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A spatial analysis of violent crime cold spots: testing the capable guardian component of the routine activity theory

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A spatial analysis of violent crime cold spots: testing the capable guardian component of the routine activity theory

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A Spatial Analysis of Violent Crime Cold Spots: Testing the Capable Guardian
Component of the Routine Activity Theory

by

Brian David Jopp

A Thesis Presented to the
Faculty of the USC Graduate School
University of Southern California
In Partial Fulfillment of the
Requirements for the Degree
Master of Science
(Geographic Information Science and Technology)

December 2016

Copyright © 2016 by Brian David Jopp

iii

Dedication
I dedicate this document to my wife for all of the times she has filled in for me as a parent, as I
studied by night and by weekend. Without Marnie's help, there is no way possible that I could
have had the time to gain the necessary knowledge and skills to complete a Master's Degree.
Thank you.

iv

Table of Contents
List of Figures ................................................................................................................................ vi
List of Tables ................................................................................................................................ vii
Acknowledgement ....................................................................................................................... viii
List of Abbreviations ..................................................................................................................... ix
Abstract ........................................................................................................................................... x
Chapter 1: Introduction ................................................................................................................... 1
1.1 The Rationale for Using the Routine Activity Theory.......................................................... 5
1.2 Research Question ................................................................................................................ 7
1.3 Thesis Structure .................................................................................................................... 7
Chapter 2: Theory and Literature Review ...................................................................................... 9
2.1 Broken Windows Theory .................................................................................................... 11
2.2 Conflict Theory ................................................................................................................... 13
2.3 Social Disorganization Theory ........................................................................................... 14
2.4 Collective Efficacy, an Extension of the Social Disorganization Theory .......................... 15
2.5 Routine Activity Theory, Spatial Analysis, and the Capable Guardian ............................. 17
2.5.1 Definition of a Capable Guardian ............................................................................ 17
2.5.2 Housinig and Homeowner Characteristics as a Proxy for the Capable Guardian
Component ........................................................................................................................ 17
2.6 A Review of Literature that Used the Routine Activity Theory ......................................... 20
Chapter 3: Methods ....................................................................................................................... 26
3.1 Data Sets ............................................................................................................................. 31
3.2 The Study Area, Federal Land, and Aggregation Choice ................................................... 31

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3.3 Hot Spot Analysis ............................................................................................................... 34
3.4 The Explanatory Variables ................................................................................................. 35
3.5 Exploratory Regression and Ordinary Least Squares (OLS) .............................................. 39
3.6 Geographically Weighted Regression (GWR).................................................................... 39
Chapter 4: Results ......................................................................................................................... 42
4.1 Hot Spot Analysis of the Violent Crimes ........................................................................... 44
4.2 Exploratory Regression and Ordinary Least Squares of the Violent Crimes ..................... 51
4.3 Exploratory Regression and Identifying Explanatory Variables for OLS .......................... 53
4.4 Results of Ordinary Least Squares Model and Details ....................................................... 55
4.5 Geographically Weighted Regression................................................................................. 55
Chapter 5: Conclusions and Discussion ........................................................................................ 62
5.1 Violent Crimes Using Hot Spot and Regression Analysis.................................................. 62
5.2 The Model Developed to Measure Capable Guardianship ................................................. 63
5.3 Future Work in the Application of Spatial Analysis of Violent Crime .............................. 66
Works Cited .................................................................................................................................. 69

vi

List of Figures
Figure 1: Map of study area: Rock Creek Park and federal land .................................................... 4
Figure 2: Venn diagram of the routine activity theory ................................................................... 5
Figure 3: Crime points plotted to one of three positions on the block .......................................... 29
Figure 4: Modified study area ....................................................................................................... 32
Figure 5: Homicide hot spots by census block group .................................................................. 46
Figure 6: Assault with a dangerous weapon hot spots by census block group ............................. 47
Figure 7: Robbery hot spots by census block group .................................................................... 48
Figure 8: Sexual assault hot spots by census block group ........................................................... 49
Figure 9: Combined violent crime hot spots by census block group ........................................... 50
Figure 10: Variable distributions and relationships in the guardian model .................................. 56
Figure 11: Histogram of standardized residuals for the guardian model ...................................... 57
Figure 12: Residual vs predicted plot guardian model ................................................................. 58
Figure 13: Distribution of the values of the explanatory variables in the guardianship model .... 59
Figure 14: GWR guardianship model coefficients ....................................................................... 60

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List of Tables
Table 1: Data sets and variables.................................................................................................... 28
Table 2: Violent crime variable examples .................................................................................... 29
Table 3: Violent crime Z-scores for nearest neighbor analysis of each violent crime by year ..... 30
Table 4: Spatial autocorrelation and Z-scores when violent crime is aggregated ........................ 34
Table 5: Normalizing the explanatory variables ........................................................................... 37
Table 6: An example of count data for an explanatory variable ................................................... 39
Table 7: Variable after grouping and as a ratio ............................................................................. 39
Table 8: Exploratory regression results for four violent crimes ................................................... 51
Table 9: OLS results for violent crime models ............................................................................. 52
Table 10: Exploratory regression phase one - negative linear relationships to violent crime ...... 54
Table 11: Exploratory regression phase two - four standing significant explanatory variables ... 54
Table 12: Summary of OLS results for the guardian model ......................................................... 55
Table 13: OLS diagnostics for the guardian model ...................................................................... 56

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Acknowledgments
I want to give a special thanks to the entire committee: Dr. Kemp for many key ideas and ways
to improve spatial analysis and organization of content within the thesis, with a focus on
quantitative analysis; Dr. Lee for helping me to turn a null hypothesis into a working model; and
Dr. Loyola for dealing with many revisions, always maintaining a professional and positive
demeanor! For the initial work on my thesis, I owe a lot to Dr. Sedano, who kept me headed in
the right direction and provided counsel to advance my thoughts into a thesis. Finally, I want to
thank Dr. Oda for cartography and visualization advice and all of the professors at USC as being
exceptional in guiding me along my path to earning a master’s degree.

ix

List of Abbreviations
DC District of Columbia
CPED Crime Prevention Through Environmental Design
GWR Geographically Weighted Regression
GIST Geographic Information Science and Technology
LAPD Los Angeles Police Department
LBACH An explanatory variable: log of percent of the total number of the population who
are twenty-four years of age and over and earned a bachelor’s degree or higher
LDET An explanatory variable: the log of percent of the total number of homes that are
detached
LMAROWN An explanatory variable: the log of the percent of the total number of homes
owned by married couples
LV1M An explanatory variable: the log of percent of total number of homes with values
over $1,000,000
MPD Metropolitan Police Department
MAUP Modifiable Areal Unit Problem
OCTO Office of the Chief Technology Officer
OLS Ordinary Least Squares
PHDCN Project on Human Development in Chicago Neighborhoods
USC University of Southern California
VIF Variance Inflation Factor

x

Abstract
According to the routine activity theory, violent crime may be deterred by a capable guardian.
Cohen and Felson’s routine activity theory asserts three conditions need to be met for a crime to
take place: a likely offender; a suitable target; and the absence of a capable guardian (Cohen and
Felson 1979). A hot spot analysis of violent crimes for Washington, DC shows a divided city. In
northwest DC, the census block groups correlate with low violent crime rates. To understand
why northwest DC has low crime rates, a quantitative spatial analysis uses housing
characteristics as proxies for capable guardianship to test whether a correlation exists between
capable guardianship and the deterrence of violent crime. The rationale behind using housing and
homeowner characteristics in a model relies upon fusing capability with perception of success.
Accordingly, if the criminal perceives a capable guardian to be present, then the criminal will not
commit the crime. Following this logic, neighborhoods displaying capable guardianship through
housing characteristics ought to have lower violent crime rates. Using exploratory regression,
Ordinary Least Squares, and Geographically Weighted Regression the construction of a
guardianship model with significant explanatory variables suggests a relationship between
capable guardianship and areas with lower violent crime rates do exist. Furthermore, quantitative
spatial analysis suggests a strong relationship between low violent crime rates and obtaining
higher levels of education exists.

1

Chapter 1: Introduction
Homicide and other violent crimes cost the government and its citizens a significant amount of
money and cause a severe amount of emotional pain for the victim, and the victim’s relatives and
friends. Various sources state the cost to be between $2 and $22 million per homicide (Delisi,
Kosloski and Sween 2010, McCollister, French and Fang 2010). These figures usually break
down as follows: fifty percent applies to the lost quality of life for the victim’s family and other
loved ones affected by the homicide, for example, costs associated with the mental state of those
who will need to come to terms with the death which includes grief and potential depression;
twenty-five percent in tangible victim costs such as income and payments because of the
homicide; twenty percent in criminal justice costs; and five percent in productivity losses. The
National Institute of Health provided a narrower range from $4.1 to $11.4 million per homicide.
Using this mean, each homicide costs $7.8 million. In 2015, there were 162 homicides in
Washington, DC (Bowser 2016), meaning the cost of homicide in Washington equaled
approximately $1.3 billion. Homicide related criminal justice costs by the government in 2015
were $260 million, or roughly fifteen percent of DC’s income tax revenues (DeWitt 2015) (this
is a relative comparison not meant to suggest homicide costs are paid by income tax dollars alone
or at all).
Additionally, more resources ought to be expended toward Geographic Information
Systems (GIS) to cross-examine, question, verify, or nullify existing theories and qualitative
analyses. Criminal analysts use theories to define criminal behavior, to aid in selection of data, in
interpretation of their results, and to construct models to predict locations where a crime will
likely occur next. “There is a strong body of evidence to support the theory that crime is
predictable (in a statistical sense) – mainly because criminals tend to operate within their comfort

2

zone. That is, they tend to commit the type of crimes that they have committed successfully in
the past, generally close to the same time and location” (Perry, McInnis and Price 2013, 2). Perry
et al are in agreement with Cohen and Felson’s routine activity theory, whereby a crime takes
place due to a convergence of the victim and criminal in time and space. If crimes take place in
similar locations, then the activity can be studied using GIS.
Homicide and other violent crimes are rarely quantitatively studied due to the complex
nature of the crime, such as the dynamic relationships between the perpetrator and the victim
along with the mental state of the perpetrator (Nicolaidis, Curry and Ulrich 2003, Bozeman
2014). Although these factors needs to be considered, quantitative spatial analysis, by its nature,
can be applied without the need to dig into the mind of the perpetrator. Tobler’s first law of
geography, “Everything is related to everything else, but near things are more related than distant
things” (Tobler 1970) can be applied to the study of violent crimes in Washington, DC. For
example, when the violent crime “assault with a dangerous weapon” is clustered in an area, there
is a strong likelihood that “homicide” will also be clustered in the same area. Thus, one of the
most important risks for the occurrence of homicide is spatial proximity to “assault with a
dangerous weapon.” More details on these relationships are provided in chapter four.
In 2014, Washington, DC’s area measured 68.3 square miles and the population estimate
was 659,836, so the population density per square mile equaled 9,661. However, with the federal
park land subtracted (twenty-five percent of DC is federal park land) then the proper area to use
in the formula would be 51 square miles of land. The more realistic population density per
square mile is therefore 12,937: using this figure, Washington’s population density ranks fourth
in the United States amongst cities with a population above 500,000, behind New York City
(28,056), San Francisco (18,187), and Boston (13,586); just above Miami (11,997), Chicago

3

(11,959), Philadelphia (11,635), and Long Beach, California (9,416). The population densities
above include federal land. However, removing the federal land and recalculating the population
density would not change the numbers nearly to the extent that it did for DC. Although the whole
city is considered for spatial analysis, the concentration is on northwest DC because violent
crime cold spots remained in this area throughout the study period. This area is located north and
west of Rock Creek Park, as shown in Figure 1 below. A more detailed description of the study
area follows in Chapter 3.

