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STUDYING EFFECT OF THE SPATIAL AUTOCORRELATION ON THE SOCIAL
DISORGANIZATION THEORY: REPLICATING THE STUDY OF BALLER AND HIS
COLLEAGUES

By

IN GUL KIM

A THESIS

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

MASTER OF SCIENCE
School of Criminal Justice

2005

ABSTRACT

STUDYING EFFECT OF THE SPATIAL AUTOCORRELATION ON THE SOCIAL
DISORGANIZATION THEORY: REPLICATING THE STUDY OF BALLER AND HIS
COLLEAGUES

By

IN GUL KIM

Guided by social disorganization theory and the concept of spatial
autocorrelation, this thesis examined if there is the presence of spatial autocorrelation in
crimes, such as robbery, auto theft, and drug crime. Much of this thesis builds on Baller et
al.’s study, but the addition of two independent variables, immigrant concentration and
residential stability, was tried to apply social disorganization theory effectively. Census
data from ICPSR and three kinds of crimes from the Uniform Crime Report (UCR) was
used from the 19803 to 1990s. This thesis did not ﬁnd diffusion procedure of three crimes
at the US. level but found the clustering of crimes. To improve separated OLS models,
two models of spatial autocorrelation were used (e. g., spatial lag model and spatial error
model). This study suggests that the relationship between ecological characteristics and

crime are more effectively explained, when controlling for spatial autocorrelation.

TABLE OF CONTENTS

LIST OF TABLES ................................................
LIST OF FIGURES -------------------------------- , ...............
CHAPTER 1
INTRODUCTION ------------------------------------------------
CHAPTER 2
REIVIEW OF LITERATURE ---------------------------------------
Spatial Autocorrelation ------------------------------------------
Diffusion Of Crime ---------------------------------------------
Application of Spatial Autocorrelation and Diffusion in Former Studies. - ° -
Exploratory Spatial Data Analysis (ESDA) -------------------------
Study Of Baller Ct a1. (2001) on Spatial Autocorrelation -----------------
Social Disorganization Theory ------------------------------------
Theoretical Development of Social Disorganization Theory -------------
Measure of Independent Variables -------------------------------
Residential Stability ---------------------------------------
Ethnic Hoterogeneity/Immigration ---------------------------
CHAPTER 3
METHODOLOGY ........................................ ' ........
Hypotheses ----------------------------------------------------
Data °°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
Variables ------------------------------------------------------
Analytic Strategy -----------------------------------------------
Limitation of This Study -----------------------------------------
CHAPTER 4
RESULTS -------------------------------------------------------
Section I ------------------------------------------------------
SectionII --..--................-......'. .......................
Structural Stability and Heteroscedasticity --------------------------
Section III ---------------------------------------------------
Robbery ----------------------------------------------------
Auto theft ---------------------------------------------------
Drug crime --------------------------------------------------

iii

vi

13
15
20
20
28
31
33

36
36
36
38
39
40

44
44
55
62
67
67
69
72

CHAPTER 5

SUMMARY AND DISCUSSIONS ----------------------------------- -- 75

Consideration for Future Study ------------------------------------ 77
ENDNOTES ------------------------------------- ~ ................ 79
BIBLIOGRAPHY ------------------------------------------------ 8 1

iv

Table 1:

Table 2:

Table 3:

Table 4:

Table 5:

Table 6:

Table 7:

Table 8:

Table 9:

LIST OF TABLES

Ordinary Least-Square Regression of County Homicide Rates
1980-1990a ------------------------------------------------
Comparison of Spatial Regression Models of South Homicide rates,
19230-19903 -------------------------------------------------
Comparison of Spatial error Models of Non-South Homicide rates, 1980-

1990a ......................................................
Collinearity Statistics (Tolerance) among independent variables -------

Comparison of Ordinary Least-Square of County Robbery Rates
19230-1990a -------------------------------------------------
Comparison of Ordinary Least-Square of County Auto theft Rates
1980.1990a -------------------------------------------------
Comparison of Ordinary Least-Square of County Drug Crime Rates
19908 ------------------------------------------------------
Stability of Regression Coefﬁcients by Spatial Regime- County Other
Crimes 1980-1990 -------------------------------------------
Robust Lagrange Multiplier Lag and Lagrange Multiplier Error of
County Other Crimes 1980-1990 -------------------------------

Table 10: Comparison Between OLS and Spatial model of County Robbery Rates

19230-1990a ................................................

Table 11: Comparison Between OLS and Spatial model of County Auto theft

Rates 1980-1990‘5l -------------------------------------------

Table 12: Comparison Between OLS and Spatial model of County Drug Crime

Rates 1990a ................................................

45

46

47

56

57

59

61

63

65

68

70

73

Figure 1:

Figure 2:

Figure 3:

Figure 4:

Figure 5:

Figure 6:

Figure 7:

LIST OF FIGURES

Spatial Process --------------------------------------------- 20
Bursik and Gramick’s Basic System Model of Crime -------------- 25
Moran Scatterplot Map Auto Theft 1980 Rate (W=10 nearest

Neighbors) ----------------------------------------------- 50

Moran Scatterplot Map Auto Theft 1990 Rate (W=10 nearest
Neighbors) ----------------------------------------------- 51

Moran Scatterplot Map Robbery 1980 Rate (W=10 nearest Neighbors) - 52

Moran Scatterplot Map Robbery 1990 Rate (W=10 nearest Neighbors) - 53

Moran Scatterplot Map Drug 1990 Rate (W=10 nearest Neighbors) ' - 54

vi

Chapter I: Introduction

This thesis examined whether spatial autocorrelation exists in three kinds of
crimes (e.g., robbery, auto theft, and drug crime) and how it is applied to social
disorganization theory. According to Baller et al. (2001), a spatial autocorrelation is
deﬁned as “a situation in which values on a variable of interest are systematically
related to geographic location.” First, in order to understand the relationship between
spatial autocorrelation and social disorganization theory, readers need to know the
theoretical development of social disorganization theory. Social disorganization
theory has varied and especially has been changed since Shaw and McKay (1969).
They argued that destroyed zones near the Chicago’s central business district and
industrial areas, showing low socioeconomic status, had the highest delinquency rates
and nearby zones in commercial and industrial areas experienced the most population
loss. In addition, the efforts of Sampson and Groves (1989) to explain informal
control, such as local friendship networks, unsupervised peer groups, and
organizational participation, affected the social disorganization theory further, and
since then social disorganization theory has been studied increasingly by many
scholars. But it seems that various problems lie in the future of social disorganization
theory (Kubrin and Weitzer, 2003). In fact, the causality of crime has been debated by

sociologists and criminologists over ﬁve decades. As a result, there are a lot of

l

theories in relation to the various kinds of crimes. There have been many valuable
ﬁndings, but' some authors noticed the inconsistency of results even though
researchers examined the same theories with similar variables.

One of the problems presented by many authors (e.g., Messner et al., 1999;
Rice and Smith, 2002; Kubrin and Weitzer, 2003) is spatial autocorrelation. However,
issues of spatial autocorrelation have recently been debated by several authors.
Moreover, some authors deﬁned various variables as spatial autocorrelation (e.g.,
Loftin, 1986; Rice and Smith, 2002), whereas others used statistical methods (e.g.,
Cohen and Tina, 1999; Baller, et al., 2001). No matter what they used, study on spatial
autocorrelation remains incomplete.

In addition, it is useful to understand how, why, and when geographical
aspects, from variables of the social disorganization theory, appeared. In combining
social disorganization and routine activity theories, Smith et al. (2000) and Rice and
Smith (2002) argued that spatial aspects of variables should be considered. Actually, it
makes sense that regimes, such as the criminal justice system as well as the economic
system, affected homicide rates as time passed, and consequently homicide was not
distributed randomly in space. For example, some counties have an aggressive policy
on policing, but others have concentrated on community policing. The evidence

showed these differences affected crime rates. However, many researchers have tried

2

to explain just the causality between independent variables, affecting crime, and crime
as a dependent variable without considering spatial autocorrelation. For example, it
was hard for readers to ﬁnd articles in relation to spatial autocorrelation and crime
until 1997. Since Morenoff and Sampson (1997) used spatial autocorrelation, studying
violent transition in Chicago, the research of automobile theft by Rice and Smith
(2000), the study of street robbery by Smith et al. (2000), the study of homicide by
Messenr et al. (1999), and the study of drug misuse by Frischer et al. (2000) used the
spatial autocorrelation. In addition, in “New Direction in Social Disorganization
Theory,” Kubrin and Weitzer (2003) said that spatial autocorrelation should be
considered together with the explanation of how variables connect to each other in
social disorganization theory. Probably, the failure of the application of spatial
autocorrelation is because it seems that it was not easy to ﬁnd how to adapt spatial
autocorrelation in former statistical techniques.

Recently, responding to this difﬁculty, some scholars, such as Anselin (1995),
have introduced a new analysis technique, called “Exploratory Spatial Data Analysis
(ESDA),” which may be an effective answer to solve the problems of spatial
autocorrelation. With this technique, showing that homicide rates were not distributed
at random, Baller et al. (2001) argued that there is a spatial autocorrelation not

explained by measured and unmeasured variables. They asserted that if researchers do

3

not solve this problem, they will not have consistent results. Several researchers have
already stressed the importance of autocorrelation on violent crime. For example,
Smith and Davison (2000) said that street robbery has the feature of diffusion, which
“can be understood as having been poured out and permitted or caused to spread out
freely” (Paulsen & Robinson, 2004), and Rice and Smith (2002) concluded that
researchers should consider spatial autocorrelation when studying automotive theft.
F rischer et al. (2000), in their study of diffusion of drug misuse in Scotland, said that
spatial autocorrelation should be considered in the study of drug use because drug
crime could not be explained by demographic factors and housing environments. Hunt
and Chambers (1976) also found that diffusion of drugs occurred from Boston to
Washington along the coast and in Southern California, and heroin use appeared to
diffuse to the interior from areas of large population to those with a small population.

This thesis follows the study of Baller et al. (2001), in which they argued that
there was a spatial autocorrelation in homicide. One of the new ideas presented by
Baller et a1. (2001) is the spatial lag model and the spatial error model to estimate
spatial autocorrelation more accurately, concluding that statistically signiﬁcant
diffusion of homicide existed in the South from 19603 to 19905 and the combination
of structural components could not perfectly explain the spatial autocorrelation.

However, some questions remain unsolved.

4

First, Baller et al. (2001) only investigated spatial autocorrelation of homicide,
but it is possible that spatial autocorrelation exists in other crimes. As seen above,
some authors argued that auto theft, robbery, and drug crimes had aspects of spatial
autocorrelation, although there were not many studies in relation to these crimes.
Second, as stated by Baller et al. (2001), the Baseline Model of Land et al. for
independent variables suffered inconsistent results. Land et al. aggregated the
correlated independent variables into one variable to avoid multicollinearity, by using
Principle Components Analysis (PCA) based on literature reviews. However, two
important variables were not used by Baller et al. (2001), i.e. the residential stability
and the immigrant concentration used by Sampson et al. (1997). As will be seen in
Chapter II, residential stability and immigrant concentration have been used and have
been proved important by most authors. This thesis expects that better speciﬁcation of
variables will present more consistent and correct results.

Much of this thesis builds on the Baller et al.’s study, but a few
developmental components were added, and the several arguments differ from Baller
et a1. (2001). First, Ballet et al. (2001) only concentrated on spatial autocorrelation.
They tried to ﬁnd the existence and division of spatial autocorrelation, but were not
interested in issues of social disorganization theory, such as the relationship between

independent and dependent variables. In contrast, the objective of this thesis is to ﬁnd

5

a better model to explain the relation between ecological characteristics and crime,
controlling a spatial autocorrelation. Therefore, this thesis includes new independent
variables, such as residential stability and immigrant concentration. Second, this
thesis also examines whether or not there are spatial autocorrelations between robbery,
drug crime, and auto theft. The reason that this thesis focuses on the three kinds of
crimes is based on the argument, in which these crimes already had the peculiarity of
spatial autocorrelation.

