to identify whether precise geographies are high risk for a large proportion of the year or if cells’ risk levels vary on a month-to-month basis. This has important implications for place-based policing efforts, specifically in the identification of target areas. In particular, if high-risk areas persist for large portions of the year, then intervention target areas can perhaps remain stable over time. Conversely, if high risk-areas exhibit a large amount of spatial variation, then target areas may need to be rotated on a monthly basis in order to maximize the effect of the police-led intervention (Connealy and Piza, 2019).

Each row in the CACC table indicates a unique combination of months that a particular set of cells were at risk. The number of cells that this combination was empirically observed in is indicated in the number of cells column. Individual cells contained within the CACC table contain a binary indicator (yes/no) of whether that particular month was high risk or not in the combination. The final column of the CACC table contains the percentage of time that those cells that had that particular combination of high risk months were also high risk in a full yearly model. For example, for the combination with ID number 3, February, March, May, June, August, October, and November were high risk. Combination 3 was composed of 7,240 high risk cells, but none of these cells were high risk in the full year model.

Results from the CACC (see Table 5) indicate the majority of high-risk areas experience some type of variation throughout the year. A small subset of all cells, roughly 2.8% (1,894 / 66,613), were high-risk throughout the entire year. However, aside from the month of May, if a cell was risky in one month, then it was risky at least one other time throughout the year. The CACC also indicated that just because a cell was risky multiple months of the year, does not mean that it was risky in the model for the entire year. However, all cells that were risky for ten or more months of the year were high-risk in the model for the entire year.

Table 5: CACC Results

ID

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

# of Cells

% Related to 2013 Highest

1

No

No

No

No

Yes

No

No

No

No

No

No

No

28931

0%

2

No

No

No

No

No

No

No

No

No

No

No

No

16687

0%

3

No

Yes

Yes

No

Yes

Yes

No

Yes

No

Yes

Yes

No

7240

0%

4

No

No

No

No

Yes

No

No

Yes

No

No

No

No

4872

0%

5

No

Yes

Yes

No

Yes

No

No

Yes

No

No

Yes

No

2108

0%

6

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

1894

100%

7

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

No

Yes

Yes

Yes

1757

100%

8

No

Yes

Yes

No

Yes

Yes

No

Yes

No

Yes

Yes

Yes

808

0%

9

No

Yes

Yes

Yes

Yes

Yes

No

Yes

No

Yes

Yes

Yes

723

84%

10

No

No

Yes

No

Yes

No

No

Yes

No

No

Yes

No

712

0%

11

No

Yes

Yes

No

Yes

No

No

Yes

No

Yes

Yes

No

557

0%

12

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

324

100%

Discussion

This study utilized both yearly and monthly risk terrain models for crimes involving firearms in Baltimore, Maryland to accomplish three goals: 1) To look at whether spatial risk factors experience seasonal variations, 2) To see if RTM retained its predictive validity when it was used in a tactical month-to-month capacity, and 3) To see if the same areas remain high-risk throughout the year. The results indicated that not only were there changes in the risk factors that were significant month-to-month, but that RTM identifies different risk factors when used on a monthly basis versus when used over a longer time period. In addition, when RTM was used in the short-term capacity, it retained its predictive validity – the areas identified as most at-risk using data from month 1 had far higher odds of having a crime involving a firearm occur there in month 2. Support was also found for the spatial variation of high-risk areas across monthly temporal units. Areas that were identified as high-risk for one month were not necessarily high-risk in the subsequent month, but overall were found to be high-risk for at least one other time period throughout the year. All of these findings add significantly to both the academic literature surrounding RTM, and perhaps more importantly, to the practical applications of RTM by police departments.