4

Figure 1: Map of study area: Rock Creek Park and federal land

5

1.1 The Rationale for Using the Routine Activity Theory
Routine activity theory states that “criminal acts require convergence in space and time of
likely offenders, suitable targets and the absence of capable guardians against crime” (Figure 2)
(Cohen and Felson 1979, 588). The focus for this thesis centers on the third component of the
routine activity theory.

Figure 2: Venn diagram of the routine activity theory. Felson 2006.
However, testing the absence of a capable guardian may prove difficult, so the inverse
will be used. In the same article, Cohen and Felson suggest that the routine activity approach will
work in the inverse (1979, 589), that a perceived presence of a capable guardian will deter crime.
Therefore, the aim of this research will be to test if correlations exist between the perceived
presence of a capable guardian and the deterrence of violent crime, which stays within the
parameters of the theory. A later article defining the capable guardian reaffirms that a person will

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choose not to commit a crime if he “feels” somebody is watching him (Hollis, Felson and Welsh
2013, 66 - 67). This paramount implication suggests the physical setting itself may deter crime.
If so, then a physical environment with a set of features aligned with a capable guardian ought to
show different crime rates than an environment lacking these features.
The authors provide a specific definition: “A guardian is any person and every person on
the scene of a potential crime that may notice and intervene (whether they intend to or not)”
(Hollis, Felson and Welsh 2013, 73). Working through the above definition, the point-of-view
for the criminal hinges on potential assumptions of both presence and capability of the guardian.
The criminal makes a decision based on the concept of being observed or not observed by a
capable guardian. The guardian does not necessarily need to be present, only the assumption of
being present need exist for the deterrence of crime.
Although Hollis et al did not go beyond defining capability “as the presence of a human
element of intervention” (2013, 73-74), a well-accepted reality is that humans, even criminals
make judgments. These judgments would be based on perceptions of the environment. If the
criminal thinks he can commit a crime and get away, then there is a much stronger likelihood
that he will commit the crime in comparison to the opposite. Criminals who think they will be
caught, due to the environment, will not commit the crime.
Under this theory, criminals make intentional decisions based on assessment of risk, and
these decisions take the environment into consideration. For example, detached homes provide
physical buffers. The criminal would need to move over this buffered private space, allowing
more time for a capable guardian to notice. Detached homes ought to provide a stronger element
of guardianship, or at least the perception of the presence of a guardian. More physical space
attaches with it a higher risk of being observed in a private space.

7

Given the above reasoning, housing characteristics may represent the presence of a
capable guardian. Housing characteristics, to some degree, define the occupier. In other words,
the value of the home, whether or not the structure is occupied, and whether or not it is an
apartment or detached home, to some extent show an element of capability. If the criminal even
perceives the presence of a capable guardian due to the physical attributes of a neighborhood,
then the criminal will not commit the crime, according to the routine activity theory.
1.2 Research Question
According to Cohen and Felson’s routine activity theory, capable guardianship may deter
crime. If a criminal perceives the presence of a capable guardian, then the criminal will decide
not to commit the crime because of the increased risk of being caught. If this this true, then areas
where housing characteristics suggest capable guardianship should correlate to low violent crime
areas or cold spots. The following spatial analysis uses housing characteristics as proxies to
represent capable guardianship to test whether a negative correlation exists between housing
characteristics and violent crimes in DC: Using quantitative spatial analysis, are there negative
correlations between housing characteristics and low crime areas in the Washington, District of
Columbia area?
1.3 Thesis Structure
The thesis consists of five chapters. Chapter One introduced the routine activity theory,
the thesis question, and the study area. Chapter Two will take a closer look into the application
of criminal theory historically and narrow the focus to the routine activity theory. Furthermore, a
literature review will be given to emphasize the need for more quantitative spatial analysis of
violent crime and the study of negative correlations between capable guardianship and violent
crime. Chapter 3 will describe the data sets, a hot spot analysis, the method of linear regression

8

analysis, and an explanation for each step taken to arrive at the results from Ordinary Least
Squares (OLS) and Geographically Weighted Regression (GWR). Chapter Four will show the
results of the analyses and provide a suggested model derived from exploratory regression. Also,
the results for the model will be shown using Esri’s ArcMap OLS and GWR tools. Chapter Five
will provide potential explanations for the spatial relationships between housing characteristics
and violent crime cold spots. Furthermore, a discussion concerning future quantitative spatial
analysis when studying violent crimes will be provided.

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Chapter 2: Theory and Literature Review
This chapter’s two primary concerns are theory and the review of literature. A closer look at five
theories for understanding violent crimes will be provided: 1) broken windows theory; 2) conflict
theory; 3) social disorganization theory; 4) collective efficacy theory; 5) and the routine activity
theory. Additional focus will be given to the routine activity theory, specifically capable
guardianship and housing characteristics. Then, a review of literature will be provided to
emphasize that quantitative spatial analysis and capable guardianship may benefit researchers
when trying to understand violent crime.
Different crime types require different theories to understand the motivation of the
criminal. For example, “stranger crimes,” those committed by an unknown offender to the
victim, such as burglaries and thefts, involve a motivation based on money, and seldom occur
more than one time between the offender and the victim (Perry, McInnis and Price 2013).
However, in more than half of all homicides, the victim and the murderer know each other (US
Department of Justice–Federal Bureau of Investigation 2012). These relationships provide a
basis for the victim and criminal to converge in time and space. On the other hand, the victim
may cross into a location where criminals lurk. If so, then a spatial analysis may identify these
locations and would be a useful tool for researchers when attempting to understand violent
crimes.
Police use GIS more and more as software becomes available and as people understand
how to use it (Perry, McInnis and Price 2013). However, for the most part, geospatial analysts
who work for police departments mostly focus on non-confrontational crimes rather than violent
crimes. Non-confrontational crimes consist of crimes such as theft, grand theft auto, and
burglary.

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Homicide may be different than other crimes in other ways as well. In most homicides,
research suggests there is an escalation of an existing crime and most of the murderers show a
pattern of committing other violent crimes (Bozeman 2014). In a study where twenty-seven
murderers were interviewed and qualitative analysis was applied, 100% of the murders were the
result of an escalation of violence, sixty-six percent confessed to either previously committing
robbery or the homicide escalated from a robbery, and forty-four percent had either previously
committed a form of assault or the homicide escalated from an assault (Bozeman 2014). These
statistics provide valuable information for studying violent crime, specifically homicide.
Homicide occurs as an escalation within a crime, and usually the offender has committed a
violent crime in his past. These salient points heighten the potential of spatial analysis between
violent crimes. If assault with a dangerous weapon precedes homicide, then areas with high
incidences of assault with a dangerous weapon may likely be high in homicide rates as well. For
this reason, studying all four violent crimes may lead to strong correlations between these crimes
to be used in future analysis.
Within Predictive Policing: The Role of Crime Forecasting in Law Enforcement
Operations (2013), the routine activity theory, rational choice theory, and crime pattern theory
were combined to construct a blended theory. The author admits, “This blended theory best fits
stranger offenses [non-confrontational crimes] such as robberies, burglaries and thefts…and does
not fit well [when applied to violent crimes] due to the break from criminal rational choice
framework” (Perry, McInnis and Price 2013). Although the blended theory may not be properly
applied to homicide, routine activity theory does seem to apply to homicide. However, before
moving into the examination of the routine activity theory, a brief analysis of four other theories

11

will be examined: broken windows theory, conflict theory, social disorganization theory, and
social efficacy theory.
Although portions of each of these four theories may seem valid when applied to
homicide, other portions of these theories do not apply. Below, specific details are provided to
show all of the theories apply to some extent, and a rationale is provided for choosing the routine
activity theory as the most relevant theory within which to study violent crime.
2.1 Broken Windows Theory
Broken windows theory gained ground in the early part of the twenty-first century. Both
physical and social disorder in neighborhoods indirectly result in higher crime rates (St. Jean
2007). To counteract the negative results, intervention needs to happen early. Although
intervention to prevent crime seems intuitive, the theory implies the movement of people in and
out of an area at a high rate precludes this. There is also a strong emphasis placed on the physical
condition of the buildings such as condemned buildings as a basis for crime, thus broken
windows theory.
“Society cannot ignore these problems, or there looms a strong likelihood that the
conditions will get worse. If left unchecked, neighborhood disorder will continue
to increase, petty crimes will increase, and residents will perceive that more
serious crimes are also on the increase. Fearful of crime, law-abiding citizens will
then refrain from using public spaces, become less attached to the neighborhood,
and eventually move out of the area only to be replaced by less attached people.
Serious crimes will then follow” (P. K. St. Jean 2007, 2).

Although there are elements within this theory that parallel results from qualitative studies such
as Bozeman’s outcome of ‘escalation of violence’ and ‘low income areas’ as factors that
contribute to homicide (Bozeman 2014), by itself, was insufficient to explain high levels of drug
dealing, robbery, and battery on neighborhood street blocks” (P. K. St. Jean 2007, 195).

