2. of murders of police has been carried out at various levels of
areal aggregation. However,
although the general homicide research has been extended to
counties in the United
States, research on murders of police has yet to follow suit. To
begin to fill this gap, this
study extends research on the structural covariates of police
homicides to the county level.
Controlling for the number of law enforcement officers at risk,
we find that police were
more likely to be murdered in economically depressed counties
and in counties with
larger percentages of African Americans, persons aged 25 to 34,
and nonsheriff agencies.
Police homicide risk was significantly lower in urbanized
counties and in counties located
in the Northeast, whereas the South was no riskier than the
West or Midwest. Murders of
police were unrelated to population mobility, divorce, and
levels of violent crime.
Keywords: police; murder; homicide; victimization; counties
With few exceptions, the extant regression-based research on
homicides of police
emphasizes the role of adverse structural conditions that
generate criminal
motivations or free individuals to engage in crime, a perspective
consistent with tra-
ditional macrosocial theories developed to explain crime and
violence generally
(Merton, 1938; Shaw & McKay, 1969). The implicit assumption
in most studies is
that crime and violence in general and violence against the
police in particular share
3. common structural causes, and thus the factors that predict the
former should also
predict the latter (Kaminski & Marvell, 2002; Peterson &
Bailey, 1988). An exami-
nation of the regressors employed in the police homicide
literature (discussed later)
shows that they are often the same as those used in studies of
general homicides,
with many reflecting various dimensions of the control, strain,
or criminal opportunity
theoretic perspectives (Land, McCall, & Cohen, 1990; Parker,
McCall, & Land,
Kaminski / County-Level Covariates of Police Homicides 351
1999). Most commonly, though, these studies include one or
more of the core indi-
cators of the social disorganization perspective, that is,
population size and density,
racial/ethnic heterogeneity, economic deprivation, population
mobility, and family
disintegration (Kornhauser, 1978; Sampson, 1986; Shaw &
McKay, 1969). As noted
by Land et al. (1990),
The central hypothesis of the neoclassical community-control
theory is that these and
related community-level characteristics . . . directly or
indirectly affect informal social
control networks, community attachment, anonymity, and the
capacity for surveillance
and guardianship. A weakening of these dimensions of social
organization is posited to
lead to increased rates of deviance and crimes such as homicide.
4. (p. 925)
Further examination of the police homicide literature leads to
two other observa-
tions. First, more than two decades of research on police
homicides has failed to
identify virtually any regressor that is statistically significant
and of the same sign
across all models or studies (Batton & Wilson, 2006; Kaminski
& Marvell, 2002), a
situation similar to that described by Land and his colleagues
more than a decade
ago regarding research on general homicides (Land et al.,
1990). Thus, additional
research is needed to better understand the social and economic
conditions that give
rise to serious violence against the police.
Second, all of the studies attempting to explain the spatial
variation in police homi-
cides have been limited to the use of cities or states as units of
analysis.1 Although var-
ious arguments as to the strengths and weaknesses of these two
areal units may be
made, extending the study of structural covariates and police
homicides to counties is
important because geographic boundaries are arbitrary with
respect to social theory,
and a general theory of how structural conditions affect
homicide rates should, there-
fore, be capable of accommodating all levels of spatial
aggregation (Land et al., 1990).
Furthermore, although the appropriateness of the use of large
enumeration units such
as counties to study the effects of community structural
characteristics derived from
5. social disorganization theory on crime has been questioned
(Bailey, 1984; Petee,
Kowalski, & Duffield, 1994, p. 118), a growing body of
research has extended such
analyses to counties (e.g., Baller, Anselin, Messner, Deane, &
Hawkins, 2001; Kposowa,
Breault, & Harrison, 1995; Osgood & Chambers, 2000; Weisheit
& Wells, 2005;
Wilkinson, 1984). As a first step in extending this line of
inquiry to murders of police,
this paper presents a county-level analysis relating police
homicides to the structural fea-
tures of communities specified by social disorganization theory
and its extensions.
