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DOI: 10.4018/IJAGR.2018040102
Volume 9 • Issue 2 • April-June 2018
This article published as an Open Access Article distributed under the terms of the Creative Commons Attribution License (http://cre-
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Rick L. Bunch, University of North Carolina Greensboro, United States
Christine Murray, University of North Carolina Greensboro, United States
Xiaoli Gao, University of North Carolina Greensboro, United States
Eleazer D. Hunt, Greensboro Police Department, United States
Domestic violence is an important public health issue, and there is limited research to date that
examines community-level influences on this serious form of violence. This article investigates
the neighborhood characteristics of domestic violence incidents in the city of Greensboro, North
Carolina. US Census block group boundaries and corresponding tables were used as proxies for
neighborhoods. The article addresses an important gap in domestic violence research by combining
geographic and statistical analyses at the block group level. Geographic data were analyzed using an
Optimized Hot Spot Analysis (OHA) along with features selected by penalized Poisson regression
model. The OHA was used to identify spatial clusters of high and low values while the penalized
Poisson regression model was used to select the important variables from over 7000 candidates.
The results of high-dimensional analysis produced six categories and 20 variables that were used to
examine the characteristics of spatial clusters.
Block Groups, Census, Crime Incidents, Domestic Violence, Geographic Information Systems (GIS), Intimate
Partner Violence, Neighborhoods, Penalized Poisson Regression Model
Domestic violence (DV) is a serious public health issue that occurs in all communities, regardless of
race, ethnicity, age, gender or socioeconomic status. Victims often suffer unfavorable health outcomes
that arise from emotional, physical, and psychological abuse, as well as financial abuse (Bogat et al.,
2005; Kessler, Molnar, Feurer, & Appelbaum, 2001). High rates of DV also place significant amounts
of pressure on community resources, such as those offered by family service agencies, violence
prevention networks, support organizations, and local law enforcement.
A survey conducted by the National Network to End Against Domestic Violence (NNEDV)
recorded an astonishing 21,332 hotline calls over a 24-hour period from individuals in the U.S.
Volume 9 • Issue 2 • April-June 2018
15
who were identified as victims in danger or in need of support (NNEDV, 2015). Likewise, a study
conducted by the Centers for Disease Control and Prevention (CDC) reported that an average of 20
people are physically abused by an intimate partner every minute (Black et al., 2011). This equates
to over 10 million cases of abuse annually. The high prevalence of DV and its devastating impacts on
victims, families, and communities underscore the need for further research that can inform practice,
support victims, educate communities, guide law enforcement policies, and reduce rates of abuse.
Recent research on DV has increasingly focused on understanding how the characteristics of
neighborhoods can influence and predict rates of DV. A portion of this research has attempted to
identify correlates between neighborhood influences and rates of DV, with some being underpinned
by social disorganization and contagion theories (Beyer, Layde, Hamberger, & Laud, 2013; Beyer,
Wallis, & Hamberger, 2015). Although key to DV research, the delineation of a neighborhood has
proven to be a difficult task mostly because the definition is subjective and imprecise (Benson, Fox,
DeMaris, & Van Wyk, 2003). To address this problem, several studies have used U.S. Census Tracts
as surrogates for neighborhoods (Lee, Zhang, & Hoover, 2013; Raul, Suhasini, & Harris, 2010).
Beyer, Layde, Hamberger, and Laud (2015), for example, used U.S. Census Tracts to examine the
characteristics of victims (individual-level) in relation to neighborhood demographic variables, such
as proportion below poverty, single-parent households, and unemployed.
Surprisingly, there has been very little DV research conducted at the U.S. Census block group
level, despite the perceived benefits (Beyer, Wallis, et al., 2015). Murray, Bunch, and Hunt (2016)
argued that block group level analysis provides the most promising approach for conducting DV
research since data are readily available as geospatial datasets, act as better proxies for neighborhoods,
and provide smaller enumeration units for conducting detailed geographic analysis. Additionally, DV
studies on rates and neighborhood influences have received far less attention when compared to other
health research (e.g., cancer incidence rates, birth defects etc.), and very little work has employed
the use of a Geographic Information Systems (GIS) (Beyer, Layde, et al., 2015; Beyer, Wallis, et al.,
2015; Murray et al., 2016). Much like other health studies, well established GIS-based crime research
has not specifically focused on DV. Many of these studies have opted to wrap DV cases into broader
categories such as violent crimes (Law, Quick, & Chan, 2015). However, given the relational patterns
that underscore DV, this form of violence warrants special consideration in both research and practice.
The purpose of this study is to examine the distribution of DV incident locations and the
characteristics of their neighborhoods in the city of Greensboro, North Carolina (NC). Block group
geometry and corresponding attribution from the U.S Census Bureau were used as surrogates for
neighborhoods. This study addresses an important gap in DV research by combining geographic and
statistical analyses at the block group level (Beyer, Wallis, et al., 2015; Murray et al., 2016). Data
were analyzed using an Optimized Hot Spot Analysis (OHA) and a penalized Poisson regression
model. The OHA was used to identify spatial clusters of high and low values of DV percentages
while, the penalized Poisson regression model, was used to select from over 7000 neighborhood-level
variables that influenced DV incident counts. The results were summarized by zone (hot spots and
cold spots) and compared using descriptive statistics. The foundation of this research is based upon
three research questions. First, are there any statistically significant spatial patterns with respect to
the distribution of DV incident locations within the city limits? Second, if spatial patterns exist, what
are the characteristics of the underlying neighborhoods? And third, how do the results compare to
the larger body of work on DV and neighborhood level influences?
