Investigating the Applicability of the Near-Repeat Spatio-Temporal Phenomenon to Shot(s) Fired Incidents: A City-Level Analysis

1. Introduction

In the last few decades, studies have demonstrated that in addition to the fact that crimes do concentrate spatially, certain locations are repeatedly victimized or tend to experience elevated risks for subsequent crimes during a relatively short period of time (Bernasco, 2008; Bowers & Johnson, 2004; Johnson & Bowers, 2004; Sherman & Weisburd, 1995; Weisburd, Morris, & Ready, 2008). These phenomena are generally referred to as “repeat” and “near-repeat” patterns. Attention has been drawn particularly to the need to identify “near-repeat” patterns of crime in order to enhance police proactive, preventive and other strategies. Early studies of the near-repeat phenomenon focused on burglaries (Bernasco, 2008; Bowers & Johnson, 2005; Johnson & Bowers, 2004; Johnson et al., 2007; Sagovsky & Johnson, 2007; Townsley, Homel, & Chaseling, 2003). All of the studies suggested that incidents of burglary tend to show a near-repeat phenomenon because after an initial occurrence, nearby locations run increased risks of becoming burglary targets within a relatively short period of time. These studies identified not only locations where there was an elevated risk of crime, but also the specific time bands in which the risks were unusually high.

Results of these studies heightened interest in finding whether such phenomenona also existed in the distribution of other crime incidents. Researchers have employed the concept to analyze and examine the spatial and temporal distributions of other incidents such as shootings (Ratcliffe & Rengert, 2008; Wells & Wu, 2011), gun assaults (Wells, Wu, & Ye, 2012), robberies (Grubesic & Mack, 2008; Haberman & Ratcliffe, 2012), motor vehicle theft (Block & Fujita, 2013; Lockwood, 2012; Tonkin, Grant, & Bond, 2008; Youstin, Nobles, Ward, & Cook, 2007), and insurgent activity in Iraq (Townsley, Johnson, & Ratcliffe, 2008).

To date, scarcely any research exists that has distinctly investigated the extent to which near-repeat patterns are discernible in the spatio-temporal distribution of shot(s) fired incidents (unlawful discharges of firearms). Many police departments deal with these incidents of shot(s) fired; incidents that fortunately do not result in killing people (murders or homicides) or hurting or assaulting people (non-fatal shootings). As research has not yet explicitly examined the existence of near-repeat patterns for unlawful firearms discharges, little is known about whether near-repeat patterns exist for these incidents. Analyzing the near-repeat nature of unlawful firearms’ discharges, therefore, may have value for proactive policing, crime prevention and crime reduction.

The study reported here seeks to expand upon what is known about near-repeat patterns by determining the extent and nature of near-repeat patterns for an offense that has not yet been tested: unlawful discharges of firearms [“shot(s) fired”]. The study examines the extent to which shot(s) fired incidents concentrate in space and time simultaneously. If such patterns exist, do they differ from patterns demonstrated for other types of incidents? The present study seeks to extend existing empirical research by not only applying the near-repeat phenomenon to a relatively unexamined crime incident type, but also to quantify the extent to which the near-repeat phenomenon is influenced by the time of day in which the incidents occur. Research on the near-repeat phenomenon has generally focused on the dates incidents occurred. Not much is known about how these patterns differ by the time of day; i.e. how they differ by day and night. This study examines the extent to which near-repeat patterns identified in shot(s) fired incidents differ by day and night. Understanding what near-repeat patterns exist in unlawful firearms discharges and how the patterns differ by day and night could not only enhance the literature on near-repeats, but also help police formulate more efficient and effective prevention strategies in dealing with reports of shot(s) fired in many city neighborhoods. The brief report focuses exclusively on near-repeat patterns at the city-level in New Haven, Connecticut.

2. Setting and Data

The study relies upon data from the New Haven, Connecticut Police Department. New Haven is the second-largest city in Connecticut with a population of 129,779 people in 2010. The data used in this study consist of reported incidents of verified unlawful firearms discharges from January 1, 2013 to December 31 2015, using a total of 507 shot(s) fired incidents. The study uses incidents in which police found evidence of shell casings at the location of occurrence. The data analysis was undertaken by using the Near-Repeat Calculator (Ratcliffe, 2008, go to: http://www.cla.temple.edu/cj/center-for-security-and-crime-science/projects/nearrepeatcalculator/) and as such consisted of three values: the x-coordinate, the y-coordinate, and the date of the incident. The data was further grouped into daytime (0600 – 1759) and nighttime (1800 – 0559) incidents.