Explaining Murders of Police
Precisely how structural conditions influence risk of police
homicide victimiza-
tion has not been well explicated in much of the police
homicide literature, which
is partly due to several studies that focused on the impact of
various crime-control
352 Homicide Studies
policies on murders of police, with structural measures simply
included as controls
(Bailey, 1982; Bailey & Peterson, 1987, 1994; Moody, Marvell,
& Kaminski, 2002;
Mustard, 2001). Generally, however, the assumption has been
that adverse structural
conditions such as poverty, racial heterogeneity, divorce, and
population mobility
6. generate crime and that these structurally induced opportunities
increase the likeli-
hood of police coming into contact with offenders, some of
whom are willing to
resist, assault, and murder police officers (Chamlin, 1989, p.
353; Kaminski, 2002,
2004; Peterson & Bailey, 1988). According to this perspective,
felonious killings of
police are primarily a byproduct of ordinary criminal violence,
with most police
being killed by offenders who wish to avoid apprehension and
punishment
(Cardarelli, 1968; Creamer & Robin, 1970; Jacobs &
Carmichael, 2002; Kaminski,
2002, 2004; Margarita, 1980b). Support for the traditional
structural covariates
examined is mixed, with few consistent findings within or
across studies (Table 1).
A second, but related perspective, draws more directly on
criminal opportunity
theory to explain areal or temporal variation in violence against
police (Fridell,
Faggiani, & Brito, 2004; Kaminski, 2002, 2004). According to
this view, variation in
structural conditions affects both motivations for crime and
opportunities for crime
(Cohen & Felson, 1979; Hindelang, Gottfredson, & Garofalo,
1978; Miethe &
McDowall, 1993). Criminal opportunity models, for example,
commonly measure
proximity to motivated offenders using indicators of adverse
structural conditions
(see, for example, Hough, 1987; Miethe & Meier, 1994;
Sampson & Wooldredge,
1987). Miethe and McDowall (1993) explained how, from a
7. social disorganization
perspective, criminogenic conditions in areas increase
motivations for crime, whereas
from an opportunity perspective they “increase victimization
risks by increasing indi-
viduals’ exposure to motivated offenders, target attractiveness,
and reducing the level
of social control or guardianship” (pp. 747-748). In other
words, criminogenic forces
such as population density and heterogeneity, family disruption,
residential mobility,
and economic strain “generate a facilitating context for crime
by increasing the pool
of potential offenders. The greater one’s proximity to these
criminogenic areas, the
greater one’s risk of victimization” (Miethe & Meier, 1994, p.
44).
According to this view, adverse structural conditions facilitate
opportunities for
serious and fatal assaults of law enforcement officer by
increasing the likelihood of
the convergence in time and place of offenders engaged in
serious crime who are
motivated to avoid apprehension and punishment, and law
enforcement officers
whose mandate is to intervene in crime and apprehend offenders
(Cardarelli, 1968;
Creamer & Robin, 1970; Kaminski, 2002, 2004; Margarita,
1980b). The more
adverse the structural conditions over time or place, the larger
the pool of motivated
offenders and the greater the risk of officer victimization, other
factors being equal.
Additional opportunity factors that arguably influence police
8. vulnerability and
exposure to offenders include police officer density, arrests, and
organizational poli-
cies designed to harden officers as targets, such as mandatory
vest-wear policies,
(text continues on p. 358)
353
Ta
bl
e
1
R
eg
re
ss
io
n-
B
as
ed
S
tu
di
128. un
de
rg
ro
un
d
ec
on
om
y)
.
two-officer patrols, and the replacement of revolvers with
semiautomatic sidearms
(Kaminski, 2002, 2004).2 Except for the level of police officer
density (proximity)
and aggregate numbers of arrests (exposure), the limited
empirical research on orga-
nizational opportunity factors has been unable to demonstrate a
significant impact on
police victimization risk (Fridell et al., 2004; Kaminski, 2002,
2004).
A third perspective, rooted in conflict theory and the racial
threat hypothesis (Eitle,
D’Alessio, & Stolzenberg, 2002; Jackson, 1989), maintains that
variation in the rate
of police homicides across enumeration units can be explained
in part by political fac-
129. tors, specifically the economic and political subordination of
Blacks by the state
(Chamlin, 1989; Jacobs & Carmichael, 2002).3 According to
this view, many murders
of police by Blacks are a response to this subordination in the
form of inarticulate
protest or primitive rebellion directed against repressive state
agents (Jacobs &
Carmichael, 2002). Jacobs and Carmichael (2002) provided the
most comprehensive
test of this perspective. Using cities as the unit of analysis, they
found that the presence
of a Black mayor—whose presence they consider a direct
political explanation—was
consistently significant and inversely related to police killings
across many model
specifications. Thus, their study provided strong support for
their key theoretical find-
ing and the racial threat hypothesis. However, a reanalysis and
extension of Jacobs
and Carmichael found no support for a Black mayor effect
(Kaminski & Stucky,
2005). Findings from research that included other measures that
may be interpreted
as being consistent with the conflict/racial threat perspective
(e.g., percentage Black
and income inequality) have been inconsistent (Table 1).