12

The theory concentrates on physical buildings being vacant, abandoned, and the overall
environment dissipating to signs of disorder, but these probably work like symptoms of a
disease, and do not necessarily motivate criminals. In other words, fixing up buildings, cleaning
parks, demolishing abandoned buildings, or any other activity to literally change the physical
environment from being unkempt to tidy may only mask the criminal activity. This may enable
criminals in these areas because an unaware person may let his or her guard down. Most likely,
the changes named above do not actually influence the criminal’s reasoning for committing a
crime. Broken windows theory does not address the motivations or the reasons for the disorder in
the neighborhoods. To find the motivations of criminal behavior, researchers will need to look
elsewhere (Sampson and Raudenbush 2004).
Broken windows theory uses poverty, large movements of people in and out of
communities, and deterioration of buildings indicators of social deterioration within a
community and as a basis for crime. A possible indicator for this change would be high
percentage of foreclosures with an area of crime. However, in a study released by Indiana
University, where 142 metropolitan areas were analyzed using weighted regression analysis, the
results led to conclusions that higher levels of housing-mortgage stress did not result in higher
levels of violent crimes (Jones and Pridemore 2012). The research used a multilevel model with
individual, familial, and neighborhood levels. Amongst the dependent variables, at least two
were violent crimes: assault and robbery. The main explanatory variables were negative equity,
loan-to-value ratio, and cost-to-income. Foreclosure does not support broken windows theory as
a fully applicable.
Some parallels to broken windows theory to this thesis were captured. Although the
theory will not be employed, some of the underlying assertions concerning physical

13

environment, whereby criminals may feel more comfortable committing a crime are in line with
the rationale for this thesis. However, this finding is slight. Overall, broken windows would not
provide enough substantial input to employ as a theoretical basis for this thesis.
2.2 Conflict Theory
Conflict theory (Marx and Engels 1848) asserts crime is caused by political leverages
used by the upper socio-economic class against the lower socio-economic class to promote their
interests. Under conflict theory, the powerful construct policy for the upper socio-economic
classes to maintain their power, thus, supplying the cause of conflict. The effect from their
leverage creates a class conflict, whereby some of the people in the lower socio-economic
classes commit crimes. Research efforts to validate the conflict approach, however, have not
produced significant findings (Siegel 2000).
Essentially, the central focus of the conflict theory is the conflict between the wealthy
and the poor. Although income may both inhibit and encourage homicide and violent crime, low
income by itself does not lead to homicide or violent crime. Even though Pratt and Lowenkamp
support that an inverse relationship between poor economic conditions and crime exist, they
state, “conflict theorists often specify an inverse relationship between economic conditions and
crime. Empirical support for this contention in time-series analyses, however, has been
inconsistently revealed in the literature, where positive, inverse, and null results have all been
found” (2002, 61). The inverse relationship between economic downturns and violent crime is
not consistent throughout the decades. For example, in the1960s and 1970s the economy grew
along with the escalation of crime rates, but the economic boom in the 1990s showed a drop in
crime rates, and these crime rates reached all-time lows in the early 2000s (Scheider, Spence and

14

Mansourian 2012, 3). The inverse relationship between economic conditions and crime is
sporadic when the researcher takes into consideration decades of work.
If wealth and poverty were the main driving mechanisms of crime, then one would expect
to see a strong relationship between the economy and unemployment with violent crime.
However, in 2015, homicide spiked by fifty-six percent in Washington, DC, yet there were no
major economic downturns in the economy. In fact, the unemployment rate went down and the
average wages went up (United States Department of Labor 2016). Most likely, an economic
attribute could be applied in all theories concerning crime, but the idea of economic change as
directly increasing the number of homicides was not the case in the DC area. For the most part,
crime analysts include socio-economic variables within their analysis, in one way or another.
However, when studying violent crime, economics should not be the only variable.
2.3 Social Disorganization Theory
Social disorganization theory developed in 1942 from mapping juvenile delinquency,
whereby Shaw and McKay plotted crime patterns on a land use map. Shaw and McKay gathered
the data and recognized certain areas show high numbers of crimes, for example, certain
neighborhoods exhibited high crime rates in a continuous spatial pattern. Their findings showed
crimes happen where negative social change occurs, for example, neighborhoods with large
numbers of transients.
Within the theory, the community loses its moral consensus leading to the deterioration
of social control (Anderson 2014). If this theory were employed to explain violent crime, then
one would expect to find correlations between high violent crime areas and the following
characteristics: poverty, high population density, ethnic diversity, close proximity to

15

industrialized areas, high percentage of immigrants, with a high percentage of transients
(Sampson and Groves 1989, Regoeczi and Jarvis 2011).
In 2015, homicide spiked by fifty-four percent in Washington, DC (Bowser 2016). At the
same time, net domestic migration was 82% less than the annual average of the prior three years
(Bowsner and DeWittt 2015). Given the data, immigration most likely did not play a major
factor for the homicide spike nor violent crimes. Therefore, the social disorganization theory
may no longer be applicable to study violent crimes in DC. However, the idea that emphasizes
place appears to be valid. Hot spot crime areas and spatial analysis is routine for the Los Angeles
Police Department to a large extent, which can be seen as easily as going to their website
LAPDonline.org (Departmet 2016). Although the element of place in both the social
disorganization theory and broken windows theory may apply, other parts of the theory may no
longer apply. The routine activity theory incorporates place, so there would be no reason to
include social disorganization theory as a theoretical basis.
2.4 Collective Efficacy, an Extension of the Social Disorganization Theory
An off-shoot of the social disorganization theory, the collective efficacy theory may
provide a more modern approach and deserves some attention. Collective efficacy occurs in
neighborhoods where people are willing to intervene because they are connected to one another
through social cohesion (Browning 2002). Neighborhoods with higher levels of collective
efficacy will show lower levels of crime (Sampson, Raudenbush and Earls, 1997). Within the
above study, the results showed that collective efficacy was correlated with a reduced rate of
homicide by 39.7%. However collective efficacy only provided a partial explanation.
The article “Neighborhoods and Violent Crime: A Multilevel Study of Collective
Efficacy” provides statistical legitimacy for the concept of collective efficacy (Sampson,

16

Raudenbush and Earls 1997). However, the data may be biased due to being survey data and
asking participants to predict crimes in the future. Each participant answered questions according
to his or her opinion about crimes and intervention of crimes that may happen in the future. The
data was tallied by the Project on Human Development in Chicago Neighborhoods (PHDCN).
The results showed collective efficacy was negatively related to violence. However, the method
relied upon qualitative analysis, which leaves open the potential for bias and expressions of
uncertainty. “Overall, humans do not do well with predicting probability when using subjective
or personal probability, the belief that a certain explanation or estimate is correct; it is
comparable to a judgment that a horse has a three-to-one chance of winning a race” (Heuer, Jr
1999, 152). Rather than using human opinions as a way to measure collective efficacy, this study
uses quantitative spatial analysis to measure a similar component, where collective efficacy will
be replaced by guardianship, for reasons discussed in the next section.
However, in another study, it is suggested that collective efficacy does lower crime rates.
Browning assessed that collective efficacy is negatively associated with intimate homicide
(including people who are or were in a relationship and consider themselves to be partners,
cohabitating, or dating) for homicides from 1994 through 1995 in Chicago (Browning 2002). A
potential reason Browning et al findings showed a negative relationship may be due to the study
being limited to intimate homicide and not all homicide.
Collective efficacy, measured using qualitative analysis yields mixed results as noted
above, as well as others. A potential reason for the mixed results may hinge on the groups chosen
for the analysis. When groups who state their purpose is to proactively stop crime are entered
into the analysis, then there is a stronger likelihood a correlation will be measured, in comparison

17

to selecting groups with collective efficacy but not necessarily with a direct goal to stop crime
(Sampson, Raudenbush and Earls 1997).
Collective efficacy did not measure as being significantly correlated with homicide,
according to a study in Chicago in 1995 (Morenoff, Sampson and Raudenbush 2001). Social
institutions and neighborhood groups were not significantly correlated with a lower rate of
homicide. Instead, Morenoff et al highlight spatial proximity as the major factor to consider
when attempting to understand homicide.
A major difference between collective efficacy theory and the capable guardian
component relies on the players involved. The collective efficacy theory targets social groups
and organizations, and the routine activity theory limits capable guardianship to an individual. In
fact, Felson et al make it clear not to use social groups and organizations when applying routine
activity theory (Hollis, Felson and Welsh 2013).
2.5 Routine Activity Theory, Spatial Analysis, and the Capable Guardian
The Routine Activity Theory relies on a convergence of a likely offender and a suitable
target along with the absence of a capable guardian (Cohen and Felson 1979), as shown in Figure
2. Although no single accepted theory explaining the behavior of homicide exists (Bozeman
2014), a different approach combining the routine activity theory with quantitative spatial
analysis may provide a framework of understanding where homicides do not occur. In a review
of criminal studies, based on thirty-three articles written between 1995 and 2005, Spano and
Freilich limit the third component of the routine activity theory to the absence of a capable
guardian (2009). Some of the theories wrongfully equate guardianship to carrying a weapon,
using cameras, and social groups (Felson 2006); these types of analysis are not discussed. This

18

study suggests the routine activity theory can also be used to show where violent crimes are less
likely to occur. Later in this section, the definition for capable guardian is given.
There are many qualitative analysis studies that could benefit greatly from spatial
analysis. For example, in a study published in the Journal of General Internal Medicine,
qualitative analysis involving interviews of women who survived an attempted homicide by an
intimate partner, revealed twenty-eight of the thirty women “had previously experienced physical
violence, controlling behavior, or both from the partner who attempted to kill them” (Nicolaidis,
Curry and Ulrich 2003). A spatial analysis of the women’s locations of these attempted murders
may have shed some light on other factors associated with the environmental conditions where
the attempted crime took place. Place could be a vital component to understand the problem set.
Although these violent crimes may be complex, crime analysts ought to use all available tools to
understand the problem. The routine activity theory emphasizes the importance of time and
place, but neither were looked at. This is just one example where the application of the basics
within the routine activity theory may be able to enhance a qualitative analysis.
Spatial analysis may shed some light on such a dark topic, even though the answers may
be more complex than spatial analysis can provide, merely asking the questions can open up a
discussion leading to possible solutions. Did these victims come from a low income area? Did
the victims live in areas where violent crimes were more prevalent? What did the victim’s
neighborhood look like? What are the elements of the physical surroundings? However, spatial
analysis on its own may lead to more questions than answers. When studying violent crime, it is
fundamental to include theory. By utilizing spatial analysis in a theoretical framework, data,
methods, and results can be better understood. Through this understanding, solutions may

19

surface. The routine activity theory seems to be an excellent candidate for examining violent
crime.
The main focus in this study is the third component of the routine activity theory, capable
guardianship. Being capable may be synonymous with other characteristics such as success,
achievement, and individual autonomy. Therefore, explanatory variables such as housing
characteristics could be chosen for quantitative spatial analysis.
2.5.1 Definition of a Capable Guardian
“Guardianship can be defined as the presence of a human element which acts – whether
intentionally or not – to deter the would-be offender from committing a crime against an
available target” (Hollis, Felson and Welsh 2013, 76). Hollis et al reinforce that the guardian
must be a human element and not an official such as the police. However, dogs could be
guardians, but cameras and other tools only reinforce an already present guardian. This thesis
works within the author’s intent that the capable guardian is a person. The physical properties
inherent with housing characteristics portray information about the owner, which suggests a
measurement of capability. Criminals are able to identify these neighborhoods as more likely to
contain capable guardians, and this perception may deter crime. This thesis asserts the perception
of the capable guardian, regardless of whether or not the guardian was present, correlates with
less crime. If so, then this ought to be measurable if the proper explanatory variables are chosen.
2.5.2 Housing and Homeowner Characteristics as a Proxy for the Capable Guardian Component
Housing and homeowner characteristics gained from the United States Census Bureau are
used to act as potential proxies representing a capable guardian. Along with housing
characteristics, education level attained and financial variables are considered for the capable
guardian model. The explanatory variables ought to be defensible by quantitative statistics.