This thesis divides all counties into two distinct regions: the Clustered regions
and Non-clustered regions of crime through Exploratory Spatial Data Analysis
(ESDA). After that, the stability of coefficients across regimes is examined by a
spatial regime regression (Ballet et al., 2001). This method allows the research to
choose which model, between the spatial lag and the spatial error models, ﬁts each
area. Finally, the reliability and validity of new models will be tested through
comparison between OLS models and the spatial models, such as a spatial lag model
or a spatial error model. This study expects that the relationship between ecological
characteristics and crime will be more signiﬁcant and consistent when controlling

spatial autocorrelation.

Chapter II: Review of Literature
Spatial Autocorrelation

In his report, Doreian (1981) said that if researchers use spatial units as units
of analysis, such as census tracts or counties, the interactions between an origin area
and adjacent areas will make ﬁndings inconsistent, because of spatial autocorrelation.
Among a few of the deﬁnitions of spatial autocorrelation, Baller et al. (2001) claimed
“a situation in which values on a variable of interest are systematically related to
geographic location (p. 563).” In terms of the cause of spatial autocorrelation, Doreian
(1981) said that “regression analysis of social data across geographical space often
violates regression’s assumption of independent errors.” In addition to this, Rice and
smith (2000) argued that researchers could not all ﬁnd indispensable variables in
studies using spatial units as units of analysis, and accordingly, examiners did not
know how many unmeasured variables affected others, especially adjacent spatial
units.

Speaking of the importance of spatial autocorrelation, Baller et al. (2001)
argued as follows:

Statistically, if spatial processes operate and are not accounted for, inference

will be inaccurate and estimates Of the effects of independent variables may

be biased. Explicit modeling of spatial effects is thus important in any effort

7

to assess ‘invariance’ in the structural covariates of homicides. In addition,
causal processes do not necessarily operate identically in all places, and
spatial analysis can reveal sub-areas of geography in which the effects of
predictor variables differ. Spatial effects can be suggestive of diffusion
associated with the phenomenon under investigation (p. 562).

In Baller et a1. (2001), diﬁusion of crime is described as an element of spatial

autocorrelation.

Diffusion of Crime

Generally, diffusion is synonymous with scattering or becoming transmitted,
especially by contact (Merriam-Webster’s Collegiate Dictionary, 2002). But, viewed
from a criminological standpoint, diffusion “can be understood as having been poured
out and permitted or caused to spread out freely” (Paulsen & Robinson, 2004). More
importantly, Baller et al. (2001) referred to similarity between diffusion and the
spatial lag model of spatial autocorrelation in their study. Therefore, reviews of the
diffusion of crime will help give an understanding of deeper spatial autocorrelation.

According to Cohen et a1. (1999), there are various kinds of diffusion. They
started by dividing diffusion into two types. First is contagious diffusion, which

means it is spread by direct contact like a disease. In other words, the homicide rate of

8

an origin place affects other homicide rates. Contagious diffusion is divided into two
kinds of diffusions: relocation diffusion and expansion diffusion. Relocation diffusion
spreads outward from an origin place but the homicide rate of the origin goes close to
zero automatically, whereas in expansion diffusion, the origin place maintains
homicides continuously.

The second is hierarchical diffusion, which means that it is not necessary to
have direct contact, but it needs a medium for diffusion. For example, when Chinese
see Hollywood movies, they imitate the lifestyle of Hollywood, even though they do
not live in US. and cannot speak English. They just learn what they like and did not
know before and follow the actor’s style voluntarily via the medium called “movie.”

In terms of the cause of diffusion, Cohen et al. (1999) said that the cause of
homicide diffusion is ascribed to crack markets and violent youth gang organizations.
In detail, many youth gangs involve themselves in the crack business because high-
level skill is not necessary for selling crack, and they can easily make a great deal of
money compared to other jobs. So, youth gangs ﬁght with one another to protect their
beneﬁts, and many homicides occur because youth gangs rely on violent and lethal
tools like guns. That is why Cohen et al. saw the area of gang activity and the racial
residential pattern, mainly Black youth, as factors affecting homicide rates.

Frischer et al. (2000), in their study of diffusion of drug misuse in Scotland,

9

said that drug use could not be explained only by demographic factors and the
environment of housing, and argued that there clearly remains diffusion of drug
misuse in Scotland. Hunt and Chambers (1976) also stressed that there is drug
diffusion in the study of US. heroin use. In addition to drug misuse, Messner et al.
(1999) said that aggressive violence was very similar to an infectious disease, and
violent behavior could be conveyed from origin place to another place via social
communication systems like mass media. Moreover, the distribution pattern was not
random because mass media could not be transported from the origin place to another
randomly.

Interestingly, from time to time, physical and socioeconomic features of a
region play a role as a barrier preventing violent behavior from being transmitted. For
example, Messner et al. (1999) found that there were obstacles that prevented
diffusion of crime from spreading. In their study of the diffusion of homicides in St.
Louis, Missouri, they argued that agricultural activity affected the homicide rates of
rural areas, and aspects of agriculture and rural-ness would be barriers blocking the
diffusion of violence. The barrier against diffusion would be a typical example to
explain why the distribution of homicides was not random.

In conclusion, spatial clustering is statistically signiﬁcant, and the diffusion

phenomenon was attributed to spatial autocorrelation (Messner et al., 1999). As seen

10

above, there are various kinds of diffusion, and therefore, it is possible that types of
spatial processes are diverse like spatial lag effect and spatial error effect. However,
according to Ballet et al., diffusion of crime clearly differs from clustering of crime. A
Cluster is a place with high crime rate that also has adjacent neighborhoods with high
crime rate, while diffusion is related to a complicated mechanism, called spatial lag

model.

Application of Spatial Autocorrelation and Diffusion in Former Studies

There are not many studies of spatial autocorrelation and diffusion of crime
because they recently appeared. But it is said that studying social disorganization
theOry without considering spatial autocorrelation led to a contradictory consequence.
(Ballet et al., 2001) Roncek and Montgomery (1993) suggested a new variable, the
so-called “population potential,” ' to control spatial autocorrelation in examining
relationships between migration and other spatial processes. Morenoff and Sampson
also created “population change potential” 2 to eliminate spatial dependence of the
dependent variables, in investigating the relationship between violent crime and
neighborhood transition. To avoid the shortcoming of Roncek and Montgomery’s
approach, in which the error term was correlated, Morenoff and Sampson (1997)

followed Land and Deane’s (1992) “two-stage least squares” (ZSLS) technique “to

11

derive consistent estimators in spatial- effects models with potential variables.”
Morenoff and Sampson (1997) assumed that the homicide rate of a census tract affects
residents of adjacent tracts because a census tract is an arbitrary boundary, and ﬁnally,
adjacent areas experience depopulation. Also, they hypothesized that although two
cities have the same violent crime rates, a city surrounded by an area having high
crime rates will lose more population than another city because fear of crime affects
residents’ motivation to move. Morenoff and Sampson (1997) concluded that
homicide diffusion, as well as homicide itself, affected population loss.

In recent attempts to integrate social disorganization and routine activity
theories, some authors have argued that spatial characteristics must be considered
carefully (e.g., Smith et al., 2000; Rice & Smith, 2000). Rice and. Smith (2000)
created a new variable, a so-called “automobile theft potential variable,” 3 to handle
the spatial autocorrelation. Rice and Smith concluded that auto theft was affected by
variables Of adjacent face blocks, as well as independent variables of face blocks,
after comparing models, including automobile theft potential variables, with others
not including potential variables. In their report of street robbery, Smith et al. (2000)
found street robbery in a place was affected by street robbery of adjacent places.
Accordingly, to control the diffusion process, Smith et al. created a new independent

variable, which is called “street robbery potential.” 4 After comparing models,

12

including the street robbery potential, with the others not included, they found more
improved results, which showed R squared of results increased from 0.149 to 0.165,
and a unit increment in street robbery potential led to 32 percent growth of the
number of street robberies. In summary, even though primary concern of the authors
varied, the consistent argument was that the value in adjacent places could have an
inﬂuence on the value of dependent variables in a place (Smith et al., 2000).
Accordingly, if authors do not consider spatial autocorrelation when they use spatial

units as the unit of analysis, they will ﬁnd inconsistent and unfruitful results.

Exploratory Spatial Data Analysis (ESDA)
Recent authors used a statistical means to ﬁnd spatial autocorrelation, stressing the
importance of the location where the crime occurred, because the distribution of crime
is not random. For example, Dennis Roncek said that just knowing to whom and by
whom a crime are committed, does not explain the crime perfectly without the
knowing place where it occurs (Messner et al., 1999). Also, Loftin (1986) said that
violent behavior is almost the same as epidemic disease spread by contagion.
However, as seen above, most scholars have tried to solve the problems by adding
new variables as a regressor in a conventional linear model. In contrast to previous

researchers, in their examination of spatial clustering of homicide in St. Louis,

13

Missouri, Messner et al. used the newly advanced ESDA method. Messner et al.
(1999) deﬁned ESDA as follows:
ESDA is a collection of techniques for the statistical analysis of geographic
information to describe and visualize spatial distribution, identify atypical
locations or spatial outliers, and discover patterns of spatial association,
clusters or hot spots. By combing descriptive and traditional graphs in an
interactive computing environment, it augments visualization through maps
with hypothesis tests for spatial patterns and ﬁnally suggests spatial regimes

or other forms of spatial heterogeneity (p. 424).

In addition, Messner et al. (1999) argued that because conventional ways,
such as visual maps and multivariate regression analysis, are not sufficient enough to
detect spatial covariates, researchers often found doubtful results and that is why they
need to consider spatial autocorrelation. Besides, Ballet et al. (2001) argued that
conducting an Exploratory Spatial Data Analysis (ESDA) is very important, because it
identiﬁes “spatial clusters and spatial outliers and diagnos[es] possible
misspeciﬁcation in analyses, wherein we assess the effects of structural variables and

formally model spatial processes.” ESDA will be explained in detail later.

14

The Study of Ballet et al. (2001) on Spatial Autocorrelation

Although multivariate statistical techniques enable researches to analyze
more variables in detail, sometimes readers are confused. This is because many
studies showed inconsistent results with one another when using similar
measurements and data (Land et al, 1990). There are several explanations of the
inconsistent results. Land et al. said multicollinearity was a key element, which
hinders researchers from having reliable results. In other words, investigators did not
consider a correlation even though the independent variables used were very
interrelated to each other. Note that an examination of the study by Land et al. (1990)
is important because independent variables of Ballet et a1. (2001) used the Baseline
Model of Land et al. Based on multicollinearity, Land et al. said that mOst ﬁndings on
Southern subculture of violence with various kinds of covariates were disappointing.
In detail, it happened very often that one study having signiﬁcant results easily turned
into a non-signiﬁcant or negative effect at a different time or different unit of analysis.
Land et al. (1990) thought inconsistency of the ﬁndings resulted from difference,
which was generated when researchers used different units of analysis and statistical
inference. Accordingly, to ﬁnd a consistent outcome on homicide rates, Land et al.
extracted 11 independent variables, which had a signiﬁcant inﬂuence on homicide

rates from 21 former studies: population size, population density, percentage of the

15

population that is Black, percentage of the population age 15-29, percentage divorced,
percentage of children 18 years old or younger not living with both parents, median
family income, percentage of families living below the ofﬁcial poverty line, the Gini
index of family income inequality, and the unemployment rate.