It is important to note that we adopted the term “Domestic Violence” for this paper to broadly capture
domestic relationships that suffer from some form of abuse. It is recognized, however, that most cases
of DV involve Intimate Partner Violence (IPV) and that the two terms are often used synonymously.
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The National Coalition against Domestic Violence (NCADV) provides the definition that will be
used throughout this paper:
Domestic violence is the willful intimidation, physical assault, battery, sexual assault, and/or other
abusive behavior as part of a systematic pattern of power and control perpetrated by one intimate
partner against another. It includes physical violence, sexual violence, threats, and emotional or
psychological abuse. (NCADV, 2015, p. 1)
Research on neighborhood characteristics and their influence on DV has produced mixed results
(Beyer, Layde, et al., 2015; Beyer, Wallis, et al., 2015; Raul et al., 2010). This may reflect a failure
to consider the interactions among neighborhood variables with influences at other levels, such as
government policies or family relationships. However, of the studies reviewed on this topic, a majority
of the work demonstrated at least some evidence that neighborhood influences are associated with
DV (Beyer, Wallis, et al., 2015).
To illustrate the methods used and variables studied in past research, this section includes an
overview of key research studies that have examined neighborhood influences on DV. The studies
are listed in chronological order to demonstrate how research in this area has evolved over time. In
addition, GIS studies within the context of DV, and crime mapping and analysis are also discussed
in this section.
Benson et al. (2003) analyzed data from the first two waves of data (i.e., 1988 and 1994) from the
National Survey of Families and Households, combined with data from the 1990 U.S. Census, in
order to examine the impact of neighborhood characteristics on DV perpetrated against women. Their
findings revealed that, after controlling for violence at the first-time point, the following neighborhood
variables impacted violence at the second time point: economic disadvantage, residential instability,
male employment instability, and subjective financial strain. Contrary to what the researchers
hypothesized, however, higher residential instability was associated with lower rates of DV, which
they suggested may be indicative of people in lower income neighborhoods moving less due to fewer
economic resources for moving. An advantage of this study was that the data were derived from an
anonymous study, rather than police data that require participants to report DV to local authorities.
O’Campo, Burke, Peak, McDonnell, and Gielen (2005) used concept mapping to identify
neighborhood domains that impact DV, using a participant sample of 37 women living in Baltimore
City, most of whom were African American and at least 30 years old. Many of these women had
prior experiences of DV, although it was not required for participation to be a survivor of past abuse.
The researchers used three main activities to generate the data: brainstorming groups, sorting and
rating groups, and groups to discuss how neighborhood factors were related to experiences of DV.
The concept mapping approach identified seven clusters of characteristics of neighborhoods that are
linked to DV experiences: deterioration, negative social attributes, violence attitudes and behaviors,
stabilization factors, neighborhood monitoring, communication networks, and community enrichment
resources. Similarly, Button (2008) demonstrated that neighborhoods in which there are higher levels
of crime showed higher levels of approval of DV. In general, people who accepted one form of
violence were more likely to have accepting attitudes toward other forms of violence (Button, 2008).
The study concluded that attitudes toward different types of family violence can be considered both
an individual- and community-level phenomenon.
The density of alcohol outlets has also been studied as likely influences on neighborhoods and
rates of DV. Roman and Reid (2012), for example, were interested in both on-premise alcohol outlets
(i.e., restaurants and nightclubs) and off-premise outlets. The findings of their study highlight the
importance of making this distinction. Off-premise outlets were significantly associated with higher
rates of DV, while on premise outlets were related to decreased rates of DV. More specifically, the
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increased risk of DV in areas with higher densities of off-premise outlets was present for weekends,
but not for weeknights. The researchers propose that these findings suggest that there are different
ways that alcohol use may impact perpetrators use of violent, abusive behaviors at different times
during the week.
The type and location of community organizations, such as churches, located in and around
neighborhood communities have also been studied within the context of DV. Triplett, White, and
Gainey (2013) compared the relationships of churches within a neighborhood to rates of street and
domestic violence. Churches were theorized to play a stabilizing role within a neighborhood, and
they were thought to be present in all types of neighborhoods, so different church characteristics
could have unique influences on their surrounding neighborhoods. Their findings showed the exact
opposite. More churches in a neighborhood were associated with higher rates of both street crime
and domestic violence. However, the researchers stated that there were no known reasons to assume
that, as may be the case with alcohol outlets, there was a certain pathway through which churches
actually promote violence. Rather, the researchers speculate that churches may be limited in their
ability to change the surrounding community with respect to violence.
Geographic analysis is useful for mapping spatial patterns and analyzing relationships among features.
Coy, Kelly, Foord, and Bowstead (2011) provided one of the few studies that used GIS to analyze
DV. Their study mapped the female populations and the locations of DV support services throughout
England, Scotland, and Wales. When considering the underlying female population, they found that
the distribution of DV support services were the highest in urban areas and lowest in areas that were
on the edge of urban development. The second part of their study examined the relocation of women
fleeing domestic violence by capturing the direction and distance of travel. The study revealed that,
on average, relocating women traveled 30.47 miles to obtain services either north to south or east
to west of their prior residents. Hetling and Zhang (2010) also used GIS and spatial statistics to
examine the locations of DV assault rates, DV serving agencies and levels of poverty using bivariate
correlations and testing for spatial patterns. They found a strong correlation between poverty rates
and domestic violence assaults. The study also discovered that DV serving agencies were located in
more disadvantaged areas with higher rates of overall crime. It is important to note that their study
used cities and towns in Connecticut as the geographic unit for the analysis.