20

When placed into a model, the variable is expected to show a negative linear relationship to
violent crime. In no way is the intention of this model to predict violent crime.
Crime Prevention through Environmental Design (CPTED) studies the spatial
characteristics of environments that may enable or deter criminal activity (Cozens and Love
2015). Similar to a camera being an aid to the capable guardian, defensible space may enable
people to be more capable. There are four design elements for defensible space that apply to the
above housing characteristics being used as variables in a model meant to represent capable
guardianship: 1) Perceived areas of clearly defined ownership of space (detached homes); 2)
Image and milieu built for the perception of space promoting well maintained and orderly places
(high-valued homes); 3) Opportunities for surveillance for residents (occupied); 4) Geographical
juxtaposition being the capacity for surrounding spaces to influence adjacent areas (potentially
many characteristics) (Cozens and Love 2015, 393-395; Taylor and Harrell 1996; Reynald
2015). Therefore, housing characteristics may be a good variable to examine for a negative linear
relationship to violent crime.
2.6 A Review of Literature that Used the Routine Activity Theory
Historically, spatial science researchers used the routine activity theory to study risk
associated with time and space, whereby a likely offender crosses paths with a suitable target,
and without a guardian present (Cohen and Felson 1979). A major focus of researchers who base
their rationale on the routine activity theory, is on the victim’s movements, whereby the parents
(guardians) are not present (Vazsonyi, Belliston and Hessing 2002; Lauritsen and Quinet 1995).
Many of the studies place the crimes during travel times, for example, traveling to and from
school. The other focus is on places where capable guardians are not present (Garofalo, Siegel
and Laub 1987). A couple of articless cite juveniles or college students straying from their

21

normal routes as increasing the risk and exposure to likely offenders (Nofziger and Kurtz 2005,
Tewskbury and Mustaine 2003). By moving away from the safeguards of a home, neighborhood,
or place where capable guardians are present, the students enter areas with greater risk to
criminal activity.
Two common themes used by most researchers of the routine activity theory are
victimization and deviance. Spano and Freilich (2009) published an accredited review of
research articles on the routine activity theory from 1995 to 2005. In the titles of the thirty-three
articles cited, “victimization” appears thirty-one times and “deviant” shows up four times. In
this assessment, the dependent variable crime/deviance showed a negative linear relationship to
capable guardianship in seventeen out of eighteen of these studies (Spano and Freilich 2009).
Throughout the research cited, strong evidence supports the absence of a capable guardian to be
a significant component linked to crime.
As stated above, the bulk of articles concentrate on travel and being away from a capable
guardian. To capture these crime events, the researchers generally gain access to surveys and
interviews for analysis. In “Personal Criminal Victimization in the United States: Fixed and
Random Effects of Individual and Household Characteristics,” Tseloni attempts to use a
multilevel model to “disentangle the unexplained heterogeneity between individuals and between
households by linking surveys to explanatory variables concerning personal crimes (assault,
purse snatching, rape, sexual assault, and robbery are examples)” (2000, 415). Tseloni used
several household variables such as income, number of household members, number of vehicles,
education, and marital status. Essentially, the results of negative linear relationships depended on
the proximity to the crime areas. As households with similar characteristics became closer to the
crime areas, the impact of the household characteristics lessened.

22

Tseloni asserts that the results for housing characteristics were difficult to interpret
without considering the lifestyles of the occupants. Tseloni ends the journal article by asserting
more research needs to occur at the census tract level, building on various comments concerning
the lack of research using explanatory variables (such as household explanatory variables) to
attempt to better understand victimization and crime (2000).
Some studies cite the routine activity theory but they do not use the capable guardian
component in accordance with the originator’s definition. The results of a cross-sectional study
of Bogota, Colombia showed an overlap between victims and perpetrators, whereby one-third of
the sample of 3,007, engaged in activity of being both the victim and the perpetrator over the
course of a year (Klevens, Duque and Ramirez 2002). Place appears to be a salient feature for
crime, as a cross-analysis between victim/perpetrators and victims-only showed both answered
questions such as “Avoids going out at night alone,” “Stays home at night,” and “Avoids
dangerous neighborhoods” with a range of less than two percent, according to the interview
answers. This study minimized the potential intervention of the capable guardian.
In another article, geo-located 911 calls in Minneapolis, Minnesota showed violent
crimes were clustered: All robberies were committed in 2.2% of the area within the city, and all
rapes were in 1.2% of the area in Minneapolis, sometimes tied to a specific building or lot
(Sherman, Gartin and Buerger 1989). Within the study, strong evidence is provided that confirms
these areas lacked a capable guardian. Sherman et al sum up the argument for capable
guardianship on page forty-six, “If the distribution of crime hot spots was determined -solely by
the concentration of offenders, then how can we explain the complete 1-year absence of
predatory crimes from 73% of the places in high-crime crime areas in Minneapolis (compared
with the expected absence from only 57%)?”

23

Although, “Violent Disorder in Ciudad Jaurez: a spatial analysis of homicide,” used
social disorganization theory, the study revealed negative linear relationship correlations
between explanatory variables and homicide (Vilalta and Muggah 2014). This study was placed
in this chapter to highlight homicide can be better understood using regression analysis
aggregated by police district (similar to census tract), and that significant negatively linear-
related explanatory variables are attainable. Six negative linear explanatory variables for
homicide were cited: Female population between six and eleven that do not attend school,
Population with employment, Population ascribed to Seguro popular (state funded health
insurance), Population over twelve that is married, Number of people in temporary housing, and
Occupied home units with land floor. Within the areas where these variables show a negative
relationship to homicide, Vilalta and Muggah suggest possible reasons as being wide
socioeconomic and socio-behavioral dividends due to family support, social ties such as
marriage, supportive welfare programs, and employed populations (Vilalta and Muggah 2014).
Regardless of explanation, the point is that explanatory variables with a negative relationship to
homicide were found using regression analysis, even in an exceedingly complex environment
such as Ciudad Juarez. Even though Ciudad Juarez towers Washington, DC in homicide with
6,436 homicides between 2007 and 2010, and the socio-economic situation and culture of
violence is much more complicated, cold spots were identified along with six significant linear
regression explanatory variables.
In the aforementioned research, violent crimes are spatially clustered. However, most of
the studies use qualitative analysis in the form of interviews, and all of the analysis employed the
absence of a capable guardian, even though routine activity theory includes the inverse to be part
of the theory: the presence of a capable guardian deters crime. However, one article was found

24

that used the presence of a capable guardian as having a negative linear relationship to violent
crime. Below, the main ideas and similar details are provided, along with a justification for using
Geographically Weighted Regression (GWR) within this analysis.
In “Using Geographically Weighted Regression (GWR) to Explore Local Crime
Patterns,” (2007) Meagan Cahill and Gordon Mulligan used regression analysis to study violent
crimes in Portland Oregon. Similar to DC, high crime and low crime spatial clusters were
identified in the city. Although the regression analysis used variables with positive and negative
linear relationships to violent crimes (homicide, sexual assault, robbery and aggravated assault),
two guardianship variables were highlighted that had a negative linear relationship to violent
crime: residential stability, and percent of married families. In addition, the aggregation method
was census block group and the data used consisted of a five-year study period for the years
1998 – 2002. Given the similarity of the dependent variable, aggregation, inclusion of the
routine activity theory, and some of the independent variables directly showing negative linear
relationships to violent crimes, the results and conclusions for this study were noted for similar
application in this study.
“The application of GWR to a model of violence rates and its comparison to an OLS base
model has yielded several striking results” (Cahill and Mulligan 2007, 190). Four of the eight
parameters showed non-stationarity, and the measure of affluence produced a counterintuitive
result, being positively related to violent crime. Through the use of GWR, Cahill and Mulligan
identified 20% of the census block groups as being affluent and positively related to violent
crime. Furthermore, single-person households, married families, and population density were not
highly correlated to crime. Through the use of GWR, an exploratory regression analysis, more
information can be better understood and applied in future analysis. For example, Cahill and

25

Mulligan suggested using a higher level of income for the affluent variable, moving the
benchmark of $50,000 to $75,000, which may be enough to change the counterintuitive results.
Given that Cahill and Mulligan’s article holds many similarities to this study: violent
crime as the dependent variable, census block aggregation, the inclusion of the routine activity
theory, in a similar-sized city being Portland, GWR may be another tool to use in the study of
violent crimes in DC. A possible reason for heterogeneity when studying violent crime may be
that “While structural characteristics of neighborhoods influence crime, it can also be said that
crime influences the structural characteristics of neighborhoods” (Hipp 2010, 205). With regards
to other studies suggesting violent crimes may be non-stationary, researchers who employ OLS
may want to consider using GWR as well to double check the variables used for heterogeneity.

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Chapter 3: Methods
This chapter describes the methodology developed to test the capable guardian component of the
routine activity theory. The main objectives are to conduct a spatial analysis of violent crime
cold spots and to build a model of housing characteristics as the explanatory variables. Many
problems within the study area needed to be resolved prior to finding a model to test whether
housing characteristics indicate the likelihood or perceived likelihood of a capable guardian
being present, thereby deterring crime. This chapter is broken down into six main sections: 1)
Data sets; 2) The study area, federal land, and aggregation choice; 3) Hot spot analysis; 4) The
explanatory variables; 5) Exploratory regression and Ordinary Least Squares (OLS); and 6)
Geographically Weighted Regression (GWR).
3.1 Data Sets
Eight data sets are used to complete the analysis, as shown in Table 1. The first data set
consists of census block group boundaries, formatted as polygons. The second data set consists
of four violent crimes, made up of point data. Data sets three through eight consist of twenty-
five variables relating to homeowner or housing characteristics in the form of count data.
The dependent variable is made up of four violent crime datasets (homicide, assault with
a dangerous weapon, robbery, and sexual assault) from 2012 through 2015. These datasets are
provided by the Metropolitan Police Department, District of Columbia. Given the data source
consists of police reports, the accuracy of the points is not being challenged. The georeferenced
crime points are plotted at either end or in the middle of the block on which the crime occurred,
as shown in Figure 3. Being within a city block provides enough spatial accuracy to be analyzed
at the spatial scale of data that is aggregated by census block group, which is the aggregation

27

used throughout the study. In addition, all of the points are clearly located within a single census
block group, none occurring on the boundaries.
All of the explanatory variable data sets were obtained on March 5, 2016 from the US
Census Bureau. The data sets are 2010 – 2014 American Community Survey 5 – Year Estimates,
extracted online via the American Fact Finder search tool: http://factfinder.census.gov/. The
accuracy for each data set differs greatly for each data set and for each census block group. The
details for sample size, data quality measures, data accuracy and statistical testing can be found
on the American Community Survey website in the Data and Documentation section.