After analyzing problems of former results, Land et al. concluded that
disparity between time periods, units of analysis, samples, model of speciﬁcation and
problems of statistical inference led to inconsistent ﬁndings, and those problems could
be controlled by adjusting the model (e.g., conformity of time periods, unit of analysis,
sample size, model speciﬁcation, data transformation, and so on). Using the Principle
Components Analysis (PCA), Land et al. combined 11 independent variables into ﬁve
categories in considering aspects of spatial clustering to overcome the problem on
structural covariate of space. For example, population size and population density
were compounded into a population structure component; and a resource-
deprivation/affluence component was made of three variables related to money, such
as median family income, the percentage of families living below the ofﬁcial poverty
line, and the Gini index of family income inequality as well as two social variables,
such as the percentage of the unit population that is Black and the percentage of
children age 18 or under not living with both parents.

Finally, Land et al. (1990) created six independent variables affecting

16

homicide rates, called the Baseline Model: population structure, resource
deprivation/affluence, percentage of the population age 15-29, unemployment rate,
percentage divorced, and South/non-South. In addition, Land et al. found that the
positive effect of homicide in the South was different from the size of unit of analysis,
such as city, metropolitan area, and states. However, Land et al. (1990) only
conjectured inconsistent results were ascribed to a southern subculture of violence.
Ballet et al. (2001) attributed inconsistent results of Land et al. to spatial
autocorrelation. Accordingly, Ballet et al. (2001) made the null hypothesis, in which
all variables are randomized in space, and an alternative hypothesis that has a spatial
autocorrelation in order to test spatial autocorrelation of variables.
According to Ballet et al. (2001), yi is deﬁned as homicide rate$ on structural
factors at location i and 8; is a stochastic error term.
y, = 2k in Bk + 5i, where each in is an element in a 1 x K matrix row vector
of covariates and Bk is the corresponding element in a K x 1 vector of
regression coefﬁcients. If homicide rates are determined solely by the
structural factors included in the model, there should be no spatial patterning
of homicide beyond that created by sociodemographic similarities of
geographically proximate counties. In other words, no remaining spatial

dependence should be found once the structural similarity of neighboring

17

counties has been explicitly controlled for, or, E[8,- 81-] = O for neighboring i, j.

(p. 565)

Ballet et al. (2001) assumed a spatial pattern could not be explained by only a
structural model and introduced two ways to specify new approaches. One is a
“spatial effect model, in which spatial dependence is illustrated as an additional
covariate in the model, as it were, spatial lag, or a weighted average of values for the
dependent variable in neighboring locations, and the other is a spatial disturbance
model, in which the spatial dependence is incorporated in the regression error term”
(Ballet et al., 2001). The former means that a spatial dependence shows a possibility
of diffusion process, but the latter spatial dependence implies the existence of omitted
covariates being spatially correlated somewhere in the model. In addition to spatial
autocorrelation, Ballet et al. (2001) stressed that researchers have to consider spatial
heterogeneity, in which “coefficients or error patterns vary systematically across
geographic areas.” Actually, because it is not easy to differentiate spatial dependence
from spatial heterogeneity based on regression residuals, Ballet et al. (2001) assumed
an evident coefficient for the South. That is because the South showed potential
structural difference in the regression relationship between geographic regions based
on Land et al.’s model. Therefore, if there is spatial dependence controlling for spatial

heterogeneity, researchers need to compare a spatial error model with a spatial lag

18

model.

follows:

Ballet et al. (2001) explain a spatial error model and a spatial lag model as

The spatial error model evaluates the extent to which the clustering of
homicide rates not explained by measured independent variables can [be]
accounted for with reference to the clustering of error terms. In this sense, it
captures the spatial inﬂuence of unmeasured independent variables. The
observed spatial clustering in homicide rates is accounted for simply by the
geographic patterning of measured and unmeasured independent variables.
The spatial lag model, in contrast, incorporates the spatial inﬂuence of
unmeasured independent variables but also stipulates an additional effect of
neighbors’ homicide rates, i.e., the lagged dependent variable. This is the
model most compatible with common notions of diffusion processes because
it implies an inﬂuence of neighbors’ homicide rates that is not simply an
artifact of measured or unmeasured independent variables. Figure 1 shows
[the] difference between spatial error effects and spatial lag effects
geometrically and a dashed arrow is indicative of the inﬂuence of homicide in

neighboring counties (p. 566-577).

19

Figure 1. Spatial Processes

Univariate Spatial
Autocorrelation

Structural
Similarity

Spatial Error
Effects

Spatial Lag
Effects

Source by Baller et al. (2001)

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Based on Messner et al.’s argument (1999), in which there is signiﬁcant
evidence that is indicative of spatial autocorrelation of homicide rates in counties,
Ballet et al. (2001) examined global autocorrelation and local spatial autocorrelation.
Ballet et al. (2001) used the SpaceStat software package to carry out all computations.
If the value of Moran’s I statistic of global autocorrelation is positive and signiﬁcant,
it means clustering in space (Ballet et al., 2001). Local spatial autocorrelation, which
is a relationship between the pattern of speciﬁc locations and the values at
neighboring locations in the homicide rates by Moran’s I statistic, shows whether or
not there is spatial randomness of a given place on crime. In other words, “rejection of
this null hypothesis indicates local clustering of high (high surrounded by high) or
low (low surrounded by low) values, or local spatial outliers in the form of high
values surrounded by low neighbors or low values surrounded by high neighbors”
(Ballet et al., 2001). Ballet et al. (2001) concluded there was an obvious spatial
pattern in homicide rates between southern and non-Southem regions and much of
homicide was clustered in the South.

Besides, stability of spatial heterogeneity was tested by “Spatial Chow tests”
which can estimate stability of coefficients across regimes. Based on ﬁnding
instability of regime, Ballet et al. (2001) conﬁrmed the existence of spatial

autocorrelation and at the same time, they divided the original model into the South

21

and non-South. From examining spatial dependence through investigation of the
residuals of OLS estimation, the authors ﬁnally decided that the spatial lag model is
ﬁt for the South and the spatial error model (except for the 19603) is ﬁt for the non-
South. Technically, use of the spatial lag model differs from the spatial error model. In
the spatial error model, stochastic errors had an inﬂuence on the value of dependent
variables whereas in the spatial lag model, dependent variables of adjacent counties as
well as stochastic errors affected origin dependent variable (Ballet et al., 2001).

After analyzing results, Ballet et al. (2001) argued that the distribution of
homicide is not random in space and spatial clustering remains even after controlling
for ecological characteristics of homicide. Also, the baseline regression model did not
explain homicide rates completely and regional differences were generated
signiﬁcantly by regimes. Finally, diffusion was not applied in non-South regions
because unmeasured variables fully explained residual autocorrelation in non-South
regions whereas a spatial lag model described homicide rates in southern regions as

well.

Social Disorganization Theory
Theoretical Development of Social Disorganization Theory

Generally speaking, it seems that social disorganization theory seeks a

22

relationship between structural characteristics, informal and formal controls derived
from community members and public agencies, and crime. The essence of this theory
is that if a community suffered from environmental and structural characteristics, such
as poverty, ethnic heterogeneity, and residential stability, this community would lack
informal and formal control, and ﬁnally, crime would increase (Rose & Clear, 1998).

In the beginning, however, social disorganization theorists tried to ﬁnd which
ecological characteristics of society affected crime. As most researchers state, Shaw
and McKay had a tremendous inﬂuence on sociologists and criminologists. In 1942,
Shaw and McKay found traditional components of the social disorganization theory,
and in their report, Juvenile Delinquency and Urban Areas (1969), Shaw and McKay
said that low economic status, ethnic heterogeneity, and residential mobility had an
inﬂuence on the stability of social structure, and then a collapse of social organization
increased crime and delinquency.

Based on Shaw and McKay’s study, in 1989, Sampson and Groves showed
the improved mechanism of how social disorganization theory works. Socioeconomic
status, ethnic heterogeneity, residential stability, family disruption, and urbanization,
as independent variables, were used in their report. In addition to these, they created
local friendship networks, unsupervised peer groups, and organizational participation,

as intervening variables, from national surveys of England and Wales. Sampson and

23

Groves (1989) argued that local ﬁiendship networks, unsupervised peer groups, and

organizational participation had an inﬂuence on crime by affecting traditional

components. Since Sampson and Groves’ (1989) argument, many authors have

examined the relationship of informal and formal control. In other words, the attention

of authors moved social characteristics, such as socioeconomic composition,

residential stability, and racial/ethnic heterogeneity, into relationships among

community members, local institutions, and governmental agencies. Likewise, Bellair

(1997) also said that the quantity and frequency of a neighborhood’s network affected

traditional characteristics. A shared common norm or value is another expression of

community network. For example, Komhauser (1978) said that in a community, in

which residents did not have common goals and norms on community, ordinary

crimes increased, and Bursik and Grasmick (1993) argued that one of the goals of

residents sharing common values is to hope they live safely in their residence.

Rose and Clear (1998) said that Bursik and Grasmick added public control to

the result of Sampson and Groves, in highlighting that service provided by outside

agencies varied, and quality and quantity of the service affected crime in the

community, whereas Sampson and Groves focused on just private and parochial

control.

24

Figure 2. Bursik and Grasmick’s Basic System Model of Crime

 

Solicitation of
External
Response

Residential Primary
/1 Stability 7” Relational ’

Networks
Socioeconomic
Composition
.
Racial/ Secondary
Ethnic Relational
Heterogeneit Networks

Exercise of
Public
Control

i

Exercise of Privat
Control

Effective
Socialization . Crime Rate

/'

Exercise of
Parochial
Control

 

Source by Rose and Clear (1998)

Figure 2 presented by Bursik and Grasmick (1993) shows their argument on

25

basic procedure clearly. According to Bursik and Grasmick (1993), private control is

deﬁned as close observation and opinion derived from the relationship between

family and close friends; parochial control is intervention and supervision within

community, including residents and local institution such as schools, churches, and

stores; public control is relationship between community and government agencies.

However, Ruse and Clear (1998) argued that the distinction of three kinds of control

by Bursik and Grasmick is not obvious, and they are correlated with one another. For

example, the greater the private control the greater the parochial control, and vice
versa. Besides, a relationship between public control and other controls could not be
explained explicitly. In other words, policing can be carried out regardless of private
and parochial control, but attenuated informal control could increase public control
(Rose and Clear, 1998). Moreover, Black (1976) said that formal control rose when
informal control became worse because informal control caused lots of crime, and
then the police tried to reduce crime rates.

In contrast to most studies that were carried out in urban areas, Osgood and
Chambers (2000) studied whether social disorganization theory would be generalized
in non-metropolitan counties or not, by using per capita rates of juvenile arrest for
violent Offenses as dependent variables. They found residential instability, family
disruption, and ethnic heterogeneity were strongly associated with violent crime
except unemployment. In addition, they hypothesized, that increased population size
would increase crime because the anonymity of juveniles increased, but results
showed crime rates varied regardless of population size. Recently, Markowitz et al.
(2001) examined the relationship between disorder, cohesion, fear of crime and
burglary in a non-recursive model. According to Markowitz et al (2001), the biggest
problem of social disorganization studies is investigators could not discover the role

of neighborhood’s cohesion in social disorganization theory although a

26

neighborhoods’ cohesion affected traditional characteristics of social disorganization.

However, the suggestion that close and friendly relationships between
residents reduced crime was not welcomed by all researchers. Warner and Rountree
(1997) said that assault rates, as well as ecological characteristics, were not affected
by neighboring activities. Also, Patillo (1998) argued that close social networks could
not reduce crime rates effectively. In his report, Patillo explained not all social
networks were good things because gang members and criminals also had their
relationships and values. Additionally, Markowitz (2001) concluded there was a
signiﬁcant relationship between ecological characteristics, disorder, cohesion, and
burglary as noted by former researchers. But, Markowitz argued that there is another
element, such as the cultural inﬂuence of the region, which could nOt be explained
before. Another concern of Markowitz et a1. (2001) was the feedback effect of crime.
Markowitz argued that unless effects of feedback are considered, results would be
biased. In other words, because disorder, fear, and cohesion were correlated in the
non-recursive model, feedback processes should be considered.