A review of the literature clearly demonstrates the major role geography plays in the understanding
of the dynamics between neighborhood influences and cases of DV. The literature also highlights the
existence of a relatively few studies that have used GIS to address fundamental geographic questions
within the context of DV. This opens up a wide range of opportunity for geographic researchers to
work collaboratively with those who have expertise in DV (Murray et al., 2016). A major problem for
many studies has been centered on acquiring data, since many have had to rely on expensive and time-
consuming surveys while some have settled on over generalized data. At least in the U.S., exploiting
the rich data from the U.S. Census Bureau at the block group level seems to be a good starting point,
especially when considering the maturation of GIS, geospatial datasets, and corresponding methods.
The well-established research on crime mapping and analysis provides a solid foundation for studying
the influences of neighborhoods on cases involving DV.
Classic hot spot analysis and mapping studies have operated under the assumption that locations of
crime incidents are unevenly distributed across geographic space. Crime incident locations are often
scanned by algorithms that take into account the local pattern (a target feature and its neighbors) in
relation to the global pattern (all features) within the study area (Chainey & Ratcliffe, 2005). Some
algorithms address random and nonrandom point patterns while others focus on spatial autocorrelation
by incorporating attributes at locations. Crime incident locations can be aggregated by points (the raw
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counts of crime incidents at one particular location) or by polygon (e.g., raw counts of crime incidents
by Census block group or grid). In some cases, the crime incidents are normalized to produce rates
(e.g., per 100,000 people) and used as inputs instead of raw counts. Areas identified as hot spots are
often explained in terms of the interaction between victims and offenders as well as the opportunity
to commit a crime (Cohen & Felson, 1979). Socioeconomic and demographic factors have also been
used to explain high concentrations of crime rates with respect to the underlying population (Wang
et al., 2013). The main goals of crime hot spot mapping are to efficiently visualize threats, allocate
crime reduction resources, and provide predictive measures (Chainey, Tompson, & Uhlig, 2008;
Cohen & Felson, 1979).
There are many approaches to mapping and analyzing crime incident locations (Chainey &
Ratcliffe, 2005). Nearest neighbor analysis, for example, is a discrete point pattern technique that
examines global patterns to uncover randomness or clustering (Clark & Evans, 1954). However, the
method only uses distances between points and does not take into account spatial autocorrelation.
Additionally, techniques of simple point and choropleth mapping and density estimations are very
useful for visualizing the distribution of crime incidents, but they do not incorporate the capacity to
conduct statistical comparisons among clusters of values. Local Indicators of Spatial Association
(LISA) is a technique that detects spatial autocorrelation at the local level using Moran’s I (Anselin,
1995). The method calculates an index and a Z-Score for each feature, allowing comparisons against
the mean. However, the use of the Moran’s I does not show whether clustering consists of either low
or high values. As an alternative, many crime studies have used the local version of the G-statistic
which can make the distinction between clusters of high (hot spots) and low values (cold spots) (Getis
& Ord, 1992; Getis & Ord, 1996; Wang et al., 2013). The use of any particular method for analyzing
the location of crime corresponds directly with the research questions and needs of those conducting
the study. In some cases, it may make sense to analyze crime incident locations as discrete points and
use the results for visualization or as inputs for subsequent queries. In other cases, researchers may
need to aggregate crime incident locations by a geographic unit to incorporate attributes and tests
for spatial autocorrelation (Hart & Zandbergen, 2014).
Census boundaries and fishnets (grids) are commonly used as polygons for aggregating crime
incident locations. The use of Census boundaries has a built-in advantage since they provide a wide
range of socioeconomic variables that can be used to further explain the relationship between crime
and the underlying characteristics of the population. Producing crime rates are also possible since
estimates of the population, residents, households and other totals are available. However, aggregating
by Census boundaries can be problematic since police jurisdictions and Census boundaries are often
not coincident. In this case, areal interpolation can be performed or fishnet polygons can be generated
and positioned over crime incident points where counts are produced for each polygon cell. Several
researchers have developed methods for computing the appropriate size for fishnet polygons while
others have provided methods for adjusting for multiple testing and spatial dependency (Caldas de
Castro & Singer, 2006; Chainey & Ratcliffe, 2005; Sun, Reich, Tony Cai, Guindani, & Schwartzman,
2015). The use of the raster data model and corresponding cells rather than polygons to aggregate
crime incidents have also been studied in the context of risk surfaces (Kennedy, Caplan, & Piza, 2011).
Risk Terrain Modeling (RTM) was developed as a method for identifying, visualizing, and
predicting crime risk (Caplan, Kennedy, & Miller, 2011). The fundamental approach to conducting
RTM is to create raster surfaces based on spatial influence for each individual risk factor, and then
combine them to produce a composite surface. RTM leverages the concept of map algebra and is similar
to the concepts applied to raster based site suitability studies (Nowlin & Bunch, 2016). Caplan et al.
(2011), for example, generated point density surfaces for three risks factors that were associated with
crime shootings. Each density surface was subsequently reclassified to ordinal rankings (0 – 3) using
standard deviation values. The reclassified raster surfaces were summed using a local operation to
produce a composite map with the highest values representing the highest risk. Past shooting incident
locations were overlaid on top of the composite surface and assessed for accuracy. This work was
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extended later to include thirteen selected risk factors (e.g., gang hot spots, bus stops, etc.) associated
with aggravated assaults, their spatial influences, and a weighted composite surface (Kennedy, Caplan,
Piza, & Buccine-Schraeder, 2016). The assessment showed that RTM was able to accurately predict
the locations of places that are likely to experience future crime (Kennedy et al., 2016). RTM requires
point features and conducts the underlying analysis and rendering using the cells that make up raster
surfaces. This limits the inclusion of other attributes and geographic analysis units such as those that
capture neighborhood level influences on crime (Drawve, Moak, & Berthelot, 2016).