28

Table 1: Data sets and variables

Data Set Type Variable Description
Boundary Polygon Aggregation
N/A Census Block Group 2010
Violent Crime Point Dependent Variables
Hom Homicide (2012 - 2015)
Dan Assault w Dan Weapon (2012 - 2015)
Rob Robbery (2012 - 2015)
Sxa Sexual Assault (2012 - 2015)
US Census Survey Explanatory Variables
Edcuation Count Highest Education Level Obtained
NoDip No High School Diploma
HSDip High School Diploma
SColl Some College
Bach Bachelor's Degree or Higher
Home Value Count Value of Home
V199 Under $199,999K
V999 $200,000K - $999,000K
V1M Over $1M
Income Count Household Income
I39 Under $39,999K
I74 $40,000 - $74,999
I199 $75,000 - $199,999
I200 Above $200K
Occupancy Count Percentage of Occupied Homes
Occ Occupied
Vac Vacant
Housing Type Count Type of Home in Relation to Other Homes
Det Detached
A4 Attached 1 - 4 Units
A9 Attached 5 - 9 Units
A10 Attached 10 Units or More
Marital and
Ownership Count Marital and Ownership Status
MarOwn Married and Owns the Home
MarRen Married and Rents the Home
ManOwn Man Without a Wife, Owns the Home
ManRen Man Without a Wife, Rents the Home
WomOwn Woman Without a Husband, Owns the Home
WomRen Woman Without a Husband, Rents the Home
NFOwn No Family, Owns the Home
NFRen No Family, Rents the Home

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Figure 3: Crime points plotted to one of three positions on the block. Source:
Metropolitan Police Department.
Each violent crime is georeferenced as a point. Along with the coordinates, additional
information such as date, type of offense, method, and data at different scales is provided, as
shown in Table 2 below.
Table 2: Violent crime variable examples
ID
X Y Report Date Offense Method Block Site Address
1
-77.03143305 38.91112616 2/3/2013 Robbery Knife 1330 - 1399 Block of Q Street NW
2 -76.93432072 38.88311158 2/3/2013 Robbery Gun Benning Road SE and 46th Street SE
3
-76.98928103 38.90020276 2/3/2013 Robbery Others 1200 - 1299 Block of H Street NE

ID
X Coord Y Coord W N D P NC BG CT
1
397274 138140 2 2F Third 307 7 005001 2 5001
2
405698.82 135031.7 7 7F Sixth 608 33 009907 2 9907
3
400930 136927 6 6A First 104 25 008402 1 8402
W = Ward, N = Neighborhood, D = District, P = Police Service Area,
NC = Neighborhood Cluster, BG = Block Group, CT = Census Tract
In 2013, there were 104 homicides, including twelve people who were murdered in the
Navy Yard on September 16, 2013 (Bowser, Muriel 2013). I assessed this to be an outlier event,

30

so these twelve homicides were deleted from the study lowering the number of homicides to
ninety-two (92) for 2013, as shown in Table 3. Without deletion, the event would skew the study
area as well as the results of a hot spot analysis. No other outlier events are known concerning
violent crimes for the years included in this study.
Esri’s nearest neighbor tool is used to show that each of the violent crimes for each
category and year are clustered at a 99% confidence level, as shown by the Z-Scores in Table 3
below. The lowest Z-Score found is homicide in 2012, Z=-4.5481 (well below the critical value -
2.58), meaning there is a less than one percent likelihood that these clustered patterns could be
the result of random chance.
Table 3: Violent crime Z-scores for nearest neighbor analysis of each violent crime by year
2012 2013 2014 2015 2012-15
Crime N Z-Score n Z-Score n Z-Score n Z-Score N Z-Score
Homicide 87 -4.5481 92 -6.3119 105 -6.0076 156 -9.8856 440 -17.1721
Assault w
Dan
Weapon 2,358 -51.7878 2,393 -53.836 2,467
-
54.9157 2,385
-
52.9673 9,603 -136.099
Robbery 4,209 -69.0641 3,994
-
67.9034 3,269 -58.408 3,352
-
59.7989 14,824 -166.838
Sexual
Assault 258 -8.6571 292
-
12.4553 311 -12.061 275
-
10.5234 1,136 -30.1684

N

Total 26,003

Since there are only 440 homicides included in the regression analysis, homicide is given
a fraction of measurement (less than two percent weight) when the analysis shifts to regression
analysis in comparison to assault with a dangerous weapon (n = 9,603; thirty-seven percent
weight), robbery (n = 14,824; fifty-seven percent weight), and sexual assault (n = 1,136; four
percent weight). If the violent crimes generate violent crime hot and cold spots along with
showing a relationship in regression analysis, these differing sample counts, most likely, will

31

have minimal impact. The overarching purpose of the study is to show the negative correlation to
violent crime overall, not the deterrence of a specific violent crime.
All data are converted to the geographic coordinate system NAD 1983 NSRS 2007 State
Plane Maryland FIPS 1900 (US Feet), and the projection Lambert Conformal Conic is used
throughout the study.
3.2 The Study Area, Federal Land, and Aggregation Choice
As stated in Chapter 1, Washington, DC consists of 68.3 square miles, but twenty-five
percent of this land is federal land, under federal jurisdiction. Since this land is not covered by
the Metropolitan Police Department of Washington, DC (MPD), the violent crime data for these
areas may not be accurate (Perry, McInnis and Price 2013). To ensure these areas do not skew
the analysis, as these would show up as cold spots, the largest census block groups are removed
from the study area as highlighted in red, displayed in Figure 4. The number of census block
groups are reduced from 450 to 446.The census block groups outlined in orange in the top center
of Figure 4 are retained because these areas include park land as well as populated areas with
proper census data.
After the omission of these areas, the remaining areal units are checked for spatial
autocorrelation of violent crimes. Since, Esri’s incremental spatial autocorrelation tool did not
provide a meaningful distance to apply for conceptualization of spatial relationships, two other
options are used to ensure spatial autocorrelation exists for violent crime when aggregated by
census block group. Inverse Distance and Inverse Distance Squared are chosen to represent the
crime data over Contiguity Edges Corners because the borders for blocks and block groups are
not cultural and did not employ a meaningful relationship to violent crime.

32

Figure 4: Modified study area
A well-known problem called the Modified Areal Unit Problem (MAUP), results when
inappropriate spatial units are used in a spatial analysis (Bolstad 2012). Although MAUP cannot
be completely avoided in this study because the polygons are not constructed specifically for the

33

analysis, a finer spatial aggregation may reduce the number of different types of homes and
homeowner characteristics. Therefore, I chose census block groups as a better scale than census
tracts to minimize the inclusion of multiple types of housing. Although census block groups may
still contain differing neighborhoods, the crossover ought to be less in comparison to census tract
aggregation.
More than likely, due to the census block groups being divided up without regard to
housing, heterogeneity or non-stationarity may cause misspecification to some degree and the
model may be missing a key variable (Wilson and Fotheringham 2008). To fix this problem
would require new polygons to be drawn according to housing type and then a survey be applied
to fit the aggregation, which is beyond the scope of this study. Although census block may refine
the analysis even more than census block group, the census bureau does not provide housing data
at this level of aggregation.
Esri’s spatial autocorrelation tool is used to make sure violent crimes are significantly
clustered, as this would need to be the case to apply a spatial study to violent crimes. According
to the Z-Scores, violent crimes are clustered in all three forms of aggregation measured: census
block, census block group, and census tract, as shown in the Table 4.

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Table 4: Spatial autocorrelation and Z-scores when violent crime is aggregated
Inverse Distance

Aggregation n mod n Z-Score Index
Block 6,507 6,094 96.0043 0.1426
Block Group 450 446 18.472 0.2363
Census Tract 179 175 8.7657 0.2203

Inverse Distance Squared

Aggregation n mod n Z-Score Index
Block 6,507 6,094 8.4172 0.1797
Block Group 450 446 11.4657 0.252
Census Tract 179 175 6.2667 0.2344

Z-Scores at the census block group level are well above the accepted level of 2.58, meaning this
aggregation method, when using violent crime data, ought to show significant hot and cold
violent crime spots when analyzed via a hot spot analysis. All of the violent crime datasets are
normalized using log transformation.
3.3 Hot Spot Analysis
Each violent crime data set (homicide, assault with a dangerous weapon, robbery, and
sexual assault) is independently tested for hot and cold spots using Esri’s Optimized Hot Spot
Analysis tool. The resulting graphics are overlaid as well as combined in a separate analysis to
demonstrate that violent crimes occur in the same areas, suggesting a strong relationship between
violent crimes exists. Therefore, I assess that all four violent crimes can be combined together to
form a single dependent variable providing a larger sample size. This allows for a more defined
aggregation method, such as census block group instead of census tract. The results of the
analysis benefits with a higher probability, which may lead to more conclusive results
concerning finding areas with capable guardians. Areal units with less space may better represent
individual neighborhoods, so homeowner and housing characteristics ought to be more similar.

35

Census block group is closer to the ideal than census tract. This may highlight certain areas and
may lead to higher adjusted R-squared values when regression analysis takes place. It is very
important to show that the violent crimes are related and occur in the same areas. Hot spot
analysis is used to show this relationship exists prior to choosing any potential explanatory
variables.
Given that the Optimized Hot Spot Analysis tool automatically applies scale and spatial
dependence to its formula to generate a statistical measurement, both saves time and ensures
human error is reduced (Esri 2016). Other hot spot analysis tools require the analyst to choose
parameters that can change the results drastically.
Since no distance can be justified through the evaluation of violent crime in concerns of
scale of analysis, the automatic strategies built into Esri’s tool are used. In the first strategy, the
tool uses incremental spatial autocorrelation to measure the intensity of clusters using Z-scores to
identify a peak to establish a distance (using Global Moran’s I statistic). However, when no peak
is found, then the distance is determined by computing the average distance that yields K
neighbors for each feature, when K is computed as 0.05 * N (N is the number of features in the
Input Features layer). The tool automatically adjusts so K is no less than three and no greater
than thirty neighbors are used. Outliers are identified and not included in the analysis. Finally,
the hot and cold violent crimes for census block group aggregation is displayed at high
confidence levels: 90%, 95%, and 99%.
3.4 The Explanatory Variables
The main purpose for using linear regression analysis is to find variables with a negative
linear relationship to violent crime, so a model can be built using housing and homeowner
characteristics. Given prior research highlighted in Chapter 2, variables chosen are rationalized,

36

as to why these are proxies for the perceived presence of a capable guardian. In other words,
random variables without rationale for being related to a capable guardian are not considered. A
seventy-five percent negative linear relationship figure is used as the benchmark for advancing to
the next phase of testing, for inclusion in the final model, with a goal to show 100% negative
linear relationships for all variables included in the final model. This study is mostly concerned
with showing a negative linear relationship between the proxy explanatory variables and violent
crimes. A benchmark for a minimum R-squared score is not set. However, each explanatory
variable needs to measure as being significant in the final model.
All of the explanatory variables are changed to a ratio by computing a percent using the
raw number divided by the total number within each dataset. The Census Bureau provides the
count as well as the total number used within the sample, so computing a percent can be easily
done using Esri’s field calculator. Prior to analysis, all of the dependent variables are normalized
using the log or arcsin function. Also, the explanatory variables, when applicable are normalized
using the log function when the variable displayed a positive skew and arcsin when the variable
displayed a negative skew. The transformations for the explanatory variables can be found in
Table 5.