Veysey and Messner (1999) admitted accomplishment of Sampson and
Groves (1989) on social disorganization, but argued that Sampson and Groves did not
more exactly explain the relationship between independent, intervening variables and

crime. Veysey and Messner (1999) concluded that the mediating effect of variables by

27

Sampson and Groves is somewhat right, but there are several mechanisms in social

disorganization theory not explained by the argument of Sampson and Groves.

In summary, in the beginning, authors tried to ﬁnd a relationship between

social and economic characteristics and crime, but since the ﬁndings of Sampson and

Groves, informal and formal control were the matter of common interest. However,

these days many researchers have tried to ﬁgure out how the mechanism of social

disorganization works. As such, many authors argued various mechanisms, but it is

too early to tell which one is right. Accordingly, because spatial autocorrelation will

be another answer, it is worth a try.

Measure of Independent Variables

As the social disorganization theory has developed, new independent variables

have been added continuously. In studying the relationship between social and

organizational characteristics of neighborhood and crime rates, Sampson et al. (1997)

argued that a collection of informal controls not enforced by police or courts, what is

called Collective efﬁcacy or neighborhood efﬁcacy, had an inﬂuence on interpersonal

violence behaviors in urban areas, regardless of demographic components. In other

words, Collective efficacy is neighborhood ability to prevent crime in their

community. Collective efﬁcacy is comprised of ten variables, derived from census

28

data. After conducting factor analysis to get a smaller number of variables and avoid
multicollinearity, Sampson et al. (1997) aggregated ten variables into three:
Concentrated Disadvantage (below poverty line, on public assistance, female-headed
families, unemployed, less than age 18, and Black), Immigrant Concentration (Latino
and foreign-bom), and Residential Stability (same house as in 1985 and owner-
occupied house). .

Similarly, Fagan and Schwartz (1986) said that delinquency and criminality of
individuals could not be explained completely by only individual-level effects without
community contextual effects created by six independent variables of census data. In
their report, Fagan and Schwartz created six area dimensions with census data and
information reported in the survey: Social Rank, Family DisorganizatiOn, Family Life
Cycle-Child Density, Urban Center versus Ring, Population Mobility, and
Unemployed-Unemolled Youth. Of six dimensions, Family Disorganization and
Social Rank were based on census data through factor analysis. Family
Disorganization is comprised of: the percentage of married, male separation rate,
divorce rate, percent bad units, and percent children in two-parent families. Social
Rank is comprised of: family income less than $ 3,000 per year, median income,
families income more than $ 15,000, percent over-crowded units, percent vacant units,

females in labor force, males in labor force, professional and managerial, percent

29

service workers and laborers, percent with some college, percent high school
graduates, and median education.

In addition, Ross and Mirowsky (1999) used age, African American population,
education, house income, and place where respondents lived, as main independent
variables to explain the relationship between disorder and decay in arguing disorder
and order are two ends of a single line.

Skogan (1990) also used similar variables in his famous book, Disorder and
Decline. He argued that neighborhood conditions, such as poverty, instability, and
racial composition, together with random shock, affected incivilities, and then
incivilities affected more victimization and increased the number of people moving to
other places.

In a study about population change in a tract’s population over prior census data
and homicide in each census tract, Morenoff and Sampson (1997) carried out
Principal Components Analysis (PCA) like Land et al. (1990) to reduce
multicollinearity between variables. Then, Morenoff and Sampson (1997) divided
ecological characteristics into four categories: socioeconomic disadvantage,
ethnicity/immigration, age composition, and residential stability.

In summary, the concept of variables in most studies is very similar to each other,

even though measurement was somewhat different. More importantly, when

30

compared former studies, the study of Land et al. did not use two independent
variables, such as immigrant concentration and residential stability. This thesis
expects that the addition of immigrant concentration and residential stability will
improve the quuared value of Ballet et al.’s study. Accordingly, this thesis uses the

Baseline Model and the two additional variables mentioned above.

Residential Stability

Residential stability differs from economic features, but is a very important
element affecting urban social community (Kasarda and Janowitz, 1974). Sampson
and Raudenbush (1999) said that the higher the home ownership and length of
residence, the stronger the community attachment, which had an inﬂuence on social
ties and cohesion. Also, frequent turnover of residents led to disorganization of the
local community and weakened residents’ willingness to curb disorder behaviors
(Bursik, 1988).

Taylor (1996) said in his study, Neighborhood Response to Disorder and
Local Attachment, stability, as well as education, was the best predictor to know local
attachment. Taylor’s neighborhood stability was combined with percentage of owner-
occupied housing units (from census), percentage of respondents who are

homeowners (from survey), average length of residence in the neighborhood (from

31

survey), and percentage of married couple households (from survey). Markowitz et a1
(2001) also found that residential stability was related to disorder. Markowitz et al.’s
residential stability is deﬁned as the percentage of the population raised within a 15-
minute walk of their current residence.

In 1997, the residential stability of the collective efﬁcacy by Sampson et al.
was measured as the percentage of the population that has lived in the same house for
more than ﬁve years and the percentage of owner-occupied homes. The study by
Morenoff and Sampson (1997) also found that residential stability is associated with
population 1033 following the collective efﬁcacy.

In contrast to stability, residential instability was described by both Sampson
(1985) and Osgood and Chambers (2000) as proportion of households moved from
another place in former ﬁve years. Osgood and Chambers (2000) argued that
residential instability was signiﬁcantly related with all violent crime, such as
homicide, rape, robbery, aggregated assault, violence to weapons, and simple assault.

In contrast, Hackler et al. (1974) argued that there was no relationship
between neighborhood stability and informal control. Besides, to estimate an indicator
of guardianship or parochial control, the number of owner-occupied places was used
by Rice and Smith (2002). The objective of the variable by Rice and Smith was

somewhat different from others, but it still holds the same concept. In the study by

32

.—.—. ‘5” ._.._.._,__.._.—.__—.__—_._.. ._

Rice and Smith, this variable was always statistically signiﬁcant in the OLS model
and the model controlling for autocorrelation. As seen above, residential stability was
a very important element for most investigators, and the omission of this would lead

to inconsistent results.

Ethnic heterogeneigg/immigration

It is essential to know the tribal and linguistic heterogeneity of society
because both of them affect the residents’ shared value, which can reduce crime rates
because community members know each other (Sampson et al., 1997). Most etimic
heterogeneity was deﬁned as the proportion of white and nonwhite in community.
With the above deﬁnition, Sampson and Grove (1989) said that ethnic heterogeneity
caused trouble in unsupervised teen groups, which led to victimization and offense.
Osgood and Chambers (2000) created the formula for ethnic heterogeneity: “l - Z piz,
where pi is equal to the proportion Of those in the neighborhood in each of the four
groups (white, black, Indian, and other)” Osgood and Chambers (2000) found a
strong relationship between ethnic heterogeneity and most violent crime. In the study
by Markowitz et al. (2001), ethnic heterogeneity was related with disorder, as well as
burglary, after controlling for cohesion. Heterogeneity is measured as the number of

Blacks because Markowitz et al. believed that African Americans were short of

33

economic, political, and social resources. Racial heterogeneity was also deﬁned as the
ratio of racial formation of a face block (Rice and Smith, 2002). In the study by Rice
and Smith, the number of African Americans was signiﬁcant in OLS model, but was
not in the model controlling for spatial autocorrelation. In the study by Smith and
Davison (2000), the heterogeneity was measured as the number of African Americans,
and racial heterogeneity was deﬁned as multiplying the proportion of African
Americans by the proportion of whites. Racial heterogeneity was signiﬁcant
statistically. Ethnicity/immigration is composed of the population that is Hispanic and
foreign-bom and the percentage of African Americans (Morenoff and Sampson, 1997).
This variable was associated with population 1033.

In summary, although ethnic heterogeneity/immigration was an essential
element in social disorganization, Ballet et al. (2001) did not use it. First of all, the
immigrant concentration of collective efﬁcacy by Sampson et al. (1997) is very
important in this thesis. This is because the resource deprivation/affluence of the
Baseline Model already included African Americans like the concentrated
disadvantage of collective efficacy by Sampson et al. (1997), whereas in other studies
Aﬁican Americans are included in the dimension of heterogeneity as seen above. The
immigrant concentration of collective efﬁcacy contained only the percentage of

foreign-bom persons and the percentage of Latinos from census data. Accordingly,

34

this thesis will use the immigrant concentration of the collective efﬁcacy to avoid the

duplication of African Americans.

Chapter III: Methodology
Hypotheses
H1: Additional independent variables, such as residential stability and immigrant

concentration would improve the Baseline Model of Land et al. (1990)

H2: There is spatial autocorrelation in robbery, auto theft, and drug crime like
homicide.

H3: Relationship between ecological characteristics and crime would be explained
more signiﬁcantly if spatial autocorrelation were controlled.

The most important point of this study is to ﬁnd whether or not there is the
presence of a spatial autocorrelation in other crimes. For example, with the better
model, if this thesis ﬁnds spatial autocorrelation of speciﬁc crime in the US, this
paper can suggest that unknown characteristics of some regions affect the speciﬁc
crime, as most researchers said that the cultural element of the southern areas is the
cause [of homicide diffusion. In addition, the relationship between ecological
characteristics and crimes will be more obvious and signiﬁcant when controlling for

spatial autocorrelation.

Data

Basically, this thesis uses Ballet et al.’s data to compare their model with

36

model of this thesis. In other words, new independent variables and other crimes were
added into the model of Ballet et al. to maintain consistency. Additional independent
variables came from census data, and the data of three kinds of crimes from the
Uniform Crime Report (UCR). In contrast, Ballet et al. used the homicide rates of the
National Center for Health Statistics (NCHS) mortality ﬁles and the Centers for
Disease Control and Prevention (CDC) WONDER system. So, this thesis expects
there are some disparities from using different data.

In terms of the combination of county groups, Ballet et al. had to merge some
counties into one because the county boundary had been changed during the period of
study. In detail, 53 counties were merged into 20 counties. In addition to this, three
counties, such as Dukes County, Massachusetts, Nantucket County, Massachusetts,
and San Juan County, Washington, as well as counties in the states of Alaska and
Hawaii, were excluded from study because they were islands. This thesis follows the
same method. However, due to the limitation of data, this thesis will examine only
data in the 19803 and the 19903. In addition, drug crime will be examined in only the
19903, because there is no data in 19803 in the UCR. Finally, all computation will be
carried out by the SpaceStat and Geoda Software programs.

Variables

As explained above, the measure of ecological characteristics for social

37

disorganization theory changed over many decades. Especially, the discovery and the
application of informal control and formal control were obvious advances, and those
were indispensable constituents when studying social disorganization theory. But, this
study will not use informal and formal controls because Ballet et al. (2001) did not
use them.

Basically, the independent variables used by Ballet et al. are completely the
same as those of Land et al. (1990). In addition, based on analysis of former research,
this study ﬁnds additional factors, such as residential stability and immigrant
concentration. Among various measures used by researchers, this study will use
residential stability and immigrant concentration of the collective efficacy by
Sampson et al. (1997). Residential stability was measured by the percentage of the
population that has lived in the same house for more than ﬁve years, and the
percentage of houses in tracts that are owner occupied. The immigrant concentration
of the collective efﬁcacy was composed of the percentage of foreign-bom persons and
the percentage of Latinos from census data, not including African Americans. One of
the reasons why this thesis uses the collective efficacy of Sampson et al. (1997) is
because the concentrated disadvantage of the collective efficacy already included
African Americans as a resource deprivation/affluence of the Baseline Model. Besides,

this study had to consider whether or not the variable could be extracted from census

38

data. For example, this study could not use the measure of Fagan and Schwartz (1986)
used by both census and survey data.