There is no set standard on which method to use when analyzing crime incident locations
for patterns. The spatial element of crime is complex, making it difficult to find one method that
addresses all circumstances. Some studies have demonstrated advantages for one method over
another in certain instances. Kernel Density Estimation (KDE) and nearest neighbor hierarchical
(Nnh), for example, have been shown to outperform several other methods, but results and the
appropriate application can vary widely depending on the parameters used, geographic scale, type
of crime, and the underlying assumptions made by researchers (Chainey & Ratcliffe, 2005; Chainey
et al., 2008; Drawve et al., 2016).
The scope of this research is to analyze and identify neighborhood level influences of the DV incident
patterns located within the city limits of Greensboro, NC. Block group TIGER/Line files were used as
surrogates for neighborhoods, and corresponding detailed tables were acquired to provide attribution.
The locations of DV incidents were aggregated using census geometry and analyzed for spatial patterns
with an Optimized Hot Spot Analysis (OHA). Attribution derived from ACS 5-years estimates was
subjected to a separate statistical analysis as a way to cull the number of variables down to those
that likely influence counts of DV incidents. The following provides a discussion on the study area,
acquired data, pre-processing procedures, and the analyses.
The study area for this research is the City of Greensboro, NC (Figure 1). The city limits of Greensboro
is an irregular shaped polygon that covers approximately 137.7 square miles of Guilford County. It
is the third largest city in the state, and the largest within the county in terms of population. As of
2015, there were 285,342 people living in the city. Overall, the population of Greensboro is diverse
with 47.7% White; 40.6% African American; and 4.5% Asian. The remaining population is a mix of
American Indian, Pacific Islander, and some other race. The median household income for residents
in the year of 2015 was $41,628, with 19.3% of persons living in poverty, and 88.7% of the people
(age 25 years and over) having at least a high school diploma or equivalent. The total crime rate in
the City of Greensboro for 2015 was 4,243 per 100,000 inhabitants, and the violent crime rate was
608 per 100,000 inhabitants.
All crime incident locations for the year of 2015 were obtained from the Greensboro Police Department
(GPD) whose jurisdiction falls within the city limits. Crime incident reports were converted to
geospatial datasets by the GPD crime analysis unit. The conversion involves geocoding address
locations of reported crimes, and populating the corresponding fields with descriptors about each
crime. In this process, the GPD also provides a marker for identifying whether the reported crime
involved instances of DV. Crime incidents identified as DV cases (n = 2,725) were selected from all
crime incidents (n = 30,655) and used as input for the analysis (Figure 2).
When considering previous research on neighborhood level influences of DV, demographic
composition, educational attainment, and economic conditions of neighborhoods have begun to
emerge as common themes (Murray et al., 2016). To examine these themes, the 2010-2014 American
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Figure 1. The city limits of Greensboro, NC (delineated by the light orange polygon) is situated in Guilford County
Figure 2. Domestic violence incident locations (n = 2,725)
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Community Survey (ACS) 5-year estimates were acquired from the U.S. Census Bureau for Guilford
County. These data are designed to be used in GIS, and made available as a geodatabase. The
geodatabase was comprised of block group TIGER/Line files and 20 detailed tables containing 7,056
fields collectively. The boundaries and tables can be joined or related by a unique key. Each table and
their associated attributes are organized by theme (Table 1). At the time the analysis for this study
was conducted, the ACS 2011-2015 5-year estimates and corresponding geodatabases at the block
group level were unavailable.
City limit geometry for this study was obtained from Greensboro’s Planning Department. The city
limits are not coincident with the boundaries of Census block groups. To address this issue, a map
overlay operation using the intersect method was performed on the block group TIGER/Line files
and the city limit boundary (Figure 3). Attributes and metrics for the newly created geometry were
recomputed using areal interpolation (Goodchild & Lam, 1980). A proportion was calculated by
dividing the area of the new polygons by the area of the original polygons. The resulting proportion
was used to update the attribution for the new polygons by multiplying the decimal equivalent by the
attribute value of the corresponding original polygon. For example, if the new polygon represented
half the area of the original polygon with a population of 200 people, the decimal equivalent of 0.5
was multiplied by 200 to produce a population of 100 for the new polygon. Any block group geometry
separated into two features by the intersect overlay operation were re-aggregated using the dissolve
Table 1. U.S. census bureau datasets used for the study
Name Vintage Geographic Level
1. Age and Sex 2010-2014 ACS 5-year estimates Block Group
2. Race 2010-2014 ACS 5-year estimates Block Group
3. Hispanic or Latino Origin 2010-2014 ACS 5-year estimates Block Group
4. Migration 2010-2014 ACS 5-year estimates Block Group
5. Commuting 2010-2014 ACS 5-year estimates Block Group
6. Children Household Relationship 2010-2014 ACS 5-year estimates Block Group
7. Household Family Subfamilies 2010-2014 ACS 5-year estimates Block Group
8. Marital Status and History 2010-2014 ACS 5-year estimates Block Group
9. School Enrollment 2010-2014 ACS 5-year estimates Block Group
10. Educational Attainment 2010-2014 ACS 5-year estimates Block Group
11. Language Spoken at Home 2010-2014 ACS 5-year estimates Block Group
12. Poverty 2010-2014 ACS 5-year estimates Block Group
13. Income 2010-2014 ACS 5-year estimates Block Group
14. Earnings 2010-2014 ACS 5-year estimates Block Group
15. Veteran Status 2010-2014 ACS 5-year estimates Block Group
16. Food Stamps 2010-2014 ACS 5-year estimates Block Group
17. Employment Status 2010-2014 ACS 5-year estimates Block Group
18. Industry Occupation 2010-2014 ACS 5-year estimates Block Group
19. Housing Characteristics 2010-2014 ACS 5-year estimates Block Group
20. Health Insurance 2010-2014 ACS 5-year estimates Block Group
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operation. This ensured that the geometry, even if multipart, contained the one and only record from
its original parent block group. The choice to conduct areal interpolation was based on the premise
that Census block groups tend to be more homogenous than Census tracts, and that they are designed,
with input from the local communities, to be relatively consistent with respect to the distribution of
the population, living conditions, and socio-economic status (Iceland & Steinmetz, 2003).