37

Table 5: Normalizing the explanatory variables
Variable Skew Pmean Pmedian Diff Pkurtosis CompTr Tmean Tmedian Diff Tkurtosis
NoDip Pos 0.11235 0.09349 0.01887 3.2492 Log 0.102 0.0892 0.01273 2.679
HSDip Pos 0.2044 0.17863 0.02577 2.499 Log 0.1733 0.1636 0.00976 2.0103
SColl Pos 0.18087 0.17057 0.0103 3.4361 Log 0.1603 0.1568 0.00355 2.6014
Bach Pos 0.58672 0.51128 0.07544 1.6973 Log 0.3912 0.3983 -0.00708 1.65
V199 Pos 0.12423 0.03648 0.08775 11.167 Log 0.1009 0.0358 0.06506 4.8804
V999 Neg 0.71136 0.82342 -0.11206 3.4763 ArcSin 0.8931 0.9674 -0.0743 2.5011
V1M Pos 0.09174 0 0.09174 9.1998 Log 0.0775 0 0.0775 7.2554
I39 Pos 0.32596 0.28585 0.04011 2.5325 Log 0.2707 0.2514 0.01927 2.2225
I74 Pos 0.21102 0.2028 0.00822 2.915 Log 0.1883 0.1847 0.00368 2.7265
I199 Neg 0.33284 0.34798 -0.01514 2.3496 ArcSin 0.3437 0.3554 -0.01177 2.4156
I200 Pos 0.13018 0.07237 0.05782 4.728 Log 0.1146 0.0699 0.04474 3.7644
Occ Neg 0.89053 0.90507 -0.01454 4.1143 ArcSin 1.1555 1.1316 0.0239 2.6326
Vac Pos 0.10947 0.09493 0.01455 4.1143 Log 0.1008 0.0907 0.01006 3.423
Det Pos 0.16264 0.04649 0.11616 6.0797 Log 0.1314 0.0454 0.08593 4.9582
A4 Pos 1.2254 1.2076 0.0178 3.1054 Log 6.5935 6.6012 -0.0077 2.6446
A9 Pos 0.0633 0.02511 0.03819 3.313 Log 0.0576 0.0248 0.03276 2.6696
A10 Neg 1.4196 1.4253 -0.0057 2.106 ArcSin 0.4196 0.4253 -0.0057 2.106
MarOwn Pos 0.24678 0.21217 0.03461 4.1004 Log 0.2126 0.1924 0.02019 3.2646
MarRen Pos 0.06961 0.05762 0.01199 4.1924 Log 0.0659 0.056 0.00984 3.7011
ManOwn Pos 0.01592 0 0.01592 2.2325 Log 0.0155 0 0.01549 2.123
ManRen Pos 0.02283 0 0.02283 8.565 Log 0.0155 0 0.01549 7.6365
WomOwn Pos 0.06467 0.04077 0.0239 5.2 Log 0.0604 0.04 0.02045 4.4616
WomRen Pos 0.10926 0.05433 0.05493 5.4765 Log 0.0968 0.0529 0.04389 4.2963
NFOwn Pos 0.20272 0.19088 0.01184 3.9489 Log 0.1793 0.1747 0.0046 3.179
NFRen Neg 0.33781 0.33912 -0.0013 2.6516 ArcSin 0.355 0.346 0.009 3.5128
Green shows the variable used. Only two variables were not normalized.
Each explanatory variable set represents housing or homeowner characteristics. The
explanatory variable datasets are as follows: log of percent of the total number of people twenty-
four years or above according to education level obtained, log or arcsin of percent of the total
home value, log or arcsin of the percent for the total house-hold income, log or arcsin of percent
of occupied homes, log or arcsin of the percentage of the total type of housing (attached and
number of attached units), and the log or arcsin of the percentage of the total head of households

38

that showed family, marital status, and ownership status. The individual explanatory variables
and the data sets are presented in Table 1.
Housing characteristics may portray capable guardianship for any passerby. Two variable
sets use housing attributes to show the perception of a capable guardian: home value and housing
type.
The first explanatory variable set is based on the ‘value of home’. The value of the home
is separated into three different levels: under $199,999, $200,000 - $999,999, and above
$1,000,000. The reason for the wide range for the middle variable rests on the high median value
of a home in DC: $535,000. Most likely, breaking this variable into two would not produce a
different result.
The second housing characteristic uses the type of home. Detached homes are chosen
because there is a physical space which increases the risk of being observed in a private area.
Below in Table 6 are the raw numbers prior to being converted to ratios. The total number of
housing units used in the survey is in the left column. The percentage is obtained by dividing the
number of each type of unit by the total number of units. Furthermore, multiple variables are
joined (Table 7). For example, instead of separating ‘1 unit attached,’ ‘2 units attached,’ and
‘three or four units attached,’ the different ranges are placed into a single variable ‘1 – 4 units
attached’ to provide a larger sample size for the alternative variable.

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Table 6: An example of count data for an explanatory variable
Total housing units

1-unit, detached 1-unit, attached 2 units 3 or 4
units
5 to 9
units
10 to 19
units
20 or
more units
2,828 220 1,233 40 209 186 115 825

Table 7: Variable after grouping and as a ratio
Total housing units

1-unit, detached 1-4 unit,
attached
5-9 units 10+
units
2,828 0.0779 0.5241 0.0658 0.3324

The third housing characteristic uses information about the homeowner. This is
composed of marital status and ownership. There are eight possibilities between married, not
married, man or woman head of household without spouse, nonfamily, and own or rent. The
Census Bureau’s survey did not consider families outside of the traditional makeup, such as
same sex couples, so a larger range of potential error within this variable may exist, depending
upon how these families chose to participate in the survey.
A fourth housing characteristic uses occupancy and vacancy percentages. This variable is
the most basic of those being tested. If merely being occupied measures as significant, then
capability is undermined.
The fifth variable set uses the household income as the measurement. There are four
different brackets: up to $39,999; $40,000 - $74,999; $75,000 - $199,999, and above $200,000.
The sixth variable shows the highest education level obtained: no high school diploma,
high school diploma, some college, bachelor’s degree and higher.
3.5 Exploratory Regression and Ordinary Least Squares (OLS)
Two phases of exploratory regression are used to find explanatory variables for further
analysis in Ordinary Least Squares (OLS). Phase one identifies variables with a negative

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relationship to violent crime. All twenty-five explanatory variables are entered into exploratory
regression, and those with a negative linear relationship to violent crime are moved for further
analysis. Phase two required three characteristics for the explanatory variable to be analyzed
further in OLS: When belonging to a model (with the other explanatory variables) in exploratory
regression, the variable must 1) show a negative linear relationship to violent crime; 2) measure
as significant (p<0.05); and 3) show a variance inflation factor (VIF) score of less than seven.
The VIF score measures the amount of collinearity between variables. After meeting these three
criteria, the explanatory variables are analyzed using OLS.
Esri’s tool Ordinary Least Squares (OLS) is used to show whether or not each
explanatory variable and the cumulative model is significant (results were considered significant
when p<0.05). There are six subdivisions or assessments.
1) The coefficient ought to be negative to ensure a negative linear relationship exists
between violent crime (the dependent variable) and the explanatory variable.
2) Esri’s OLS tool checks for co-linearity and computes an index called the Variance
Inflation Factor (VIF). Essentially this test makes sure two variables are not redundant by
providing a score based on co-linearity and the guidance is not to keep variables with scores
above seven (Esri 2016). For example, variance may be high between income and home value
because, for the most part, to be able to afford an expensive home, a person would most likely be
in the higher income bracket. However, this may not end up being the case. There may be many
high-income learners who do not buy or live inside expensive homes. In any case, variance needs
to be tested to make sure a variable can stand on its own.
3) To assess the statistical significance of the resultant model, the Koenker (BP) statistic
is run. The Koenker (BP) statistic to assesses stationarity between the dependent variable and the

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explanatory variable. Stationarity exists when relationships between the variables contain
consistency. This is also known as homoscedasticity. For example, if high-income earners are
consistently present in high percentages in violent crime cold spots all of the time, then the
relationship is stationary. However, if high-income earners are present in high percentages in
both cold and some hot spots, then the relationship is said to be heteroscedastic, and the Koenker
(BP) test shows this as statistically significant (p<0.05). To be determined as significant, the
results from the Koenker (BP) statistic needs to be greater than the chi-squared calculation based
on the number of degrees of freedom (dependent on sample size). When the results are
statistically significant, the robust probability along with the Joint Wald Statistic (described
below) is used to show the model’s significance. However, if the Koenker (BP) statistic is not
significant, then the probability along with the Joint F-Statistic (also described below) shows the
overall model’s significance. Either the Joint F-Statistic and/or the Joint Wald Statistic shows
whether the model is or is not significant (ArcGIS 2012).
4) The Joint Wald and Joint F-Statistic are used to measure the overall performance of
the model by setting the null hypothesis for the explanatory variable at ninety-five percent. The
Joint Wald statistic measures as being significant when the result is greater than the chi-squared
calculation. The Joint F-Statistic uses a t-statistic and requires normal distribution of the data. In
other words, when variables show heteroscedasticity, then this statistic is not used. So, when the
Koenker (BP) statistic is significant, then the Joint Wald statistic is used and vice versa for when
the Koenker (BP) statistic is not significant (ArcGIS 2012).
5) The Jarque-Bera statistic checks whether the residuals are normally distributed and for
model bias (Esri 2016). The residuals ought to be randomly distributed. If not, then, most likely a
key variable is missing or there is strong heteroscedasticity between the dependent and

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explanatory variables. The Jarque-Bera statistic shows to be probable when the results are greater
than the chi-squared calculation based on two degrees of freedom.
6) R-squared indicates a percentage of the response variable variation between the
dependent variable (denoted by y) and one or more independent variables (denoted by x) in a
linear regression model. The R-squared values are given as a decimal between zero and one to
show the strength of the relationship between the explanatory variables and the dependent
variable, with a value closer to one showing a stronger relationship exists. However, the R-
squared results are not the main focus for this study.
The adjusted R-squared score may measure the strength of the relationship, but high R-
squared scores are not expected nor is there a requirement to show that the model shows a
significant relationship exists between violent crime and the proxy model. The purpose is to test
whether a proxy model suggests the perceived presence of a capable guardian deters crime, but
not to what extent. Any number to show a benchmark would be arbitrary, so none is put forth.
3.6 Geographically Weighted Regression (GWR)
Geographically Weighted Regression (GWR) works well when data is nonstationary
because it uses a local form of linear regression. Instead of fitting a model to an entire study
region (global), GWR estimates coefficient values for every chosen point, giving most of the
weight to the points that are closest to the center; the results provide information about the
relationship between the dependent variable and one or more independent variables concerning
geographical differences (Fotheringham, Brunsdon and Charlton 2002). Although different
bandwidth, or the number of neighbors, can be chosen by the researcher, this analysis uses Esri’s
built in function to optimize bandwidth based on AIC. The primary use for GWR is to attempt to

43

understand the strengths and weaknesses of the relationships for each explanatory variable to
violent crime.
Prior to running GWR, a model is built and run in OLS. GWR may help a researcher
understand the variables and relationships better, but GWR cannot decipher collinear
relationships, so this must be observed using OLS. According to Esri, the VIF should not be
above seven. If the VIF is greater than seven, then GWR does not yield results that can be used.
GWR analysis enables the researcher to understand nonstationary data along with areas where
the model performs well and where it does not. This analysis provides local R-squared values
from 0.0 to 1.0. High values show high performance.
If the model run in OLS passes most tests, but the Koenker (BP) is significant, suggesting
the data is non-stationary, then the model is a fitting candidate for GWR analysis. A GWR
analysis may show where the locally weighted regression coefficients move away from their
global values, which may provide possible reasons for non-stationarity within an explanatory
variable and provide better oversight in future projects with a similar scope. For example, the
census data may need to be filtered differently, or a different aggregation may need to be applied
to improve the model’s performance.