In terms of a dependent variable, in contrast to the. study of Ballet et al.
(2001) this thesis adds other crimes: robbery, drug crime, and auto theft. Like Ballet et
al. (2001), each crime rate is rate per 100,000 people and the numerator is a 3 year
average centered on the decennial census year (e.g., 1979, 1980, and 1981) to avoid

heterogeneity. The average value is divided by census population (e.g., 1980).

Analytic Strategy

Generally, this thesis follows the analytic procedure of Ballet et al. Based on
several studies on why the homicide of the South and non-South differed, Ballet et al.
could have logical reasons for their study. In terms of three kinds of crimes of this
thesis, recent authors argued that violent crime (robbery), property crime (auto theft),
and drug crime have characteristics of diffusion and the study of those crimes should
consider spatial autocorrelation. Therefore, this thesis assumes that the above three
crimes had peculiarity of diffusion like homicide. However, robbery and auto theft
was only studied at the speciﬁc area level, different from drug crime which was
studied at the US. level. This thesis begins by adding new variables into Ballet et al.’s

model and assumes that results will be improved (e.g., the increase of R squared). The

39

second step is to ﬁnd spatial autocorrelation of other crimes. To do 30, Global
Moran’s I statistics and Local Moran’s I statistics will be carried out to ﬁnd signiﬁcant
spatial patterns and Clustered regions, and then a dummy variable will be created by
aggregating Clustered regions of each crime. Through the Spatial Chow test the next
step is to ﬁnd which model between a spatial lag model and a spatial error model is
better ﬁtted to disaggregated regions. Finally, this study veriﬁed validity and

reliability of each model through spatial lag and spatial error analysis.

Limitations of This Study

Although the analytic strategy of this thesis is better than that of Ballet et al. ’3
study, this study has three limitations like Ballet et al.’s study. For example, Messner
et al. (1999) argued that using spatial covariates by ESDA solves spuriousness of the
former result, but they could not prove the theoretical mechanism of how the spatial
pattern of diffusion precisely works. As Ballet et al. stated, authors could not explain a
clear mechanism of diffusion, although they assumed vectors of transmission exist
somewhere in the model. Also, they said that structural difference just inferred from
the regression relationship between South and non-South regions, but this mechanism
was not explained. Simply, Ballet et al. conjectured that diffusion processes were

associated with spatial autocorrelation. Further study is needed to concentrate on how

40

spatial autocorrelation occurs.

The unit of analysis will be another limitation. It is said that counties as units
of analysis are poor because of ecological fallacy (King, 1997). Although counties as
units of analysis have a few advantages (for example, easy to access), possible
diffusion processes occur at the boundary of counties like spatial heterogeneity. In
other words, some counties may have large areas consisting of various races and
many ethnic groups, and the diffusion processes perhaps happen within the counties,
but authors could not ﬁnd it. Moreover, an additional problem to be considered is if
the population of a county is very small, homicide rates are unstable (Messner et al.,
1999).

Third, as stressed by many critics, reliability and validity of the Official record
were suspect because many crimes were not reported to the police (Loeber & Blanc,
1990). For example, even if the offenders were arrested it would not be recorded
officially. In contrast, Osgood and Chambers (2000) said that late studies showed the
official record’s usefulness through additional methods, such as calls for police
assistance (Warner and Pierce, 1993), self-reports of victims (Sampson and Groves,
1989), and self-reports of offenders (Simcha-Fagan and Schwartz, 1986). However,
this thesis, using only official data, could not free itself from that limitation. Also, it is

obvious that the omission of informal and formal control will lead to another

41

limitation. In addition, this thesis used data for other crime derived from the Uniform
Crime Report (UCR), whereas Ballet et al. used data for the homicide rates of the
National. Center for Health Statistics (NCHS) mortality ﬁles and the Centers for
Disease Control and Prevention (CDC) WONDER system. This thesis expects some
disparities because generally, the number of homicides of NCHS is greater than that
of UCR.

Finally, note that this thesis could not apply “the K nearest neighbors (KNN)”
weight that was used in Ballet et al.’s study to know the value of LML and LME. That
is because the Geoda program did not work with KNN weight. The solution of this
problem is very important because the analysis of a spatial model is dependent on
which weight would be chosen. Therefore, this thesis consulted Dr. Luc Anselin, who
created the Spacestat and the Geoda programs, and Dr. Robert Ballet about the matter.
According to the staff of Dr. Luc Anselin, other weights, such as a queen or a rook,
could be used instead of the KNN weight, only if the result by other weight was
similar to one by the KNN weight. Moreover, Dr. Robert Ballet also agreed with the
opinion of the staff. As such, after comparing the result by the KNN weight with
results by other weight, this thesis found the queen contiguity of 3 order was the most
proper weight. In brief, while Ballet et al. found the difference of spatial regimes

between the South and the Non-south, using the Spacestat program with the KNN

42

weight, this thesis similarly, but not exactly, replicated Ballet et al.’s study through the

Geoda program with the queen weight. Therefore, this thesis used the queen weight

instead of the KNN weight for three crime rates to examine spatial autocorrelation.

43

Chapter IV: Results

In this chapter, results are presented in three sections. Each section relates to
each hypothesis. Section I details the ﬁndings that relate to the improvement of the
Baseline Model by adding residential stability and immigrant concentration. Section
II shows whether or not there is clustering pattern in three kinds Of crimes.
Additionally, if the clustering exists in the model, the stability of a model will be
examined by the Spatial Chow test. Section III explains how social disorganization

theory is advanced by using the spatial lag and the spatial error models.

Section I

The ﬁrst hypothesis of this thesis is that additional independent variables,
such as residential stability and immigrant concentration would improve the Baseline
Model of Land et al. (1990). Overall, adding new variables into the Baseline Model
gave this thesis somewhat satisfaction as expected. In other words, the two variables
did not greatly affect the homicide rates, but the effect was statistically signiﬁcant. In
detail, table 1 shows that in the 19803, the value of R squared of the thesis model
increased 0.431 into 0.433, even though it was small. Differently from what other
studies expected, residential stability positively affected homicide, but was not

signiﬁcant. The value of immigrant

44

Table 1. Ordinary Least-Square Regression of County Homicide Rates 1980-19902I

 

 

 

 

 

 

 

Independent 1980 1990
Variables Baseline Model Thesis Model Baseline Model Thesis Model
Resource Dep- 3.412" 3.337" 3.872" 3.892"
Pep- Comp- 0.747" 0.724** 1.353" 1.324"
Median Age -O.242** -0.234** -0.101** -0.066*
Divorce 1.250" 1.249" 0.583" 0.519"
Unemployment -0.122** -0.109** -0.306** -0.303**
South 2.113" 2.199" 2.194" 2.242"
Res-Stability — 0.014 — -0.333**
Imm-Con. — 0.342" — 0.288“
Intercept 8.541 ** 8.186“ 6.517" 5.749"
Adj. R-Squared o_431 0,43 3 0.435 0.438
N 3085 3085 3085 3085

 

a Unstandardized regression coefficients.
b Thesis model of UCR data for homicide

*ps.05

n p S _01 (two tailed tests)

concentration negatively affected homicide and is signiﬁcant like expectation.

Moreover, the coefficient of immigrant concentration is greater than that of median

age and unemployment. The other coefﬁcients are similar to those of the Baseline

model. Ballet et a1. said the negative effect of median age explained that counties

having younger people have higher homicide rate because younger people commit

more homicides. In the 19903, the R squared increased from 0.435 into 0.438 by .003

like the 19803. The value of immigrant concentration and residential stability was

signiﬁcant; immigrant concentration was positive and residential stability was

negative as expected by the literature review. In particular, the coefﬁcient of

residential stability was larger than that

45

Table 2. Comparison of Spatial Regression Models

of South Homicide rates,

 

 

 

 

 

 

 

1980-1990at
1980 1990

Baseline b Thesis c Baseline ThCSiS
Resource Dep. 3.026" 2.941" 4.028" 4.232“
Pop. Struct. Comp. 1.551" 1.707M 1.747" 1.789"
Median Age -.150" -.175" -.018 .000
Divorce .775" .892" .482" .469"
Unemployment -.244** -.270" -0.438" -.447"
Res-Stability - .597" - -.246
Irnm-Con. - -.004 - .246
Spatial Lag ( p) .182‘ .557" .230" .198"
Intercept 9.101" 8.716" 5249* 5.0013
N 1412 1412 1412 1412

 

a Unstandardized regression coefficients
* p S .05 ** p S .01 (two tailed tests)
bBaseline Model of Ballet et al.’s data
cThesis Model with Ballet et al.’s data

of median age and that of unemployment. Additionally, immigrant concentration

presents a more important element than median age in the 19903. This study examined

just two decades (the 19803, the 19903) due to the limitation of data. To know clearly

whether or not residential stability and immigrant, concentration affect dependent

variable, researchers need to investigate more decades, such as the 20005.

In summary, in view of the values of R squared, two additional variables

slightly affected the dependent variable in both decades, but their coefficients are

greater than median age in thesis model. Accordingly, new variables did not largely

affect homicide rates, but the above results provided sufficient evidence, in which the

addition of two variables improved the Baseline model somewhat. Longer terms will

give a clear answer.

46

Table 3. Comparison of Spatial error Models of Non-South Homicide rates,

 

 

 

 

 

 

198019902'
1980 1990

Baseline b Thesis c Baseline T“€815
Resource Dep. 4.143" 3.642" 2.875" 2.581"
Pop. Struct. Comp. .290' .211" .962" .858"
Median Age -304" -299" -.066" .058
Divorce L318“ 1.307" .572" .494"
Unemployment .008 -.003 -.O45" -0.051
Res-Stability - .062 - -.276"“"
Imm-Con. - 1.072" - .715"
Spatial Error (1) .329 .275" .268 .154*
Intercept 9.622" 9.317", 3.261" 3.431"
N 1673 1673 1673 1673

 

a Unstandardized regression coefficients
* p S .05 ** p S .01 (two tailed tests)

bBaseline Model of Ballet et al.’s data
cThesis Model with Ballet et al.’s data

Table 2 shows the comparison of spatial lag models of South homicide rates
in the 19803 and the 19903. Generally, the coefficients of the thesis model are similar
to those of the Baseline model. For example, all spatial lag coefficients are signiﬁcant,
and ﬁve coefficients of the Baseline model increased and decreased within small
scope. However, differently from what other studies expected, in the 19803 residential
stability had a positive inﬂuence on homicide and is even signiﬁcant. Additionally,
immigrant concentration negatively affected homicide and is not signiﬁcant. In
contrast to the 19803, in the 19903 residential stability negatively affected homicide

and immigrant concentration positively affected homicide. But, neither of them is

47

signiﬁcant. With the above results, this study cannot say that the thesis model
improved the Baseline model because residential stability and immigrant
concentration are not signiﬁcant and even affected homicide in the 19803, differently
from what the literature review expected.

In table 3, the comparison of the spatial error models of Non-South homicide
rates show more positive results compared to the spatial lag models of South
homicide rates. Basically, ﬁve coefﬁcients of the thesis model except immigrant
concentration and residential stability are similar to those of the Baseline model. In
the 19803, immigrant concentration positively affected homicide and is signiﬁcant
similarly to what the literature review expected. In contrast to literature review,
residential stability positively affected homicide, but is not signiﬁcant. In the 19903,
the coefﬁcients of two variables are desirable. Residential stability and immigrant
concentration signiﬁcantly affected homicide; the former was negative and the latter
was positive.