DV counts were computed as an attribute for each block group through a spatial join. The results
of spatial join generated the feature class that was used in OHA. All tables from the ACS 5-year
estimates were joined to the block groups using a unique key. The resulting 20 tables contained
fields populated by the unique block group identifiers, all corresponding ACS 5-year estimates, and
counts of DV incidents for each block group. The 20 tables were exported and used in the statistical
analysis. There were originally 203 block groups but the number was reduced to 200 since three
were removed due to their uniqueness. For example, the city limits covered a portion of one block
group that represented the Piedmont Triad International Airport (PTI) where no one lives. The other
two encompassed the University of North Carolina Greensboro (UNCG) and North Carolina A&T
State University (NC A&T) respectively. UNCG maintains their crime reports through their own
police department. The crime records for UNCG are not routinely shared with the GPD, and were
not included in the study. Figure 3 provides a summary of the data pre-processing steps.
DV incidents for each block group were normalized by dividing counts by the number of households
and converting them to percentages. Figure 4 is a choropleth map displaying the percentages of DV
incidents by total households for each block group. A crescent shaped pattern emerged along the
southwest to the south and southeast and upward into portions of the northeast. Additionally, the
northwest portion of the city consisted of relatively low percentages when compared to other regions.
The areas denoted by the color of black signify the three block groups that were not included in the
analysis. The area to the west is a portion of the PTI airport, and the central and east areas represent
the locations of UNCG and NC A&T respectively. Although the choropleth map helps to discern
broad patterns, there are no statistical comparisons among local clusters. To examine this issue, spatial
statistics were used to identify significant clusters of high and low values.
An Optimized Hot Spot Analysis (OHA) was used to identify statistically significant spatial
clusters of hot and cold spots using block group polygons. To test for spatial clustering and significance,
Figure 3. Data pre-processing steps
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the percentages were used as inputs in the analysis field. The OHA uses the Getis-Ord Gi* statistic
and offers optimal methods for computing the appropriate scale of analysis as well as corrections for
both multiple testing and spatial dependence (Caldas de Castro & Singer, 2006; Sun et al., 2015).
The OHA examines each local pattern (target feature and its neighbors) in relation to global patterns
(all features), and renders the results by percent confidence level.
A statistical analysis was performed to investigate how the average number of domestic violence
counts are affected by factors. If the number of factors is small and the variables are not correlated,
it was assumed that each variable has a multiplicative effect on the average counts while fixing all
other variables, and estimating those multiplicative effects using a Poisson regression model. There
were 7,056 features in the ACS 5-year estimates from 200 block groups in total. The large number of
features presents a typical high-dimensional problem since the number of variables (7,056) is much
larger than the sample size (200 block groups). In general, not all 7,056 features affect the average
number of domestic counts importantly and strong correlations exist among the large number of
features. We were interested in finding a parsimony model (choose some important variable sets
out of 7,056 variables) and investigating their effect on incident counts. Thus, the classical Poisson
regression model was not feasible due to the high-dimensionality and multicollinearity of the data.
Instead, a penalized Poisson regression model with elastic net penalty was adopted (Agresti, 2013;
Zou & Hastie, 2005) to select a much smaller subset of important variables as a way to investigate
their effect on the domestic violence counts. The model assumes that average DV counts are roughly
the same as the variability of the DV counts, and that not all features (variables) are important. After
Figure 4. A choropleth map showing domestic violence patterns in the City of Greensboro. The areas denoted by the color of
black were excluded from the analysis since they represent the Piedmont Triad International Airport, UNCG and NC&AT (ordered
from west to east).
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performing the high-dimensional count data analysis, we used 1/-1 to indicate either a positive or
negative effect on the DV incident counts (dependent variable). Generally, a variable with a positive
effect indicates an increasing variable value, causing the average incident count to scale up (with a
multiplicative effect being larger than 1), while a variable with a negative effect indicates an increasing
variable value, causing the average incident count to scale down (with a multiplicative effect being
smaller than 1).
The results of the OHA were used to categorize block groups into two significant zones based upon
confidence level. Attribute values representing the selected factors were summarized by zone to
produce descriptive statistics and metrics for comparison. This section provides a discussion of the
results of OHA and the penalized Poisson regression model, and concludes with a comparison of the
two zones using the selected variables and descriptive statistics.
The OHA yielded DV percentages ranging from a minimum of 0.00 to a maximum of 11.11 (M
= 2.68, SD = 2.56, n = 200). There were a total of 143 features statistically significant at the 90%
confidence level and higher. The analysis clearly identified a cold spot region in the northwest portion
of the city where low values tended to cluster. Conversely, the analysis also showed a hot spot region
in the southeast portion of the city where high values were clustered (Figure 5). These two distinct
Figure 5. The results of the optimized hot spot analysis on domestic violence percentages
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zones were examined in combination with the variables selected by the penalized Poisson regression
model to better understand the underlying characteristics of the neighborhoods.