In summary, the extant research provides little empirical
support for any particu-
lar theoretical perspective, no less any specific explanatory
factor. Testing compet-
ing theoretical perspectives is beyond the scope of the present
study, suffice to say
that the structural covariates examined here are most closely
aligned with social dis-
130. organization theory and the neoclassical community-control
perspective articulated
by Land et al. (1990).
Extending the Analysis of Structural Conditions to Counties
Social disorganization theory and its extensions have been
developed and tested
primarily in urban settings, and there has been some debate in
the literature as to
whether or not it is appropriate to extend the analysis of the
structural factors spec-
ified by social disorganization theory to (largely) nonurban
areas such as counties
(Bailey, 1984; Osgood & Chambers, 2000; Petee et al., 1994).
However, as Osgood
and Chambers (2000) pointed out, the concept of social
disorganization was origi-
nally developed by Thomas and Znaniecki (1958) to explain the
impacts of migra-
tion and industrialization in urban areas in Chicago as well as in
rural areas in
Poland. Drawing on the work of Bursik and Grasmick (1993)
and others (e.g.,
Wilkinson, 1984), Osgood and Chambers (2000) argued that the
private, parochial,
358 Homicide Studies
and public systems of social control are as applicable to crime
in rural areas as they
are to urban communities: “The logic by which primary,
parochial, and public
spheres would affect social control has everything to do with
131. general principles of
social relations and nothing to do with urban versus rural
settings” (p. 85). Similar
sentiments were expressed by Land and colleagues (1990) in
their tests of the invari-
ance thesis, and they argued that a general theory of how
structural conditions affect
homicide rates should be capable of accommodating all levels
of spatial aggregation.
The study by Land et al. (1990) and Osgood and Chambers’
(2000) county-level
analysis of structural factors provided substantial theoretical
and empirical support
for the generality of social disorganization theory beyond
metropolitan areas. Given
their findings and the growing number of studies examining the
impact of structural
conditions on crime at the county level (e.g., Baller et al., 2001;
Kposowa et al.,
1995; Weisheit & Wells, 2005), it is important to extend
research on structural con-
ditions and police homicides to counties.
Data and Measures
Data for the dependent variable, the number of law enforcement
officers murdered
in the line of duty between 1990 and 2000 (N = 544), were
obtained by request
directly from the Federal Bureau of Investigation.4 Because we
cannot apportion fed-
eral or state police to counties, only local law enforcement
officer deaths are
included in the analysis (municipal, county, sheriff). Using a
common identifier
(ORI code), each felonious killing was matched to data on the
132. victim officer’s
employing agency in the 1996 Directory of Law Enforcement
Agencies (Bureau of
Justice Statistics, 1998). Using the appropriate state and county
codes in the direc-
tory, we then aggregated the number of officers murdered, the
number of full-time
equivalent (FTE) sworn employees in 1996, and the number of
types of law enforce-
ment agencies in 1996 to counties and county equivalents.5
Because murders of
police are extremely rare events, they are summed over the 11-
year period (see, for
example, Jacobs & Carmichael, 2002; Kaminski & Stucky,
2005). Although shorter
temporal aggregations may be possible using larger units of
analysis, this simply is
not feasible when using counties.
Summary statistics and definitions for the dependent and
independent variables
appear in Table 2. Because felonious killings of police are
summed over a decade and
our exposure variable is based on the population of law
enforcement officers in 1996,
Census-based variables were calculated by averaging 1990 and
2000 values. Variables
controlling for economic disadvantage are poverty,
unemployment, and median
household income. These factors have been linked to higher
rates of crime because
conditions that encourage criminal behavior (e.g., need for
income, leisure time) are
more pronounced in such areas where social-control
mechanisms are weaker and
blocked opportunities generate frustrations that can lead to
133. diffuse hostility and
Kaminski / County-Level Covariates of Police Homicides 359
aggression (Brantingham & Brantingham, 1984; Bursik &
Grasmick, 1993; Krivo &
Peterson, 1996; Parker & McCall, 1999; Sampson, Morenoff, &
Earls, 1999;
Sampson & Raudenbush, 1999; South & Cohen, 1985).