In conclusion, the addition of residential stability and immigrant
concentration is useful. Small amount of R-squared increased and most coefficients of
two variables are signiﬁcant. The result of the 19903 is more desirable than that of the
19803. As Ballet et al. said that the Baseline model was overstated, the Baseline

model is not sufficient to explain the mechanism between crime and variables. As

48

shown above, residential stability and immigrant concentration must be indispensable
factors. But, one of the concerns is multicollinearity among variables. Even though
Land et al. severely examined the Baseline model and this thesis used new factors that
differed from the Baseline model, the addition of two variables would cause
multicollinearity. Next section will examine multicollinearity among independent

variables.

49

 

Figure 3. Moran Scatterplot Map Auto Theft 1980 Rate (W=10 nearest Neighbors)

 

 

 

 

 

 

 

 

Auto theft 1980

Not signiﬁcant
High-High
Low-Low
High-Low
Low-High

[Dill]

 

 

50

 

Figure 4. Moran Scatterplot Map Auto Theft 1990 Rate (W=10 nearest Neighbors)

 

 

 

 

 

 

 

 

 

Auto theft 1990

Not signiﬁcant
High-High
Low-Low
High-Low
Low-High

DDIID

 

 

51

 

Figure 5. Moran Scatterplot Map Robbery 1980 Rate (W=10 nearest Neighbors)

 

 

 

 

 

 

Robbery 1980

Not signiﬁcant
High-High
Low-Low
High-Low
Low-High

IDIIU

 

 

52

Figure 6. Moran Scatterplot Map Robbery 1990 Rate (W=10 nearest Neighbors)

 

 

 

 

 

 

:1 Not signiﬁcant
- High-High
- Low-Low
E] High-Low
E] Low-High

 

 

 

53

 

Figure 7. Moran Scatterplot Map Drug 1990 Rate (W=10 nearest Neighbors)

 

 

 

 

 

 

 

Drug 1990

Not signiﬁcant
High-High
Low-Low
High-Low
Low-High

DDIID

 

 

54

Section II

Section 11 presents whether or not the clustering exists in three kinds of
crimes, and also examines the structural stability and heteroscedasticity through a
Chow test, which is “a test for structural change to determine whether the coefficients
in a regression model are the same in separate sub-samples” (Chow, 1960).
Additionally, the value of robust Lagrange Multiplier Lag (LML) and Lagrange
Multiplier Error (LME) will be examined to know whether the spatial lag model or
the spatial error model should be used in each region.

However, this thesis examined multicollinearity among independent variables
before moving to next stage to know whether or not adding two new variables causes
multicollinearity. Unfortunately, this thesis found some multicollinearity. In Table 2,
in the 19803, Collinearity Statistics of divorce and residential stability are less than 0.7,
and in the 19903, those of resource deprivation/affluence component and
unemployment are less than 0.7. Based on the above results, this thesis can suggest
that the Baseline model of Land et al. should have ﬁxed the problem of
multicollinearity between resource deprivation/affluence component and
unemployment in the 19903. Moreover, the addition of residential stability causes
multicollinearity with divorce in the 19803. To ﬁx the multicollinearity, this thesis has

to remove related variables, but if so, this thesis can not replicate Ballet et al.’s study.

55

Table 4. Collinearity Statistics (Tolerance) among independent variables

 

 

 

Independent Robbery Auto Theft Drug
Variables 1980 1990 1980 1990 1990
Resource Dep. .872 ._5_6_3 .836 - ,531 $2
Pop. Struct. Comp. .777 .755 .850 .823 .812
Median Age .823 .743 .842 .759 .759
Divorce .6_78 .728 ,6_73 .728 .730
Unemployment .853 ._5_43 .855 ﬂ &
Clustered Regions .823 .815 .811 .805 .832
Res-Stability ._6_63 .735 .6_39 .710 .731
Imm-Con. .915 .888 .922 .896 .845

 

Accordingly, all variables will be used continuously even though this thesis knows
that multicollinearity causes several problems.

Like Ballet et al.’s study, in the ﬁrst stage, this thesis investigated Global
Moran’s I statistics for other crime rates. The coefficients of robbery rate of the 19803
and the 19903, respectively, are .255 and .274; those of auto theft rate of the 19803
and the 19903 are .370 and .365; those of drug crime of the 1990 are .351. On the
basis of a permutation approach with 999 random, all coefficients are statistically
signiﬁcant at the .001 level. That means that spatial randomness is rejected for all
crimes and decades, and there is an obvious spatial pattern. Figure 3 to 7 are Moran
scatterplot maps of all crimes rates. “High-High” in the map shows the clustering of
three kinds of crime rates. For auto theft rate, the clustering of crime rates is
concentrated on Western and Florida regions, New York City and Washington DC.

areas, and Colorado State and Wyoming

56

Table 5. Comparison of Ordinary Least-Square of County Robbery Rates 1980-

 

 

 

 

1990a

Independent 1980 1990
Variables M1 M2 M3 Ml M2 M3
Resource Dep. .017" .017" .017" .029" .032" .032"
Pop. Struct. Comp. .043M .042" .040" .051" .049" .046"
Median Age .000 .002" .001" .000 .002" .002"
Divorce .014" .008" .008" .006" .002" .002"
Unemployment -003" -002" -002" -.006" -.006** -.006"
Clustered Regions - .030" - - .044"
Res-Stability -015“ -014" -020" -019"
Imm-Con. - .013" .011" - .014" .012"
Intercept -.01 l -030" -.023" .023 -.017 -.008
Adj. R-Squared .489 0.551 0.557 .454 .538 .548
N 3085 3085 3085 3085 3085 3085

 

a Unstandardized regression coefficients
* p S .05 ** p S .01 (two tailed tests)

Ml: OLS regression of County Robbery Rates of Baseline Model without
Immigrant Concentration, Residential Stability, and Clustered Regions
M2: OLS regression of County Robbery Rates of Thesis Model without Clustered
Regions
M3: OLS regression of County Robbery Rates with all variables

State areas. The clustering of robbery rates is located in California, New York, and
Washington DC. areas. In terms of the drug crime rates, as expected by the literature
review, the clustering of drug crime rates went around the coastline of the US. Based
on the Global Moran’s I statistics and these maps, this study concludes that there are
differences of spatial regimes in three crimes.

Table 5 shows the Comparison of Ordinary Least-Squared of County robbery

Rates from the 19803 to the 19903 in adding two new variables and Clustered regions

57

into the Baseline model. In general, most results of this thesis are similar to Ballet et
al.’s study of homicide. For example, the four variables of the Baseline model except
unemployment positively affected robbery and most variables of the Baseline model
are signiﬁcant. However, the direction of median age of robbery is different from that
of median age of homicide rates. Median age positively affected robbery rates. This
thesis conjectures that older people engage in more robberies based on Ballet et al.’s
explanation, in which younger people committed homicide more than older people.

Immigrant concentration and residential stability signiﬁcantly affected
robbery; the former was positive and the latter was negative as expected by the
literature review. According to Ballet et al., the negative effect of unemployment
could be explained by the decrease of chances for potential criminals to commit crime.
As expected by the literature review, residential stability, showing stronger
community attachment, had a negative inﬂuence on crime. Also, the coefficients of
residential stability and immigrant concentration are the greatest after population
structure component. Interestingly, after controlling the residential stability and the
immigrant concentration, the population structure component was more important part
than the resource-deprivation/affluence component.

The change of Adjusted R squared is very desirable. In the 19803, adding
immigrant concentration and residential stability increased Adjusted R squared

by .062, and the addition of Clustered regions increased Adjusted R squared by .006.

58

Table 6. Comparison of Ordinary Least-Square of County Auto theft Rates 1980-

 

 

 

 

 

 

19903
Independent 1980 1990
Variables M1 M2 M3 M1 - M2 M3
Resource Dep. -.008" -.008" -007" .021" .025W 0027"
Pop. Struct. Comp. .057" .055" .053" .094" .091" 0.090"
Median Age -003" .000 -001 -001 .003" 0.003M
Divorce .029M .018" .017" .016" .008" 0.008"
Unemployment -004" -002" -002" -.006** -.006"”" -0.006"
Clustered Regions - - .051" - 0.031"
Res-Stability - -032" -029" -041" -0040“
Imm-Con. .028" .025" - .039" 0.037"
Intercept .129" .089" .101" .111M .015 0.022
Adj. R-Squared .448 .545 .554 .453 .579 0.581
N 3085 3085 3085 3085 3085 3085

 

a Unstandardized regression coefficients
* p _<_ .05 ** p S .01 (two tailed tests)

M1: OLS regression of County Auto theft Rates of Baseline Model without
Immigrant Concentration, Residential Stability, and Clustered Regions
M2: OLS regression of County Auto theft Rates of Thesis Model withOut Clustered
Regions
M3: OLS regression of County Auto theft Rates with all variables

Similarly, in the 19903, Adjusted R squared increased .84 by the addition of two
variables and increased .01 by the addition of Clustered regions.

Table 6 shows the Comparison of Ordinary Least-Square of County auto theft
Rates from the 19803 to the 19903, adding two new variables and Clustered regions
into the Baseline model. As shown by the above results for robbery, results of auto

theft are similar to Ballet et al.’s study of homicide. However, the resource

59

deprivation/afﬂuence component is different. Different from homicide and robbery,
the resource deprivation/affluence component negatively affected auto theft in the
19803 but positively affected auto theft in the 19903. In fact, it was not easy to ﬁnd the
factor like resource deprivation/afﬂuence component in the studies of auto theft. In
the study of auto theft by Rice and Smith (2002), there was also no variable related to
resource deprivation/affluence component. Rice and Smith just conjectured that the
percentage of population of African American is likely to be associated with auto theft
because they assumed African American have low socioeconomic status. In their
study, the African American positively affected auto theft. Likewise, immigrant
concentration of this study including African American positively affected auto theft
like Rice and Smith (2002).

Immigrant concentration and residential stability signiﬁcantly affected
robbery; the former was positive and the latter was negative as expected by the
literature review. Median age negatively affected robbery rates but most coefficients
of median age are not signiﬁcant. The change of Adjusted R squared is satisfactory. In
the 19803, adding immigrant concentration and residential stability increased Adjusted
R squared by .097, and the addition of Clustered regions increased Adjusted R
squared by .009. Similarly, in the 19903, Adjusted R squared increased .126 and .002

respectively.

60

Table 7. Comparison of Ordinary Least-Square of County Drug Crime Rates

 

 

 

1990a
M1 M2 ' M3
Resource Dep. .034M .039M 0.027"
Pop. Struct. Comp. .052" .049“ 0.038"
Median Age -.003** .002* 0.001
Divorce .018” .010" 0.008"
Unemployment -.006** -.007** -0.005**
Clustered Regions - - 0.087"
Res-Stability - -.043** -0.038**
Imm-Con. - .042" 0.034M
Intercept .195” .091 ** 0.080“
Adj. R-Squared . 179 .306 0.360
N 3085 3085 3085

 

a Unstandardized regression coefﬁcients
* p S .05 ** p S .01 (two tailed tests)

Ml: OLS regression of County Drug Rates of Baseline Model without Immigrant
Concentration, Residential Stability, and Clustered Regions
M2: OLS regression of County Drug Rates of Thesis Model without Clustered

Regions
M3: OLS regression of County Drug Rates with all variables

Table 7 shows the Comparison of Ordinary Least-Square of County drug crime Rates
in the 19903, adding two new variables and Clustered regions into the Baseline model.
As shown above, results of drug crime are similar to those of robbery, but the
difference is that median age is insigniﬁcant and inconsistent. Other variables except
unemployment and residential stability positively affected drug like robbery and auto

theft. Immigrant concentration and residential stability are signiﬁcant and important

61

factors. The change of Adjusted R squared is very desirable. Adding immigrant
concentration and residential stability increased Adjusted R squared by 1.127, and the
addition of Clustered regions increased R squared by .054.