Based on effect, the penalized Poisson regression model with elastic net penalty selected 20 of 7,056
variables considered in the analysis (Table 2). The 20 variables were represented by the following
categories: a) Race, b) Children Household Relationship, c) Household Family Subfamilies, d) School
Enrollment, e) Educational Attainment, f) Industry Occupation, and g) Housing Characteristics.
The results of the analysis suggested that variables associated with Race had a negative effect
on domestic violence incidents when the population was White alone, White alone or in combination
with one or more other races, or Native Hawaiian and Pacific Islander alone or in combination
with one or more other races (Table 2). A negative effect was also observed when the variable for
Children Household Relationship contained households with spouses but a positive effect when
family households was comprised of children with other relatives. There was also a positive effect
Table 2. Results of the penalized Poisson regression model for high-dimensional count data analysis. The table shows the
categories and significant variables. Categories are numbered for reference and correspond to Table 1.
Category Name Variable Effect
2. Race
1. White alone: Total population -1
2. Total: White alone or in combination with one or more other races -1
3. Total: Native Hawaiian and Other Pacific Islander alone or in combination
with one or more other races -1
6. Children Household
Relationship
4. In households: In family households: Spouse: Total population -1
5. In households: In family households: Other relatives: Total population 1
6. In households: In nonfamily households: Householder: Male: Total
population 1
7. Household Family
Subfamilies
7. Total: Households with a householder who is Black or African American alone 1
8. Total: Households with a householder who is Some other race alone 1
9. Total: Households with a householder who is Hispanic or Latino 1
10. Total: Population in households with a householder who is White alone,
not Hispanic or Latino -1
9. School Enrollment 11. Total: White alone population 3 years and over -1
12. Total: White alone, not Hispanic or Latino, population 3 years and over -1
10. Educational Attainment 13. Total: Population 25 years and over with a bachelor’s degree or high
attainment -1
18. Industry Occupation
14. Total: Civilian employed Some other race alone population 16 years and over 1
15. Total: Civilian employed White alone, not Hispanic or Latino population
16 years and over -1
16. Total: Civilian employed Hispanic or Latino population 16 years and over 1
19. Housing Characteristics
17. Total: Vacant housing units 1
18. Renter occupied: Total population in occupied housing units 1
19. Renter occupied: 1, detached or attached: Total population in occupied
housing units 1
20. Renter occupied: 2 to 4: Total population in occupied housing units 1
Volume 9 • Issue 2 • April-June 2018
26
when nonfamily households had a male as head of the household. Household Family Subfamilies
had variables that showed a positive effect when the householder was African American, some other
race alone, or Hispanic or Latino. In the same category, however, there was a negative effect when
the householder was White alone, not Hispanic or Latino. School Enrollment had variables that
showed a negative effect for children age 3 years and over who were White alone or White alone,
not Hispanic or Latino. A negative effect was also observed for Educational Attainment variables
when the population 25 years and older had a bachelor’s degree or higher. The category of Industry
Occupation revealed a positive effect for variables where employed civilians were some other race
alone or Hispanic or Latino but a negative effect when the employed civilians were White alone, not
Hispanic or Latino. All variables for Housing Characteristics selected by the analysis demonstrated
a positive effect for vacant housing units, renter occupied, and tenure of renter occupied housing
units (1 year and 2 – 4 years).
All block groups identified as significant at the 99% confidence level were selected from the results of
the OHA, and summarized to compute descriptive statistics using the selected 20 variables displayed
in Table 2. The two distinct zones are shown in Figure 6. The Cold Spot zone (blue) consisted of 40
block groups and contained 195 DV incidents (M = 4.88, SD = 3.24), and 27,347 households (0.71%
of Households). The Hot Spot zone (red) is comprised of 68 block groups, 1,488 DV incidents (M =
21.88, SD = 13.25), and 34,011 households (4.38% of Households).