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Chapter 4: Results
This study uses housing characteristics as proxies for a capable guardian and tests whether a
correlation exists between capable guardianship and the deterrence of violent crime. The
following chapter provides the results. In sections 4.1 and 4.2 the results of a hot spot analysis
and the relationships amongst violent crime data are examined. In the subsequent sections of this
chapter, regression analysis is used to explore the housing and homeowner explanatory variables,
including a proxy model that measures as being significant, suggesting that the presence of a
capable guardian deters violent crime. Finally, Geographically Weighted Regression (GWR) is
used to map the coefficients and provide a visual display of the relationship between the
explanatory variables and violent crime in relation to each of the other variables.
The overall results show violent crimes to be clustered at a ninety-nine percent
confidence level. Also, at least three hot spots and one cold spot is visually identified in the
results of the optimized hot spot analysis. The strong inter-relationships of the four violent
crimes shown in a hot spot analysis and measured during regression analysis (whereby each
violent crime is a dependent variable and the other violent crimes are the explanatory variables)
justifies combining these into one variable for use as a dependent variable in the final regression
analysis.
4.1 Hot Spot Analysis of the Violent Crimes
Hot spot analysis shows each of the four violent crimes (homicide, assault with a
dangerous weapon, robbery, and sexual assault) are clustered at a ninety-nine percent confidence
level (Figures 5 – 8). Although the hot spots and cold spots may expand and contract depending
upon the violent crime, enough overlap is visible to suggest a strong relationship exists between
the violent crimes when aggregated at the census block group level. Figures 5 - 8 depict at least

45

three hot spots and one cold spot for all of the violent crimes independently run. Overall, three
hot spots and one cold spot is identified within Washington, DC for all of the violent crimes
combined (Figure 9). A cold spot is identified near the white house for homicide and assault with
a dangerous weapon, but this cold spot is no longer identified for robbery or sexual assault. Also,
Central DC shows crimes to be along the main roads in many places, but the numbers of crimes
compared to the hot spots identified simply keep these areas from being clustered. Reference
numbers are placed near the center of the masses to show the same areas are both plagued (hot
spots) and vacant (cold spot) of violent crime, regardless of which violent crime is input.

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Figure 5: Homicide hot spots by census block group

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Figure 6: Assault with a dangerous weapon hot spots by census block group

48

Figure 7: Robbery hot spots by census block group

49

Figure 8: Sexual assault hot spots by census block group

50

Figure 9: Combined violent crime hot spots by census block group

51

The results show the violent crimes are clustered. To better understand these relationships, the
next section explains the results of exploratory regression.
4.2 Exploratory Regression and Ordinary Least Squares of the Violent
Crimes
Exploratory regression shows a 100% positive relationship exists between all four violent
crimes (homicide, assault with a dangerous weapon, robbery, and sexual assault). However,
homicide only shows to be 100% significant in relation to assault with a dangerous weapon,
whereas homicide is only fifty percent significant to robbery and sexual assault, as shown in
Table 8 below.
Table 8: Exploratory regression results for four violent crimes

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Table 9: OLS results for violent crime models

Ordinary Least Squares defines this relationship further, as shown in Table 9 above.
When assault with a dangerous weapon is input as the dependent variable, then all violent crimes
are significant (Table 8) and the adjusted R-squared score measures at 0.76 (Table 9). When
using Ordinary Least Squares, only assault with a dangerous weapon measures as being
significant to homicide. Whereas, robbery, sexual assault, and assault with a dangerous weapon
shows a significant relationship to one another. The variability remains low in all models.
These results combined with the prior hot spot analysis provides enough rationale to
combine all of the violent crimes into one dependent variable to be used in the main study testing
whether the presence of a cable guardian deters crime. The dependent variable consists of 26,003
violent crimes occurring from 2012 through 2015: homicide (n = 440), assault with a dangerous
weapon (n = 9,603), robbery (n = 14,824), and sexual assault (n = 1,136). The dependent
variable is aggregated by census block group, count data is changed to percentages, and since it
is not normally distributed, the variables are normalized using the log function.

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4.3 Exploratory Regression and Identifying Explanatory Variables for OLS
To test whether the presence or perceived presence of a capable guardian shows a
negative correlation to violent crime, six variable sets are chosen: 1) education attained for
people who were twenty-four years of age and above; 2) home values; 3) income per household;
4) occupancy; 5) type of housing; 6) and type of household (family) along with ownership. Two
phases of exploratory regression are used to isolate significant explanatory variables with
negative linear relationships to violent crime.
In the first phase of exploratory regression, twenty-five explanatory variables belonging
to one of the six data sets are tested to identify the variables with a negative linear relationship to
violent crime. The settings within Esri’s exploratory regression tool are set to allow for seven
possible variables in the model. In Table 10, five explanatory variables shows a significant
negative linear relationship to violent crime: the log of percent of the total number of homes with
values over $1,000,000 (LV1M); the log of the percent of the total number of homes owned by
married couples (LMAROWN); log of percent of the total number of the population who are
twenty-four years of age and over and earned a bachelor’s degree or higher (LBACH); the log of
percent of the total number of homes that are detached (LDET); and the log of percent of the
total number of households with income over $200,000 per year (although not as strong as the
other four explanatory variables).
For the second phase of exploratory regression, the five identified explanatory variables
with a negative linear relationship are entered into Esri’s exploratory regression analysis tool.
Due to lack of significance, income over two hundred thousand dollars is dropped, as shown in

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Table 11 by the lack of an asterisk. After the second phase of exploratory regression, a model
consisting of four explanatory variables remain (Table 11). I refer to this as the guardian model.
Table 10: Exploratory regression phase one - negative linear relationships to violent crime

Table 11: Exploratory regression phase two - four standing significant explanatory variables

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4.4 Results of Ordinary Least Squares Model and Details
The guardian model (highlighted in Table 11 above) consists of a dependent variable
encompassing all four violent crimes (homicide, assault with a dangerous weapon, robbery, and
sexual assault), and four explanatory variables (LBACH, LV1M, LDET, and LMAROWN).
When the guardian model is plugged into Ordinary Least Squares (OLS), all four variables show
a negative linear relationship (shown by the negative symbol in the Coefficient column), all
measure as being statistically significant (shown by the Robust Probability column), and register
as maintaining a low variability in relation to each of the other explanatory variables, being
under three (shown in the VIF column), as shown in Table 12 below.
Table 12: Summary of OLS results for the guardian model

Since the Koenker (BP) statistic is significant, the Joint Wald statistic is used to measure
the overall performance of the guardian model: the results show the model to be statistically
significant, p<0.05* (Table 13). Using the robust probabilities and the Joint Wald statistic, the
model suggests capable guardianship or the perception of capable guardianship deters crime.
However, the Jarque-Bera Statistic measures as being statistically significant
(p<0.000000*), and the residuals are spatially clustered at a 99% confidence level, which
suggests a key variable is not included in the model. The adjusted R-squared score is 0.46, which
supports the model is missing a key variable (Table 13).
Variable Coefficient StdError t-statistic Probability Robust SE Robust t Robust Pr VIF
Intercept 5.002586 0.10337 48.394911 0.000000* 0.084808 58.987219 0.000000* -----------
LBACH -2.306739 0.253663 -9.093728 0.000000* 0.277158 -8.322816 0.000000* 1.605068
LV1M -1.723681 0.386703 -4.457371 0.000013* 0.406172 -4.243717 0.000031* 1.613482
LDET -0.966088 0.291938 -3.30922 0.001026* 0.27787 -3.476767 0.000572* 1.718721
LMAROWN -1.37913 0.504748 -2732313 0.006540* 0.447836 -3.079541 0.002214* 2.282136

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Table 13: OLS diagnostics for the guardian model
Input Features Capable G. Dependent Variable
Violent
Crime
Number of Observations 446 Akaike's Information Criterion (AICc) 1155.096018
Multiple R-Squared 0.46964 Adjusted R-Squared 0.464829
Joint F-Statistic 97.6277539 Prob (>F), (4,441) degrees of freedom 0.000000*
Joint Wald Statistic 467.317281 Prob (>chi-squared), (4) degrees of freedom 0.000000*
Koenker (BP) Statistic 25.527869 Prob (>chi-squared), (4) degrees of freedom 0.000039*
Jarque-Bera Statistic 111.879492 Prob (>chi-squared), (2) degrees of freedom 0.000000*

Below are the histograms and scatterplots of the OLS (Figure 10) that show the
relationship between each explanatory variable and the dependent variable (violent crime). The
scatterplots for LV1M and LDET do not show to be as strongly correlated to violent crime as
LMAROWN and LBACH, which explains the potential heteroscedasticity and missing variables
signified by the Jarques-Bera statistic and clustered residuals. The positively skewed variables
LV1M and LDET suggest a different transformation or a more fitting aggregation may yield
better results.

Figure 10: Variable distributions and relationships in the guardian model
The histogram of the standardized residuals did resemble a Gaussian curve, showing the
model is probably not biased (Figure 11).

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Figure 11: Histogram of standardized residuals for the guardian model
Finally, the standard residuals are compared to the predicted plot; an archetype result does not
show any pattern. On the next page, Figure 12 does not show an obvious pattern, so the model
appears to work. The positive as well as negative standard residuals are relatively even as can be
observed through the identified colors above and below the X axis.

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Figure 12: Residual vs predicted plot guardian model
4.5 Geographically Weighted Regression
Geographically Weighted Regression’s adjusted R-squared value of 0.57 is an
improvement from the Ordinary Least Squares (OLS) R-squared value of 0.46. The dependent
variable is violent crime. The explanatory variables are LV1M, LBACH, LDET, and
LMAROWN; for reference the distribution of these values is shown in Figure 13 with the values
categorized into quintiles. Within all of the explanatory variables, non-stationarity exists, which
provides the main reason GWR shows better results in comparison to OLS. The model
coefficients are mapped and can be found in Figure 14. Reference numbers are placed in the
graphic to match with areas of interest identified in a prior hot spot analysis.

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Figure 13: Distribution of the values of the explanatory variables in the guardianship model with
values classed into quintiles

60

Figure 14: GWR guardianship model coefficients

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Figure 14 shows all four of the model coefficients on a single page for comparison. The
area of interest for this study is in northwestern DC, west of Rock Creek Park, near reference
number 4. In this area, the coefficients for LBACH ranged down to -5.02, which is the strongest
negative coefficient of any explanatory variable, suggesting LBACH is the most important factor
in the model. Furthermore, the distribution of the variables match well with the area of interest
(Figure 13), meaning numerically as well as spatially LBACH matches with the area of interest.
LDET’s coefficient, when mapped in Figure 14, shows a moderately strong negative
value in the area of interest near reference number 4. The coefficient’s minimum is -2.45, which
suggests the variable is important but to a lesser degree than LBACH. However, the distribution
(Figure 13) for LDET shows a widely dispersed number of census tracts in the top quintile
throughout DC. Furthermore, at least six census block groups within the area of interest are in
the lowest quintile, weakening the strength of the variable.
According to Figure 14, the coefficients for LMAROWN and LV1M show no particular
relationship to the area of interest. For LMAROWN, many census block groups with the lowest
coefficients are located outside of the area of interest. According to the distribution (Figure 13)
of LV1M, many of the census block groups in the area of interest are in the lowest percentile,
bringing down the significance of the variable. Furthermore, there are many census block groups
with high percentages of homes over $1 million located outside the area of interest. Census block
groups where LMAROWN shows the strongest negative coefficients are located outside of the
area of interest (Figure 14), and the percentage of homes in this category varies throughout the
study area (Figure 13).