In sum, the above results did not deviate from the former studies, and it
appears to have worth to add two variables into the Baseline Model. Accordingly, this
thesis suggests that the addition of residential stability and immigrant concentration
improve the Baseline model. However, as said before, this thesis could not know how
badly multicollinearity affected the results. Additional examination is needed to solve

the problems.

Structural stability and Heteroscedasticity

In the next stage, like Ballet et al.’s study, this study found that there were
heteroscedasticity and spatial instability in crime rates by analyzing the stability of the
regression coefficients of a spatial regime. As said above, the Spatial Chow test
examines whether the same model is proper for two dissimilar sub-samples. Table 8
shows the results of the Spatial Chow test, the stability of individual coefficients
(Clustered regions versus Non-clustered), the heteroscedastic coefficients, and the test

on heteroscedasticity.

62

Table 8. Stability of Regression Coefficients by Spatial Regime- County Other Crimes
1980-1990

 

Robbery Auto Theft Drug

 

1980 1990 1980 1990 1990

 

1. Spatial Chow Test on Overall Stability 3:
303.556“ 296.774" 245.086" 72.227” 210.503”

 

11. Stability of Individual Coefficients (Non-Clustered versus Clustered Regions)

 

Resource Dep. 102.006“ 108.452” 7.489“ 15.830** 4.715
Pop. Struct. Comp. 152.521M 92.588“ .594 10.161 ** .774
Median Age 3.617 .612 5.099* 2.310 .061
Divorce .404 3.087 .107 .004 .073
Unemployment .243 2.261 10.569" 1.149 .261
Res-Stability 9.495" .004 27.678" .957 .092
Imm-Con. 8.720" 1.238 69.102" .821 .695
III. Heteroscedastic Coefficients

Non-Clustered .002 .002 .006 .008 .01 1
Clustered .005 .005 .009 .01 7 .025

 

IV. Test on Heteroscedasticity b:
27.349" 18.929" 8.312" 30.676“ 123.605"

 

N 3085 3085 3085 3085 3085
(N ofClustered regions) (131) (131) (222) (222) (904)

 

a distributed as x2 with 8 degrees of freedom.
b distributed as x2 with 1 degree of freedom.
"’ p S .05; ** p S .01 (two tailed tests)

Table 8 says that the Spatial Chow test rejects the coefficient stability. Moreover, the
stability of Individual Coefficients (Non-Clustered versus Clustered Regions) shows
that several variables, such as resource deprivation/affluence component, population
structure component, and residential stability, exert significantly different effects
across crimes and regions. In addition, heteroscedastic coefﬁcients of Clustered
regions compared to Non-clustered ones are bigger, even though the difference is

small. Finally, the test of heteroscedasticity said that all cases do not have equal error

63

variance. Therefore, this thesis assumes that addition of Clustered regions only could
not reduce spatial heterogeneity.

In summary, similar to at Baller et al. found separated spatial regimes, there is
also an obvious difference of spatial regimes between Clustered and Non-clustered
regions in three crime rates. Therefore, like the Baseline model which was not
sufficient, thesis model developed from the Baseline model is not also enough to
detect the heterogeneity of regions, and each region is needed to be analyzed
separately, because dividing the US. into Clustered and Non-clustered regions did not
explain spatial dependence and heterogeneity sufficiently. Accordingly, like Baller et
al.’s study, this thesis will carry out disaggregated modeling method.

Following Baller et al.’s study, this thesis examined the value of robust
Lagrange Multiplier Lag (LML) and Lagrange Multiplier Error (LME) to know
whether the spatial lag model and the spatial error model should be used in each
region. In other words, if the value of LML is greater than that of LME, the spatial lag
model should be used in that model. Table 9 presents each decade’s LML and LME of
three kind crime rates. The value of LME of all regions, except the Clustered regions
of auto theft in the 19803, is greater than the value of the LML, which means only
Clustered regions of auto theft in the 19803 are fit for a spatial lag model, and the rest

of them are ﬁt for a spatial error model.

64

Table 9. Robust Lagrange Multiplier Lag and Lagrange Multiplier Error of County
Other Crimes 1980-1990

 

 

 

 

 

 

 

 

 

 

 

 

Clustered Regions Non-clustered Regions
Robust Robust Robust Robust
LML LME LML LME
1980 0.374 1.900 143.875" 297.139"
Robbery

1990 1.972 5.660* 63.171" 173.517"
Auto 1980 2.216 2.202 99.897" 385.136M
Theft 1990 0.131 0.250 75.247" 271 .848W
Drug 1990 2.174* 9.329" 2.641 * 17.668“

 

In general, this result is quite different from Baller et al.’s homicide study. Whereas
the spatial lag model was used for studying the homicide rate in the South of all years
and the Non-south of the 19605, only auto theft of Clustered regions in the 19805
among three kinds of crime rates ﬁts for the spatial lag model. Moreover, because the
auto theft’s LML in the 19808 is not even signiﬁcant, and the difference between LML
and LME is very small, this thesis assumes that there is not big difference between the
spatial lag model and the spatial error model.

Unlike Baller et al.’s study, several coefficients are small and not signiﬁcant.
According to Baller, small coefficient and insigniﬁcance do not matter if Global
Moran’s I statistics are signiﬁcant. Therefore, this thesis can proceed to next stage
because all Global Moran’s I statistics are signiﬁcant. However, it is not too much to
say that there is little diffusion in three crimes because Baller et al. (2001) said that
the spatial lag model has the feature of diffusion of crime. In fact, the all homicide

rates of the South in the US. found diffusion procedure. But different from

65

expectation, the spatial autocorrelation of three kinds of crimes could be explained by

unmeasured variables.

66

Section III

This section presents the spatial lag model for the Clustered regions of the

auto theft of the 19808 and the spatial error model for the rest of the regions. In

addition, this study examines how much the spatial model improved OLS model. To

meet the convenience of analysis, this thesis will explain the spatial model of robbery,

auto theft, and drug crime.

Robbery

First, table 10 separately shows the comparison of OLS and the spatial error

model of county robbery rates in Clustered regions and Non-clustered regions.

Basically, the coefficients of two models are similar to former OLS model before

separating one into two regions. In detail, the resource deprivation/affluence

component, the population structure component, and the immigrant concentration

always positively and signiﬁcantly affected robbery rates over time and regions. The

residential stability was signiﬁcant and negatively affected robbery in two decades.

Divorce, immigrant concentration, and unemployment are always signiﬁcant except

Clustered regions of the 19808 in the spatial error model. The difference, compared to

the former OLS model before separating, is that median age of Clustered regions in

the 19808 negatively affected robbery. But, median age does not matter due to its

insignificance.
67

 

Table 10. Comparison Between OLS and Spatial model of County Robbery Rates

 

 

 

 

 

 

 

 

1980-1990‘3
1980 ‘ 1990

Independent

_ Clustered Non-Clustered Clustered Non-Clustered
Variables b _ c _ _ .

OLS Spatial OLS Spatial OLS Spatial OLS Spat1al

Resource Dep. .088" .094" .014" .017" .120" .124" .028“ .028"
Pop. Comp. .103" .095" .037“ .040” .120M .106“ .044" .047"
Median Age -.002 -0.002 .001" .001" .001 -.001 .002" .002" r-
Divorce .005 .010 .009" .009" 012* .019" .002" .002"
Unemployment -.002 .0001 .002" .002" .0133 -.011* -.005" .005" ..
Res-Stability -.038" -.038" .012" -.011" ..018* -.025" -.018" -.017" f” ‘
Imm-Con. .0123 .010 .009“ .010" .016" .021" .009” .010"
Spatial Error (1) - .366” - .331" - .531" - .288"
Intercept .023 .010 -.017* .034" -.014 -.019 -.003 -.023‘
R-Squared .798 .810 .513 .530 .808 .832 .497 .509
N 131 131 2954 2954 131 131 2954 2954

 

a Unstandardized regression coefﬁcients
* p S .05 *"' p S .01 (two tailed tests)

b OLS regression of County Robbery Rates
c Spatial error model of County Robbery Rates

More importantly, the coefficients of the spatial error were always signiﬁcant and
affected robbery strongly and positively.

To know how much the spatial error model improved OLS model, this thesis
tried to examine the Adjusted R squared between two models. However, the spatial
model of Geoda software did not present Adjusted R squared. So, this thesis
calculated the value of F test6 between OLS model and the spatial error model. The

value of F distribution’s table between two models is consistently 3.84 because all
68

cases of the spatial models are greater than 120 and the difference between the
number of the spatial models (Kf) and the number of OLS models (K,) is always 1.
For robbery of the 19808, the F test value in Clustered regions is 10.582 and that in
Non-clustered regions is 127.515. In the 19908, the F test value in Clustered regions is
17.429 and that in Non-clustered regions is 71.976. Therefore, all F test values are
greater than 3.84, which means that the spatial model improved OLS model.

In summary, a spatial error model accounted for robbery well. In other words,
robbery could be explained by the presence of unmeasured variables. Differently from

what the former studies expected, it does not seem that there is diffusion in robbery.

Auto theft

Table 11 shows the spatial lag model for Clustered regions in the 19808 and
the spatial error model for Non-clustered regions in the 19808 and Clustered and Non-
clustered regions in the 19908. Generally, the result of spatial analysis was similar to
that of non-spatial analysis except the resource deprivation/affluence component. The
coefficient of resource deprivation/affluence component of OLS of Non-clustered
regions in the 19808 negatively affected auto theft. Median age also is inconsistent

over times and regions.

69

 

 

Table 11. Comparison Between OLS and Spatial model of County Auto theft Rates

 

 

 

 

 

 

 

1980-199031
1980 1990
Independent
Clustered Non-Clustered Clustered Non-Clustered

Variables b ‘ c . d ‘ d . d

OLS Spatial OLS Spatial OLS Spatial OLS Spatial
Resource Dep. .052” .052” -.008” .002 .108“ .107” .024“ .028”
Pop. Comp. .051" .051”I .051" .070" .115" .115“ .084" .095“I
Median Age -.005* 0005' .000 .001 -.001 -.001 .003" .003"
Divorce .014M .014" .018“ .019" .009 .010 .009" .009"
Unemployment -.012" .013" -002" -.001* -.009 -.008 -.006" -005"
Res-Stability -.022** -021" -029" .023" -.030" -.031" -.040" -.036“
Imm-Con. .030” .030" .023" .020" .040“ .041" .033” .036”
Spatial Lag ( p) - -.049 - - . . . -
Spatial Error (1.) - - - .685 " - .069 - .505"
Intercept .417“ .437“ .009” .060" .260“ .236“ .027 .013
R-Squared .482 .483 .495 .551 .646 .647 .538 .567
N 222 222 2863 2863 222 222 2863 2863

 

8 - - .
Unstandardized regre881on coefﬁcients

 

* p S .05 ** p _<_ .01 (two tailed tests)

b OLS regression of County Auto theft Rates

c Spatial lag model of County Auto theft Rates

d Spatial error model of County Auto theft Rates

Additionally, like non-spatial analysis, the unemployment and the residential
stability of the spatial error model consistently and negatively affected auto theft
crime rates, and the divorce, the population structure component, and the immigrant
concentration positively did. All values are signiﬁcant except the unemployment of
the Clustered regions in the 19808.

For the spatial lag model, all coefﬁcients of dependent variables, except the

value of spatial lag (p), were signiﬁcant. According to Baller, insigniﬁcance of the
70

coefficient of spatial lag does not matter. Baller said that the coefﬁcient of spatial lag
is just a coefficient. As shown by table 9, the difference between the value of LML
and LME of auto theft in the 19808 is very small. This thesis assumes that the tiny
difference explains that the reason why the coefficient of the spatial lag was not
signiﬁcant, which means there is not big difference between the spatial lag model and
the spatial error model in Clustered regions of auto theft in the 19808.