The finding that risk factors and risky areas can vary by month builds upon prior research. Andreson and Malleson (2013) found the spatial distribution of crime changes seasonally. While no discernable seasonal pattern was able to be determined based on the risk factor distribution, understanding this distribution was beyond the scope of this study and should be pursued in future research. More directly related to the current study, Haberman, Sorg, and Ratcliffe (2018) tested the effect of crime generators and attractors on street robbery across seasons (i.e. spring, summer, winter, and fall) in Philadelphia. Contrary to our study, Haberman et al. (2018) found few seasonal differences. Outside of high schools, the effect of all criminogenic facilities and illicit markets included in the study were not significantly different across seasons. In contrasting our findings with Haberman et al. (2018), two factors are worth mentioning. First, our use of 12 monthly time periods may be better able to detect heterogeneity of risk factor effect on crime across time than the 4 seasons. Second, RTMDx tests the effect of each spatial risk factors at various spatial distances (i.e. half-block increments out to 3 blocks) and operationalizations (i.e. density or proximity). This statistical approach may have been better positioned to identify criminogenic effects of risk factors than the approach of Haberman et al. (2018), which measured the immediate (i.e. on the census block) and spatially lagged (i.e. on the contiguous census blocks) effects of the crime generators and attractors. Yet another explanation may be that street robbery in Philadelphia is more stationary that gun crime in Baltimore, for whatever reason. In short, given these research findings, we feel that researchers should continue to analyze how seasonality influences the criminogenic effects of environmental features.

In the current study, looking at risk factors monthly revealed two important practical points. First, certain risk factors, such as schools, found in the yearly model are not found in the monthly model. The yearly model amplifies the importance of these factors. This has practical consequences, because interventions generally do not last an entire year. This results in resources being applied to a factor during an intervention period (that typically spans several months) that is not significantly risky in any given month. The second practical point is that the yearly model washes out factors that are large risk factors in some months, but are not risky when looked at in the time frame of a year. This is demonstrated by the pawn shops, which are risky in one month alone, but in that month they are the riskiest place. An analysis based on a longer temporal perspective would not see this variation. An understanding of this variation and the accompanying risk narratives that may explain this variance can help police departments tailor interventions around specific spatial features or areas during certain times of the year and ensure that they have a full understanding of crimes associations to different spatial features across different time frames. For example, with bus stops, the risk narrative explaining why bus stops highest risk score occurs in September could be that as students return to school, they begin to take the bus again and encounter individuals that they have had long-standing grievances with but have not seen since the summer. This grievance could boil over when they encounter the other individual again, resulting in more crimes involving firearms in the vicinity of bus stops. As Kennedy et al. (2018) point out these narratives help to start conversations with the public and other stakeholders about how to address these risk factors. Ideally, the narratives lead to hypotheses that can be tested, furthering idea of using data to inform police work.

The identification of different risk factors being significant in either monthly models or yearly models casts light on different crime patterns. The overlap of risk factors indicates that interventions targeting some factors, such as bus stops in this study, would pay dividends throughout the majority of the year. The finding of other factors found only in either the monthly model or the yearly model indicates that there are some trends that are so distributed across time that when they are seen in a short time frame no relationship is discernable. While other trends are concentrated into such short time periods that they disappear under the weight of the aggregation of yearly statistics. This suggests that running RTMs using both short and long time frames has value – one for seeing highly concentrated series of events, and the other for seeing dispersed series. Using only one approach would lead to missing valuable insights into variations in risk factors.

The discussion of variation in risk factors by month only has practical purposes because of the models retaining predictive validity over smaller time frames. With the full year model and the month-to-month models producing slightly different risk factors, it indicates that there is value for police departments to use two distinct models concurrently. The rolling model based on the last twelve months of data would identify subtler trends, and the other using only data from the last month would identify trends that are more concentrated temporally. Additionally, the monthly model is able to include additional variables that can be useful for understanding seasonal fluctuations in crime, such as temperature and precipitation, which in our study produced modest mixed effects, remaining significant in some instances but not in others. The CACC demonstrating that only a small percentage of total cells are high-risk for all twelve months highlights the importance of this approach. Just because an area was identified as high-risk in the yearly model, does not mean that it was high-risk for every month of that year. The inverse of this is also true, a cell identified as high-risk in one month, is not necessarily high-risk for the entire year. Using models that are both short-term and long term in nature helps to see the nuances present in spatial-temporal relationships to high-risk areas. Using both sets of models would enable police departments to identify both types of trends and work to address them, albeit in different ways.

In addition to the benefits of using monthly models, there is also risk associated with them. For example, in the present study, in the month of May approximately 75% of all cells were classified as high-risk. The identification of 75% of cells as being high-risk limits the utility of the results from that month for police departments. In May, the only identified risk factor was bus stops. This fact, combined with the large number of bus stops that were present throughout the city led to the large number of areas identified as being high-risk. A subsequent analysis found that in May roughly 39% (58 / 147) of crimes involving firearms were within the spatial influence of less than 3% (71 / 2677) of all bus stops. This indicates that while bus stops do account for a significant proportion of crime, that it is only a small percentage of them. This aligns with Eck and colleagues’ observation of the application of 80-20 rule in environmental criminology where a small subset of a particular environmental feature are responsible for the majority of crime related to that feature (Eck, Clarke, & Guerette, 2007). The strong influence of bus stops was seen throughout many months of the year, but only in May did it have such a strong effect on the classification of high-risk areas. Bus stops prevalence in the models may be attributed to buses being a primary transit path and node, which would increase the number of suitable targets and motivated offenders.