Table 3 represents a summary of all counts from the ACS 5-year 2010-2014 estimates for each
significant variable by Hot Spot and Cold Spot zones within the study area of Greensboro, NC. The
selected variables associated with Race were found to be important neighborhood characteristics
that influence the prevalence of DV. The Cold Spot zone had a higher percentage of White alone
population (77.38%) compared to the Hot Spot zone (26.67%). This suggest that regions with higher
percentages of White alone populations have relatively lower incidents of DV (negative effect). The
Figure 6. Selected block groups are grouped into two zones for descriptive comparison
Volume 9 • Issue 2 • April-June 2018
27
Table 3. Hot spot block groups and cold spot block groups summary statistics and comparison by zone
Category Variable Hot
Totals1
Hot
Count Hot % Hot
(M)
Hot
(SD)
Cold
Totals2
Cold
Count
Cold
%
Cold
(M)
Cold
(SD)Effect
Race
1. White alone: Total population
84,733
22,601
26.67%
332.37
274.65
62,223
48,148
77.38%
1203.70
607.25
-1
2. Total: White alone or in
combination with one or more
other races
84,733
24,124
28.47%
354.76
277.25
62,223
48,158
77.40%
1229.00
609.69
-1
3. Total: Native Hawaiian and
Other Pacific Islander alone or
in combination with one or more
other races
84,733
126
0.15%
1.85
9.66
62,223
106
0.17%
2.65
10.12
-1
Children
Household
Relationship
4. In households: In family
households: Spouse: Total
population
84,733
8,819
10.41%
129.69
80.00
62,223
12,586
20.23%
314.65
196.19
-1
5. In households: In family
households: Other relatives:
Total population
84,733
1,825
2.15%
26.84
32.94
62,223
321
0.52%
8.03
20.42
1
6. In households: In nonfamily
households: Householder: Male:
Total population
84,733
6,599
7.79%
97.04
70.92
62,223
3,955
6.36%
98.88
76.68
1
Household Family
Subfamilies
7. Total: Households with a
householder who is Black or
African American alone
34,011
21,519
63.27%
316.46
231.84
27,347
3,937
14.40%
98.43
93.65
1
8. Total: Households with a
householder who is Some other
race alone
34,011
584
1.72%
8.59
15.78
27,347
365
1.33%
9.13
25.47
1
9. Total: Households with a
householder who is Hispanic
or Latino
34,011
1,703
5.01%
25.04
35.38
27,347
784
2.87%
19.60
28.08
1
10. Total: Population in
households with a householder
who is White alone, not
Hispanic or Latino
62,208
17,999
28.93%
264.69
234.19
60,517
46,824
77.37%
1170.60
578.82
-1
School
Enrollment
11. Total: White alone
population 3 years and over
81,127
21,808
26.88%
320.71
263.70
60,479
46,840
77.45%
1171.00
588.37
-1
12. Total: White alone, not
Hispanic or Latino, population 3
years and over
81,127
18,294
22.55%
269.03
245.08
60,479
45,720
75.60%
1143.00
579.02
-1
Educational
Attainment
13. Total: Population 25 years
and over with a bachelor’s
degree or high attainment
52,454
12,008
22.89%
176.59
136.60
44,970
25,453
56.60%
636.33
403.96
-1
Industry
Occupation
14. Total: Civilian employed
Some other race alone
population 16 years and over
34,426
816
2.37%
12.00
20.68
31,962
618
1.93%
15.45
51.22
1
15. Total: Civilian employed
White alone, not Hispanic or
Latino population 16 years
and over
34,426
9,455
27.46%
139.04
148.57
31,962
24,465
76.54%
611.63
307.62
-1
16. Total: Civilian employed
Hispanic or Latino population
16 years and over
34,426
2,472
7.18%
36.35
59.94
31,962
1,159
3.63%
28.98
56.25
1
Housing
Characteristics
17. Total: Vacant housing units
39,539
5,538
14.00%
81.44
62.83
29,065
1,717
5.91%
42.93
48.33
1
18. Renter occupied: Total
population in occupied housing
units
82,148
48,155
58.62%
708.16
389.23
60,517
1,410
2.33%
453.38
433.93
1
19. Renter occupied: 1, detached
or attached: Total population in
occupied housing units
82,148
22,873
27.84%
109.51
126.83
60,517
5,104
8.43%
127.60
121.50
1
20. Renter occupied: 2 to 4:
Total population in occupied
housing units
82,148
7,447
9.07%
336.37
207.23
60,517
1,258
2.08%
31.45
52.27
1
Volume 9 • Issue 2 • April-June 2018
28
same holds true when considering the percentages of the White alone or in combination with one or
more races variable (77.40% for the Cold Spot and 28.47% for the Hot Spot) (negative effect). The
variable of Native Hawaiian and Other Pacific Island alone or in combination with one or more other
races also had a negative effect on DV incidents, although percentage differences were very small
(Hot Spot = 0.15%, Cold Spot = 0.17%).
The category of Children Household Relationship revealed that higher percentages of family
households with a spouse generally had lower instances of DV cases (negative effect). For example,
the Cold Spot zone had 20.23% of family households with a spouse compared to 10.41% for the
Hot Spot zone. Conversely, family households with higher percentages of other relatives living in
the household tended to have higher cases of DV incidents (Hot Spot = 2.15%, Cold Spot = 0.52%)
(positive effect). Percentages of nonfamily households were slightly higher in the Hot spot zone than
the Cold Spot Zone (7.79% and 6.36% respectively) when the householder was male (positive effect).
The Household Family Subfamilies category showed that the percentage of African American
householder were influential in the prevalence of DV cases (positive effect). The Hot Spot zone,
for example, had 63.27% of householders who were African American compared to the Cold Spot
where 14.40% of household had African Americans as householders. Households that identified as
having a householder as some other race alone demonstrated slightly higher percentages for the Hot
Spot zone (1.72%) than the Cold Spot zone (1.33%) (positive effect). The same effect was true when
the householder was Latino or Hispanic (Hot Spot = 5.01%, Cold Spot = 2.87%). However, when
the householder was White alone, not Hispanic or Latino, the effect on DV instances was negative
which suggest that the presence of higher percentages of this cohort resulted in lower incidents (Hot
Spot = 28.93%, Cold Spot = 77.37%).
Variables for School Enrollment demonstrated a negative effect on DV for both White alone
and White alone, not Hispanic for total children of school age (ages 3 years and over). DV incidents
were generally lower when percentages of children of school age were higher with respect to White
alone (Hot Spot = 26.88%, Cold Spot = 77.45%) and White alone, not Hispanic or Latino (Hot Spot
= 22.55%, Cold Spot = 75.60%).
The variable associated with Educational Attainment had a negative effect on cases of DV. For
example, the prevalence of DV incidents was lower when higher percentages of the population had
a bachelor’s degree or higher (Hot Spot = 22.89%, Cold Spot = 56.60%).