In terms of R squared, for auto theft of the 19808, the value in Clustered
regions is 3.48 and that in Non-clustered regions is 519.478. In the 19908, the value in
Clustered regions is 0.603 and that in Non-clustered regions is 191.145. The F test
values of Non-clustered regions are greater than 3.48, but those of Clustered regions
less than 3.84. Therefore, this thesis suggests that the spatial lag model‘and the spatial
error model of Clustered regions did not improve OLS model, but the non-spatial
models of Non-clustered regions are improved through spatial error models.

In conclusion, a spatial model seems to be better than a non-spatial model in
Non-clustered regions. However, Clustered regions could be sufficiently explained by
OLS model because F test value is less than 3.48. Therefore, diffusion of auto theft in
the US. hardly exists. In contrast, Rice and Smith (2002) argued that auto theft’s
diffusion exists at micro level, after combing social disorganization theory and routine

activity theory. But, their data was collected from a southeastern US. city with an

71

 

approximate population of 250,000. In other words, Rice and Smith did not use data
of all the US. Accordingly, based on above results, this thesis suggests that auto theft
was sufficiently explained by a spatial error model at the US. level. But, careful and
additional investigations are needed to know whether or not diffusion of auto theft
exists at the macro level.
Drug Crime

Like other crimes, the result of the spatial model of drug crime was alike to
that of the non-spatial model. For example, the coefficients of spatial error (it) were
always signiﬁcant over time. Resource deprivation/affluence component, population
structure component, and divorce were always positive and signiﬁcant.
Unemployment and residential stability were negative and signiﬁcant. However,
median age positively affected drug crime but was insigniﬁcant. Each coefficient of
residential stability and immigrant concentration was greater than each coefficient of
median age, unemployment, and divorce.

In terms of F test, the value in Clustered regions is 4.469 and that in Non-

clustered regions is 65.306, which means the spatial error model improved the OLS

model. Accordingly, drug crime was sufficiently explained by unmeasured variables.

72

Table 12. Comparison Between OLS and Spatial model of County Drug Crime Rates

 

 

 

 

 

1990a
1990

Independent Clustered Non-Clustered
Variables b . c .

OLS Spatial OLS Spatial
Resource Dep. .040" .042" .022M .013"
Pop. Comp. .043" .042" .037" .035"
Median Age .002 .002 .001 .001
Divorce .009” .009* .008" .006"
Unemployment -.006* -.006* -.004** -.003**
Res-Stability -.040** -.040** -.038** -.037**
Imm-Con. .033" .033“ .037“ .038M
Spatial Error (A) - .134 - .448“
Intercept . 147* .141 * .078" .084"
R-Squared . 195 . 199 .240 .271
N 904 904 2181 2181

 

a Unstandardized regression coefficients
* p S .05 ** p S .01 (two tailed tests)

b OLS regression of County Drug Crime Rates
c Spatial error model of County Drug Crime Rates

While there is no study of robbery and auto theft at macro level, several
investigators had studied diffusion of drug crime in the US. Hunt and Chambers
(1976) said that diffusion of drugs occurred from Boston to Washington along the
coast and in Southern California, and heroin use appeared to diffuse to the interior
from areas of large population to those with a small population. Similarly, Frischer et
al. (2000), in their study of diffusion of drug misuse in Scotland, said that spatial
autocorrelation should be considered in the study of drug use because drug crime

could not be explained by demographic factors and housing environments. But, this
73

thesis could not ﬁnd diffusion of drug crime in the US. This thesis does not argue that
their ﬁndings are wrong. But, if it is true that this thesis uses better model than former
investigators, the presence of diffusion of drug crime should be examined again.
Additionally, like Hunt and Chambers ( 1976), this study suggests that drug crime
appears to relate to coastlines. As shown by Moran scatterplot maps, most of drug
crimes and the clustering of drug crime were concentrated on coastline. According to
Baller et al., the clustering of crime is different from diffusion. The cluster is a place
with high crime rate that also has adjacent neighborhoods with high crime rate, while
diffusion is related to a complicated mechanism, called a spatial lag model. More

detailed explanations will be presented in summary and discussions.

74

 

 

 

Chapter IV: Summary and Discussions

This thesis replicated Baller et al.’s study to examine the presence of the
spatial autocorrelation of robbery, auto theﬁ, and drug crime. Before the replication,
this study added immigrant concentration and residential stability to improve the
Baseline Model. Adding two variables was somewhat effective to examine the
relationship between independent variables and dependent variables. But, this thesis
only examined two decades due to restricted data. The study of extended terms will
give a clear answer.

As expected, this thesis found several similar ﬁndings to Baller et al.’s study,
but there are also several important differences. In terms of common points, ﬁrst of all,
three kinds of crimes were also not randomly distributed like homicide. Most
Clustered regions have higher crime rates than Non-clustered ones. This shows that
the differences of the spatial regimes obviously affected crime rates. In homicide’s
study, Baller et al. (2001) argued that “the South and the Non-South constitute two
distinct spatial regimes in the geographic clustering of homicide” (p. 582). As such,
three crimes also showed the difference of spatial regimes.

Second, regardless of controlling structural factors, the clustering of crimes
remained in both decades in this study. According to Baller et al., in addition to

independent variables, this means that there is another ingredient somewhere in model,

75

in generating crime rates.

Third, independent variables differently affected crime rates in Clustered
regions and Non-clustered ones. When it comes to homicide, a few scholars attributed
it to “a culture of violence” (Ballet et al., 2001) For example, Hackney and Gastil
argued that different value systems, affecting violent behavior, could explain higher
homicide rates of the South. They called it “a subculture of violence” (Land et a1,
1990). In terms of three crimes, this thesis suggests the new outline of mechanism
about clustering of three crimes. Interestingly, after close examination of Moran
Scatterplot Maps, this thesis observed that clustering of robbery, auto theft, and drug
crime were consistently concentrated on regions that are famous for the tourist
industry. In detail, regardless of the kinds of crime, areas of California Las Vegas,
Florida, New York City, and Washington DC. experienced the most clustering of
crime. This trend was quite different from the homicide’s clustering focusing on the
South. This thesis does not argue that there is a relationship between the tourist
industry and clustering of three crimes. It is just a hypothesis based on the ﬁndings. In
fact, this study could not explain why clustering phenomena happen. A8 argued by
Ballet et al., further studies are required to explicate the obscure mechanism.

In contrast to points of sameness, robbery, auto theft, and drug crime hardly

have diffusion phenomena. Only auto theft of Clustered regions in the 19808 showed

76

‘1‘?“"6 . . - .1-..

a

weak diffusion. This was quite different from the former studies related to robbery,
auto theft, and drug crime to examine the presence of diffusion. In fact, former studies
are concentrated on restricted areas. In other words, researchers found the diffusion of
those crimes at the micro level, such as a city, but this thesis did not ﬁnd diffusion at
the macro level. Only auto theft of Clustered regions showed weak diffusion in the
19808. Therefore, three crimes rates could be explained by unmeasured variables, not

interaction between dependent variables.

Consideration for Future Study

During the study, this thesis found several new points to be considered for
future examiners. First, this research, including Ballet et al.’s study, missed the true
nature of the time variables. For the future study, the time variable should be
considered because diffusion itself necessarily needs an intermediary called time. In
other words, former situations affect present ones and present resulted from the past.
For example, the Butterfly Effect of chaos theory says that tiny variations of the
beginning of time caused large difference in the long term. As such, independent and
dependent variables of the former month can affect dependent variables and even
independent variables of present month. In detail, it is possible that the weak

residential stability of the former month, not only affects the present crime rate of

77

 

3m '_:¢&

community, but also affects residential stability itself of the present month or other
independent variables. But, this study and Ballet et al.’s study just used the crime rate
and independent variables of the given year. In detail, each of the four kinds of crime
rate is the rate per 100,000 people and the numerator is a 3 year average centered on
the decennial census year (e.g., 1979, 1980, and 1981) to avoid heterogeneity. The
average value is divided by census population. Other independent variables are the
same. This thesis and Ballet et al.’s study never considered how former variables
affected late ones. Even though Ballet et a1. said that spatial lag model is very similar
to diffusion process, they did not consider time. Dividing independent and dependent
variables by month would be an example.

Second, compared to the number of the Clustered regions of homicide (1679),
the number of those of robbery (131), auto theft (222), and drug crime (904) were
very small. But, this thesis does not know how that small number of Clustered regions
of three kinds of crime rates affects results. Also, this thesis could not suggest whether
or not the diffusion of crime was substantially related with the number of clustered
regions. More importantly, the procedure of deciding the number of Clustered regions
depends on investigators. Therefore, this thesis suggests that investigators should be
careful when they choose the number of Clustered regions (e.g., the homicide study

by Ballet et al.).

78

Third, this thesis found that the presence and the magnitude of spatial
autocorrelation related to what weight is used. The amount of magnitude and direction
of spatial autocorrelation is dependent on a used weight. To replicate Ballet et al.’s
study, this thesis used the queen weight that is the most similar to the 10 nearest
neighbors of Ballet et al. During the procedure which found the proper weight, this
research realized that the weight greatly affected the result. This means that examiners
need to conceptualize carefully the objective of study to decide what weight will be
used.

Finally, the multicollinearity of variables should be removed from model.
Even though this thesis knew that multicollinearity exists in the Baseline model and
the thesis model, this study did not remove it. To remove multicollinearity this thesis
would have had to take out several independent variables, but if so, this thesis could
not have replicated Ballet et al.’s study. If multicollinearity were eliminated from
models, better results would be obtained. Even Ballet et a1. (2001) did not remove
multicollinearity. Accordingly, careful investigations are needed to remove

multicollinearity.

79

 

ENDNOTES

1 This variable was deﬁned as the total population of all other places in the city. Each
adjacent tract is weighted by its geographical proximity to the reference tract.
“Formally, the population potential for a given areal unit 1', PP), is deﬁned by
PP.-=z(P,-/D.-,-)j¢i ,

where Pj is the population of the jth areal unit, D3 is the distance of unit j from unit i,
and the summation is taken over all units in the city other than i".

This variable enables Roncek and Montgomery to study in relation to spatial
phenomenon, such as the diffusion of crime (Morenoff and Sampson , 1997).

2 In the ﬁrst stage, Morenoff and Sampson created predicted values of the potential
variables “by regressing the generalized potential on the set of predictors as well as a
set of instrumental variables, which in this case are dichotomous variables
representing police districts.” They assumed that these police district variables
described some place which has an inﬂuence on the population change in the city,
except the reference census tract. Land and Deane in 1992 showed how to use
regional dummy variables as instruments. They used the predicted values for the
generalized potential variable as another regressor in the next procedure, where
population change is the dependent variable. (Morenoff and Sampson , 1997)

3 This variable is the value of the weighted average of the number of auto thefts for
the 10 next adjacent face blocks in either direction from the face block in question
(Rice and Smith, 2000).

4 According to Smith et al., street robbery potential is “the weighted average of the
street robberies on these proximate face blocks which are computed weighting those
further away less. The street robbery potential of a face block was deﬁned as the
weighted average of two directions of 10 face blocks (Smith et al., 2000).

5 This test is examined for the stability of the regression coefﬁcients over the regimes.
To do so, this test was carried out for all coefﬁcients jointly and for each coefﬁcient
separately. According to the Ballet et al., in the classic regression model, this is the
Chow (1960) test on the stability of regression coefﬁcients, and Anselin extended it
into the spatial chow test.

80

 

 

6 F test formula is as follows.

(RFZ-RR2)/(Kt‘-Kr)

 

F (KrKhN-f-l) = 2
(l-Rr -)/CN-Kr1)

Rp2: R-square for the full model

RRZ: R- square for the restricted model

Kf: number of Independent variables in the full model

K, : number of Independent variables in the restricted model
N : total number of cases

81

‘3

--\-.

.l. .1!

 

 

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