The approach of combing monthly and yearly models would be a beneficial approach whenever a large geographic area is identified as high risk, such as when only a single risk factor is identified as significant in a given month. When only one risk factor is identified as significant every area within that feature’s spatial influence is deemed to be high risk, which can be problematic when the spatial feature is present throughout the city such as what occurs in the May RTM with bus stops. In these instances, combining the yearly data with the individual monthly data can help to better target interventions to smaller geographic areas by prioritizing the feature found in the monthly model that is located in the geographic areas identified as high risk in the yearly model. When the two areas are overlaid the result can help to focus interventions on the riskiest spatial feature in the area that is most susceptible to risk based on the previous year’s data. This would enable the yearly model to continue to inform the subtler trends, while the monthly model identified which feature was riskiest for that given time period.

This study does have several limitations most notably that it was restricted to one city and used only a total of twelve months of data. The city was also a temperate one where temperatures typically do not get too hot or cold. Still, even within a temperate climate our regression models indicate modest support for the relationship between higher temperatures and higher odds of crimes involving firearms. The overall trends observed in number of gun crimes and the average monthly temperature show some similarity to each other with both rising in the summer months, but gun crimes overall did experience other peaks that did not appear related to temperature. This is also true for precipitation, which showed a strong spike in June, then a sharp drop in July and August while gun crimes remained high throughout these time periods. No discernable pattern was seen in terms of which spatial features were significant and the temperature or precipitation in a given month. The challenge remains to understand the relationship of these variations and the specific spatial features that are identified as being relating to risk for a specific crime event. To overcome the climate limitation, this study should be replicated in multiple cities with varying climates to determine if the variability in spatial features holds in other environments. Future research of this area should also incorporate a finer grained temporal unit that includes different measures of temperature and precipitation that better reflect the variations. By using different temporal units, e.g. rainy days versus non-rainy days, as the unit of analysis it may be possible to further disentangle the influence of weather on the likelihood of crime as it relates to specific spatial features. An understanding of why certain risk factors are significant at different times of the year, and during specific weather conditions, would be valuable information for both the research and practitioner communities.

Additionally, when interpreting the results, the current authors are all in the academic realm, limiting the potential development of an accurate risk narrative (see Kennedy et al., 2018). This is not to take away from the current findings, but speak to the uniqueness of our view versus practitioners in the field, such as members from Baltimore Police Department. The translational value is limited to findings of relatable studies or hypothetical reasoning to our findings as we relate them to seasonality. Our findings do add to the growing literature on spatio-temporal analyses on the risk of crime, but we also believe the findings could be enhanced through a more embedded researcher-practitioner partnership. This approach/argument is not new (see e.g. Cordner & White, 2010; Engel & Whalen, 2010; Rojek, Smith, & Alpert, 2012; Tillyer, Tillyer, McCluskey, Cancino, Todaro, & McKinnon, 2014), and we are simply speaking to our findings being further understood if practitioners were involved, even in a secondary-data analysis.

Conclusion

When short-term RTMs are used they produce valuable insight by detecting risk factors that are associated with the outcome event for a brief temporal period. These insights are lost when data from longer time periods is used. As Groff (2007) argued, “… the importance of spatio-temporal elements in routine activities is often acknowledged, the spatial structure and timing of these activities has been widely overlooked.” While the current study did not capture the interaction of offenders, victims, and guardians, it did focus on how the convergence in time and space varies along the environmental backcloth. That is, from month to month, the findings identified a changing landscape of where gun involved crimes were likely to occur throughout Baltimore. The study demonstrated how some areas are not high-risk throughout the year and others are a nuance that is missed with yearly models. Similarly, this study has also highlighted the importance of using RTMs over larger time periods, these models detect risk factors that may be missed on a shorter basis due to how dispersed the events are over time. The two types of models highlight the importance of looking at crime events from multiple temporal perspectives, when only one perspective is used important elements can be missed.

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