3. Methodology

Using the Near Repeat Calculator requires determination of which temporal and spatial bandwidths to use. For this study, 445 feet was selected as the spatial bandwidth because it is the average block length of New Haven streets. Although research on near-repeat patterns has used temporal periods of up to 2 months, the temporal bands selected for this analysis were 14 days, 7 days, and 4 days. The study is intended to identify patterns that would be more practical, meaningful and useful for the police in preventing and reducing occurrences of unlawful firearms’ discharges in the city.

The Near-Repeat Calculator software combines the revised Knox test and Monte Carlo simulation process to detect near-repeat crime (Johnson et al, 2007; Ratcliffe & Rengert, 2008). For this study, 999 Monte Carlo simulations were conducted. The Near-Repeat Calculator creates an observed pattern of event pairs within a spatio-temporal matrix (also called a Knox table) defined by the temporal and spatial bands selected. The spatial distance between events was calculated using Manhattan distance, a method that “… most accurately replicates the actual distance traveled by urban residents to get from point to point” (Ratcliffe & Rengert, 2008, p. 65). The Knox test is used to evaluate whether the number of incident-pairs that are both ‘‘close’’ in space and time is significantly larger than what is expected if the incidents were randomly distributed in space and time across the entire city. The space–time clustering identified in the data is compared against the null-hypothesis of a random distribution of incidents.

4. Analysis

The Near-Repeat Calculator was employed to find out whether the near-repeat phenomenon prevails in the occurrence of incidents of shot(s) fired in New Haven. The three selected time periods for analysis (14-day, 7-day, and 4-day) are each analyzed separately under sections A, B, and C below.

A. 14-Day Time-Span

Table 1 presents city-level results of the analysis which uses a 445-foot spatial bandwidth, a 14-day temporal bandwidth, and Manhattan distances. The table shows the significance level and observed over mean expected frequency across all the spatial–temporal bands. The significance levels of clustering are based on a pseudo p-value.

The lowest significance level for running the Near-Repeat Calculator is 0.05 while the highest significant level used is 0.001. The value in each cell is the ratio between the number of observed space–time pairs and the average expected pairs in the corresponding spatial–temporal band. It is the comparison of the observed frequency to the expected frequency that determines whether there is an overrepresentation of event pairs. Larger values indicate greater differences between an observed risk level and the risk level determined under the assumption of space–time randomness.

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As shown in Table 1, a significant and meaningful near-repeat pattern was found. The results show that after an occurrence of shot(s) fired incident, there is evidence of an over-representation of events in the local area for a certain amount of time. Within 1 to 445 feet of an initial incident, near-repeats are overrepresented for up to 14 days. Within 446 to 890 feet of an initial incident, near-repeats are overrepresented for up to 56 days and within 891 to 1335 feet of an initial incident, near-repeats are overrepresented for up to 14 days. Thus, in the immediate space-time vicinity to a source event, for example, the most over-represented space-time range that is significant is the zone from 1 to 445 feet and from 0 to 14 days from an initial incident. The 2.33 value is interpreted to mean that once a location experiences a shot(s) fired incident, the chance of a second one taking place within one street block and within the next 14 days is about 133 percent greater than if there were no discernible pattern.

Table 1 also confirms a significant and meaningful near repeat pattern. After a shot(s) fired incident, there is evidence of an over-representation of events at the same location up to 28 days after an initial incident. The most over-represented near repeat pattern range that is significant is the zone from 15 to 28 days from an initial incident. The chance of another incident occurring is about 369 percent greater than if there were no near repeat pattern.