Within the Industry Occupation category, the variable of civilian employment (16 years and
older) with some other race alone (Hot Spot = 2.37%, Cold Spot = 1.93%) and Hispanic and Latino
(Hot Spot = 7.18%, Cold Spot = 3.63%) had a positive effect on the prevalence of DV. White alone,
not Hispanic or Latino, however, had a negative effect on DV incidents (Hot Spot = 27.46%, Cold
Spot = 76.54%). The Cold Spot zone (76.54%) had higher a percentage of White alone, not Hispanic
or Latino people when compared to the same cohort for the Hot Spot zone (27.46%).
Several general patterns emerged when considering the variables individually and within the context
of their geographic clusters and selected neighborhood characteristics. Race, Educational Attainment,
and Housing Characteristics were all found to have significant influences on DV at the neighborhood
level. Race had an influence on the prevalence of DV cases, and the trend appeared across multiple
variables within several categories. Race appeared as a component in 12 of the 20 variables. All of
the variables had a negative effect for neighborhoods with higher percentages of White population
and a positive effect for neighborhoods with non-white populations. This includes counts for total
population, total population in family households and non-family households, householders, and
employed civilians. Other studies have reported no associations among violence against women
and residential racial compositions after controlling for multicollinearity. Van Wyck, Benson, and
DeMaris (2003), however, did find some evidence but cautioned against grouping people together
Volume 9 • Issue 2 • April-June 2018
29
from all social classes since it may obscure the effects of race. Even though our study did not find
direct evidence, income and poverty levels may be more useful as a neighborhood level factor for
DV since they impact all population segments (O’Campo et al., 2005).
In addition to race, other neighborhood variables had an impact on rates of DV. For example,
neighborhoods with higher populations of residents who have obtained a bachelor’s degree or higher
tended to have lower prevalence of DV. Educational levels have been found to be an important factor
in numerous other studies (Murray et al., 2016). Furthermore, housing characteristics, such as, total
vacant units, total population in renter occupied housing units and the short durations of renter
occupation all had a positive effect on the number of DV incidents. Overall, these findings suggest
that, at least in the city of Greensboro, North Carolina, neighborhoods with generally lower levels of
socioeconomic status demonstrated higher rates of DV. These results are in accordance with other
studies that have examined social economic characteristics of neighborhoods (Benson et al., 2003).
Despite these results, we issue an important word of caution regarding the interpretation of
these findings. Specifically, it is important to remember that the incidents of DV that were analyzed
for this study were only those that were reported to the police department. Therefore, these reported
incidents are only a proportion of the actual incidents of DV that occurred in the community during
the time-frame investigated. Interpersonal violence is significantly underreported in community
settings (Benson et al., 2003; Murray et al., 2016; Rennison, 2002). There are a number of reasons
why DV may be reported more frequently in neighborhoods that demonstrate lower socioeconomic
status levels, such as the closer proximity of housing in rental units and a higher presence of police
related to other crimes (Murray et al., 2016). In contrast, residents of neighborhoods with higher
socioeconomic statuses may be more inhibited from reporting DV to law enforcement due to greater
fear or embarrassment or risk of lost employment due to police involvement (Murray et al., 2016).
Therefore, future research examining the geographic distribution of DV in communities should
consider alternative methods of identifying cases of DV, such as through community surveys with
random samples and records from hospitals and/or family service agencies.
A geographic analysis of DV within communities offers many useful benefits for communities
striving to address the problem of DV and prevent future violence (Murray et al., 2016). The
identification of higher-risk neighborhoods can offer information to guide law enforcement policies,
as well as to support targeted outreach by victim service agencies. The findings from the type of
geographic analysis described in this study also can be applied in other communities to identify
community-specific risk factors for experiencing abuse. Domestic violence is a complex, significant
social issue that carries many negative consequences for individuals and communities. Therefore, it
requires comprehensive solutions that account for factors that increase the risk of future violence at
multiple levels. Geographic analyses, in particular, offer meaningful findings that can guide future
research and practice interventions to work toward the prevention of further violence.
Volume 9 • Issue 2 • April-June 2018
30
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1 Census totals for the Hot Spot zones were used to compute percentages. Total Population was used for
variables 1 - 6; Total Households for variables 7 - 9; Total Population in Households for variable 10;
Total Population 3 Years and over for variables 11 - 12; Total Population 25 Years and Over for variable
13; Total Civilian Employed Population 16 Years and Over for variables 14 – 16; Total Housing Units
for variable 17; and Total Population in Occupied Housing Units for variables 18 – 20.
2 Census totals for the Cold Spot zones were used to compute percentages. Total Population was used
for variables 1 - 6; Total Households for variables 7 - 9; Total Population in Households for variable 10;
Total Population 3 Years and over for variables 11 - 12; Total Population 25 Years and Over for variable
13; Total Civilian Employed Population 16 Years and Over for variables 14 – 16; Total Housing Units
for variable 17; and Total Population in Occupied Housing Units for variables 18 – 20.
Rick L. Bunch is a Professor of Geography at the University of North Carolina Greensboro. His research interests
are in Geographic Information Science and spatial cognition.
Christine E. Murray, Ph.D., LPC, LMFT, is an Associate Professor in the UNCG Department of Counseling and
Educational Development. She is also Director of the Guilford County Healthy Relationships Initiative.
Xiaoli Gao is an Associate Professor of Statistics at the University of North Carolina Greensboro. Her research
interests are in High-dimensional Data Analysis and Robust Statistics.
Eleazer D. Hunt is the Director of the Information Services Division for the Greensboro Police Department and
Adjunct Faculty in the Department of Geography at the University of North Carolina Greensboro. His research
interests are in Geographic Information Science and Criminology.
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