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Chapter 5: Conclusions and Discussion
In the routine activity theory there are three components that must come together in time and
space for a crime to exist: 1) a likely offender; 2) a suitable target; and 3) the absence of a
capable guardian (Cohen and Felson 1979). This thesis examines homeowner and housing
characteristics in relation to spatial cold spots of violent crimes. Variables with a negative
correlation with violent crimes are fit into an Ordinary Least Squares (OLS) and a
Geographically Weighted Regression (GWR) analyses. The final variables (LBACH, LV1M,
LDET, and LMAROWN) are chosen as the “guardian model.” The results in OLS suggests a
negative correlation exists between housing and homeowner characteristics and violent crime.
Thus, capable guardianship may be correlated with violent crime cold spots. However, when the
coefficients are mapped in GWR, only LBACH shows a strong influence within the area of
interest, west of Rock Creek Park near reference number four (Figure 14).
In the following three sections, a discussion and some conclusions are drawn concerning
the relationship between housing and homeowner characteristics to violent crimes. The first
section focus is on the relationships of the violent crimes using hot spot analysis and regression
analysis. The second section discusses the explanatory variables and the results of the model fit
into OLS and GWR. In the final section of this chapter, future work is discussed concerning the
application of quantitative spatial analysis in accord with violent crime.
5.1 Violent Crimes Using Hot Spot and Regression Analysis
A hot spot analysis of four violent crimes (homicide, assault with a dangerous weapon,
robbery, and sexual assault), from 2012 through 2015 for Washington, DC shows a divided city.
For the most part, the only cold spot by time and place throughout the study area is limited to the
north and west of Rock Creek Park. At the same time, three hot spots are identified throughout

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the time period in all four violent crimes. The cold and hot spots for all four violent crimes
remain clustered in many of the same areas throughout the whole study period. Therefore, all
four violent crimes are grouped into one dependent variable.
The four violent crimes, when being used as both dependent and explanatory variables,
measures at 100% as being positively related in an exploratory regression analysis. However,
further analysis shows homicide as a weak connection to robbery and sexual assault, but
homicide does show a significant relationship to assault with a deadly weapon. Robbery may end
up as a homicide, but generally speaking, the motivation for robbery is to gain material
possessions. Whereas, assault with a deadly weapon seems be more connected to murder, with
respect to motivation. However, the low number of homicides (n = 450) in comparison to the
other violent crimes, assault with a dangerous weapon (n = 9,603), robbery (n = 14,824), and
sexual assault (n = 1,136), may skew the results.
When using exploratory regression, the strongest relationship exists between robbery and
assault with a dangerous weapon (adjusted r-square = 0.69). Furthermore, the strongest model in
OLS is measured when assault with a dangerous weapon stands as the dependent variable and
the other three violent crimes are plugged in as explanatory variables. The adjusted R-squared
score is 0.76, suggesting strong correlations exist between assault with a dangerous weapon and
the other three violent crimes.
5.2 The Model Developed to Measure Capable Guardianship
A successful model uses the sum of all of the violent crimes from 2012 – 2015 as the
dependent variable and four housing and homeowner characteristics as the explanatory variables
to suggest capable guardianship deters violent crime. Six data sets consisting of housing and
homeowner characteristics are used to identify variables negatively correlated with violent crime.

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A model made up of four variables (LBACH, LDET, LV1M, and LMAROWN) suggests capable
guardianship is correlated to violent crime.
LBACH is the strongest explanatory variable in the model, as the coefficients ranged as
low as -5.02 in the census block groups within the area of interest. Furthermore, the distribution
map (Figure 13) shows the area of interest had a high percentage of people who are at least
twenty-four years old and who earned a bachelor’s degree or above. For the most part, the areas
with higher crime rates do not have a high percentage of people with a bachelor’s degree or
higher. There could be many reasons why a relationship between attainment of a bachelor’s
degree or higher and low crime exists. For example, a person with a bachelor’s degree or higher
may be more inclined to report crime, may be more resourceful in regards to using security
systems along with other preventative measures, and may have stronger ties to influential people
in the community. All of these reasons may lead to the deterrence of violent crime. However,
another possible reason for areas with low crime rates and high percentages of people with a
bachelor’s degree or higher may be that people who gain higher education choose not to live in
high crime areas.
Regardless of the reason, occupancy alone cannot explain areas with low crime rates.
Occupancy was discarded after the first phase of exploratory regression. If occupancy alone
made it into the final model, then capability would not be important. Occupancy ranked 22
nd
out
of the 25 variables tested with a measured significance at fourteen percent and with a fifty-seven
percent negative linear relationship in models tested during exploratory regression analysis. This
shows guardians need to be both present and capable. If occupancy alone determined deterrence,
then this model is not valuable, in regards to the capable guardian theory. However, given this

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variable measures exceedingly low, highlights capability as a possible factor to deter violent
crime.
Although the results and analysis of LBACH and LDET in OLS and GWR show strong
and moderate relationships exist between education level and detached homes, in regards to low
crime rates in northwestern DC, the other two variables are not as useful when concentrating on
northwestern DC. In OLS, the adjusted R-squared score reaches only 0.46, the Jarque-Bera test is
significant, and the residuals are clustered at the 99% level. In short, the model is missing at least
one key variable. To resolve these problems, a finer aggregation or an aggregation based on
housing type may greatly improve the results. For example, the boundaries for census block
groups did not necessarily consider housing characteristics such as detached homes or rented
versus owned.
GWR works well when data is nonstationary because it fits a model for every area and
estimates coefficient values for each chosen point within each area. GWR gives weights to the
points according to proximity, and the results show information concerning the relationships
between the independent and dependent variables (Fotheringham, Brunsdon and Charlton 2002).
GWR’s adjusted R-squared score shows an increase from 0.46 in OLS to 0.57, which suggests
the variables are nonstationary.
The purpose and intention of this study is not to show a direct cause/effect relationship
exists between these selected variables and violent crime. In fact, the routine activity theory uses
three components that must come together in time and space. In the original theory, Felson et al
use the absence of a capable guardian. The active parts of the theory consist of a likely offender
and a suitable victim coming together in time and space. A capable guardian may act as a
deterrent to keep likely offenders from entering certain areas, and therefore, would be a difficult

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model to increase to a significant adjusted R-squared value. Yet, a hot spot analysis shows a
divided DC (Figure 9), whereby a large cold spot is identified north and west of Rock Creek
Park. In addition, when the coefficients are mapped (Figure 14), LBACH is the only variable
where census block groups with the lowest coefficients match up with the area of interest. Does
education level obtained (in this case bachelor’s degree or higher) provide the best explanation
for where the most capable guardians reside? More research in other cities could be conducted to
find out if this is a universal trait: do communities with high percentages of people who have
obtained a bachelor’s degree or higher have lower violent crime rates?
5.3 Future Work in the Application of Spatial Analysis of Violent Crime
Quantitative spatial analysis may enable the researcher to better understand violent crime
cold spots, the presence or perceived presence of a capable guardian (the third component of the
routine activity theory), and housing characteristics. In an analysis of the four violent crimes
(homicide, robbery, assault with a dangerous weapon, and sexual assault), a regression model
with an adjusted R-squared value of 0.76 shows strong correlations exist when assault with a
dangerous weapon is the dependent variable and homicide, robbery and sexual assault are
entered as the independent variables. When all four violent crimes are combined and entered as
the dependent variable, and four housing characteristics are entered as the independent variables
(LV1M, LBACH, LDET, and LMAROWN) the adjusted R-squared value is 0.57 in a
Geographically Weighted Regression (GWR) analysis. Both of these models suggest quantitative
spatial analysis may be a tool for researchers to use when studying violent crimes. A future study
to expand upon this analysis could be to take a closer look at housing and homeowner
characteristics and violent crime cold or hot spots to search for other variables (the capable
guardian model is missing at least one key variable).

67

Perhaps the housing and homeowner characteristics explored in this study may be a link
for understanding how criminals decide to take on new areas to commit crimes. Do they decide
to explore areas synonymous with less capable guardians present? Likewise, do they tend to
avoid areas where capable guardians seem to live? If so, then it may be possible to predict where
existing hot spots of crime will expand or not expand. Do criminals move into the areas with the
least resistance, potentially measured by housing and homeowner characteristics? This study
produced housing and homeowner variables that may provide insight into violent crime for
researchers.
The study of physical housing characteristics may lead to a better understanding of
criminal’s decisions to expand into new areas. Although this study concentrates on violent crime
cold spots, a researcher may want to reverse the analysis and study the hot spots. Do housing
characteristics enable and deter where the criminals expand their area of operations? Studying
the hot spots may better explain the explanatory variables when mapped in GWR. If so, then a
larger-scale and more focused study concerning hot spots may show new areas where criminals
are more likely to move into before committing violent crimes. These decisions may be based on
the criminal’s judgment whether capable guardianship exists or does not exist, and physical
housing characteristics may factor into this judgment.
However, the variable with the strongest spatial relationship to areas with low levels of
violent crime are not physical housing characteristics. In the guardianship model, LBACH
measures as the strongest negative coefficient to violent crime in OLS and GWR within the area
of interest. This study highlights education as an area for more quantitative spatial research to
better understand violent crime and capable guardianship. Conducting this same analysis in other
cities in the United States may be useful to understand if these results are part of the culture

68

inherent to DC or universal to all major cities in the United States. If higher education is
negatively correlated to violent crime on a universal level, then this adds yet another reason for
society and decision-makers to invest into enabling individuals to earn a higher education.

69

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Abstract (if available)

Abstract According to the routine activity theory, violent crime may be deterred by a capable guardian. Cohen and Felson’s routine activity theory asserts three conditions need to be met for a crime to take place: a likely offender

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Asset Metadata

Creator Jopp, Brian David (author)

Core Title A spatial analysis of violent crime cold spots: testing the capable guardian component of the routine activity theory

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 10/24/2016

Defense Date 08/10/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag assault with a dangerous weapon,capable guardian,Geographically Weighted Regression (GWR),homeowner characteristics,Homicide,hot spot analysis,housing characteristics,OAI-PMH Harvest,Ordinary Least Squares (OLS),Robbery,routine activity theory,Sexual assault,spatial analysis,violent crime

Format application/pdf (imt)

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Advisor Loyola, Laura (committee chair), Kemp, Karen (committee member), Lee, Su Jin (committee member)

Creator Email bdjopp@gmail.com,jopp@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-316471

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