B. 7-Day Time-Span

Table 2 presents city-level results of the analysis which uses a 445-foot spatial bandwidth, a 7-day temporal bandwidth, and Manhattan distances. Here too, a significant and meaningful near-repeat pattern was found. After a shot(s) fired incident, there is evidence of an over-representation of events in the local area for a certain amount of time. Within 1 to 445 feet of an initial incident, near-repeats are overrepresented for up to 14 days. Within 446 to 890 feet of an initial incident, near-repeats are overrepresented for up to 7 days and within 891 to 1335 feet of an initial incident, near-repeats are also overrepresented for up to 7 days. As can be seen from the table, in the immediate space-time vicinity to a source event, the most over-represented space-time range that is significant is the zone from 1 to 445 feet and from 0 to 7 days from an initial incident. The chance of another incident happening is about 179 percent greater than if there were no discernible pattern.

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A highly significant and meaningful repeat pattern was also found. After an incident, there is evidence of an over-representation of events at the same place up to 7 days after an initial incident. The most over-represented near repeat range that is significant is the zone from 0 to 7 days from an initial incident. The chance of another incident occurring at the same location after shot(s) fired incident is about 670 percent greater than if there were no near repeat pattern.

C. 4-Day Time-Span

Table 3 presents city-level results of the analysis which uses a 445-foot spatial bandwidth, a 4-day temporal bandwidth, and Manhattan distances. A significant and meaningful near-repeat pattern was also found for this shorter time span. After an incident, there is evidence of an over-representation of events in the local area for a certain amount of time. Within 1 to 445 feet (one street block) of an initial incident, near-repeats are overrepresented for up to 8 days. Within 446 to 890 feet of an initial incident, near-repeats are overrepresented also for up to 8 days, and within 891 to 1,335 feet of an initial incident, near-repeats are overrepresented for up to 4 days. In the immediate space-time vicinity to a shots fired event, the most over-represented space-time range that is significant is the zone from 1 to 445 feet and from 0 to 4 days from an initial incident. The chance of another shot(s) fired incident is about 179 percent greater than if there were no discernible pattern.

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With regard to the level of near repeat patterns, again a significant and meaningful pattern was found. After an incident, there is evidence of an over-representation of events at the same location up to 4 days after an initial incident. The most over-represented near repeat pattern range that is highly significant and meaningful is the zone from 0 to 4 days from an initial incident and the chance of another incident is about 1,038 percent greater than if there were no near repeat pattern.

Daytime and Nighttime Patterns

As indicated earlier, we were also interested in finding out the extent to which repeat and near-repeat patterns differ between day and night occurrences of shot(s) fired incidents. Most near-repeat pattern studies have not examined whether differences in the pattern identified at the city-level continue to exist when the time periods of incident occurrence are broken down by daytime (0600- 1759) and by nighttime (1800-0559). To examine the question of whether the citywide near-repeat patterns identified for shot(s) fired differ between day and night, we used the following parameters: 4-day time span, 445-foot spatial bandwidth and Manhattan distance to demonstrate the nature of repeat and near-repeat patterns during daytime and nighttime. The same citywide data of shot(s) fired were categorized into day and night. While near-repeat patterns still exist, there are some significant differences in the patterns identified (see Tables 4 and 5). These differences have some important implications for police operations in terms of engaging in both preventive and proactive activities to reduce incidents of shot(s) fired.

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Comparison of daytime and nighttime patterns shows some significant differences in near repeat patterns. First, there is no indication of repeat pattern over-representation during the daytime (Table 4). This means that shot(s) fired incidents do not appear to cluster in a statistical and influential way immediately after a prior event during the day time. However, a significant and meaningful repeat pattern is found during the nighttime. After a shot(s) fired incident, there is evidence of an over-representation of events at the same place up to 4 days after an initial incident. The most over-represented repeat range that is significant during the nighttime is the zone from 0 to 4 days from an initial incident (Table 5). The chance of another incident is about 1,307 percent greater than if there were no repeat pattern.

Second, a comparison of Tables 4 and 5 indicates some important differences in the near-repeat patterns during daytime and nighttime. A significant and meaningful near-repeat pattern exists in the occurrence of shot(s) fired during the daytime. After an incident there is evidence of an over-representation of events in the local area for a certain amount of time. Within 1 to 445 feet of an initial incident, near-repeats are over-represented for up to 4 days. For example, the 8.26 value is interpreted to mean that once a location experiences a shot(s) fired, the chance of a second one taking place within 1 to 445 feet and within the next 4 days is 726 percent greater than if there were no discernible pattern. This finding reveals a clear near-repeat of shot(s) fired. Also shown in Table 5, near-repeats are over-represented for up to 8 days during the nighttime, within 1 to 445 feet of an initial incident. In the immediate space-time vicinity to a source event, the most over-represented space-time range that is significant is the zone from 1 to 445 feet and from 5 to 8 days from an initial incident. The chance of another incident is about 170 percent greater than if there were no discernible pattern.

Observations and Further Research

This study applied the near-repeat phenomenon to shot(s) fired incidents, an unexamined crime type, using the city of New Haven as a case study. It focused on the city-level analysis of the extent to which the near-repeat phenomenon of shot(s) fired occurs. Statistically, whether one examines this phenomenon at a 14- day, 7-day or 4-day time-span, there is a definitive spatial-temporal pattern. The chance of another incident of shot(s) fired within one street block ranges from 133 to 179 percent greater than if there were no discernible pattern. Similar to findings of other studies, it is also evident that there is a clear spatial and temporal decaying pattern of the ratios. Looking at the observed-expected ratios in Table 3, for instance, the risk of additional shot(s) fired incidents is 179 percent greater within one street block of the original incident for 4 days following the original incident. That risk drops to 78 percent greater when considering an incident one to two blocks away for the same time period, and the level of risk continues to drop to 65 percent for incidents occurring even further away.

The relevance of analyzing daytime and nighttime near-repeat patterns has been emphasized in this study. The daytime and nighttime analysis demonstrates the importance of this level of examination for the occurrence of crime especially those for which time of occurrence can be precisely determined [e.g. shooting, robbery and shot(s) fired incidents]. During the daytime, the city of New Haven generally does not expect repeat patterns at the same location to occur within a short time because the analysis shows incidents do not appear to cluster in a statistical and influential way immediately after a daytime shot(s) fired incident. This is not, however, the case during nighttime when a significant and meaningful repeat pattern is found. This means, at the city level, when considering incidents of shot(s) fired at nighttime, officers should be conscious of the fact that repeat patterns are quite possible at some locations within a short time period.

Even though the city-level analysis has shown significant and meaningful near-repeat patterns, it must be emphasized that the risk of near-repeats appears unevenly distributed in space in the city. It is, therefore, important to further examine how the near-repeat patterns that have been identified in the context of the city of New Haven operates at the local-level. This local-level analysis will provide a description of “initiator” and “follow-up” incidents and examine the extent of geographic clusters of events within and across the city. The map below shows an example of the distribution of originators, near repeat and repeat patterns for 7-day time span. The map was produced using Esri’s® new crime analysis toolbox that support crime prediction using repeat and near repeat analysis.

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Those “initiator” incidents (or “originators”) are those that occur first and those that occur later in time are referred to as “follow-ups.” It will be very informative to know, for example, the number of times a shot(s) fired incident is an initiator, follow-up, or both, as well as the percentage of the number of shot(s) fired incidents that are part of near-repeat sets or near-repeat pairs. Some studies have indicated that a small portion of crime incidents are actually responsible for the significant near-repeat pattern at the local level. In New Haven, near-repeat patterns of shot(s) fired incidents are more clustered locally and are unevenly distributed in the city as the map above illustrates.

Further studies are needed to undertake a thorough local-level analysis of each incident site and gather information on the timing of initial shot(s) fired incidents and nearby follow-ups. This local-level analysis will make it possible to gain a more thorough understanding of the interactions among the shot(s) fired incidents and such knowledge will enhance place-based police strategies to reduce and prevent future incidents.

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Charles Anyinam

Charles Anyinam holds a PhD (Geography) from Queen's University, Kingston, Ontario, Canada and a Graduate Diploma (GIS) from York College of Information Technologies, Toronto. He taught at a number of universities in Canada including University of Toronto and York University, North York, Ontario, Canada. He is currently the Supervisor of the Crime Analysis Unit, New Haven Police Department, New Haven, Connecticut. His research interests include spatial-temporal analysis, predictive analytics, and use of a variety of techniques in crime mapping and analysis.

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