Residential mobility, racial heterogeneity, family disruption,
and large and dense
populations are structural features of communities associated
with weak formal and
informal social controls and thus higher levels of crime and
delinquency (Bursik &
Grasmick, 1993; Kornhauser, 1978; Krivo & Peterson, 1996;
Sampson et al., 1999;
Sampson & Raudenbush, 1999; Shaw & McKay, 1969).
Residential mobility is a key
theoretical construct of social disorganization theory (Shaw &
McKay, 1969), which
argues that high levels of population mobility disrupt a
community’s social relations
and control, leading to higher rates of offending (Kornhauser,
1978; Sampson &
Groves, 1989). We use its inverse for the analysis—residential
stability—defined as
the percentage of the population residing in the same household
as five years earlier.
Consistent with social disorganization theory (Shaw & McKay,
1969), family
breakup is linked to reductions in informal social control as
134. single-parent households
are less able to provide supervision and guardianship for their
own children, household
property, and the community generally (Sampson, 1985;
Sampson & Groves, 1989).
Family disruption is measured by the percentage of the
population that is divorced.
Population size and density are included as measures of
population structure.
Large and dense populations are thought to increase crime and
delinquency because
they weaken interpersonal ties and inhibit social participation in
local affairs, leading
to a weakening of social-control mechanisms (Brantingham &
Brantingham, 1984;
Land et al., 1990; Sampson, 1986; Sampson & Groves, 1989).
Increases in popula-
tion size and density are also thought to increase the likelihood
of social contact and
interpersonal conflict (Blau & Blau, 1982; Blau & Golden,
1986), proximity to moti-
vated offenders (Cohen, Kluegel, & Land, 1981), and
opportunities for the commis-
sion of predatory crimes (Felson, 1998). In addition, because
counties may consist of
a mix of rural and urban areas, and urbanicity versus rurality
has been found to be an
important determinate of crime (Kposowa et al., 1995;
Wilkinson, 1984), we also
include the percentage of the county population that resided in
an urban area.
High levels of racial/ethnic heterogeneity impede
communication, patterns of
interaction, and the ability of residents to achieve consensus
135. and control, thus
increasing the potential for crime and delinquency (Parker et
al., 1999; Sampson &
Groves, 1989; Shaw & McKay, 1969).6 However, rather than
including a measure of
racial/ethnic heterogeneity, we use the percentage of the
population that is (non-
Hispanic) Black. There are three reasons for choosing this
measure. First, relative to
their representation in the population, African Americans are
disproportionately rep-
resented among felons who murder police. Specifically, Blacks
represent about 13%
of the population, but 43% of felons who kill police (Brown &
Langan, 2001). (This
disproportionality, of course, increases substantiality if one
were to consider that
most felons who kill police are male and neither very old nor
very young.) Second,
rates of violent crime tend to be especially high in poor, Black
communities (Blau
360 Homicide Studies
Kaminski / County-Level Covariates of Police Homicides 361
& Blau, 1982; Parker, 2001; Wilson, 1987), which arguably
increases police risk of
violent victimization. Third, percentage Black has been the
most commonly used
measure of race in studies of homicide (Land et al., 1990;
Parker et al., 1999) and in
studies of murders of police (Table 1). Using percentage Black,
therefore, allows for
136. a greater number of direct comparisons of the effect of race at
the county level to its
effects at other levels of aggregation.
Control Variables
Control variables are measures of age structure, region, violent
crime, and
types of law enforcement agencies within counties. Previous
studies find virtually no
Table 2
Summary Statistics for Variables Used in the Analysis
Variable Min Max Mean SD
POLKIL—No. of officers killed 0 26 0.18 0.92
feloniously, 1990-2000
SWORN—No. of FTE sworn officers 1 41,049 191 1,060
in 1996
AGENCY—No. of sheriff’s agencies in 0 100.0 32.3 24.3
county in 1996
POPULATION—Population size 87 9,191,251 84,803 303,660
DENSITY—Population density 0.10 25,054 193 836
URBANICITY—% population residing 0 100.0 15.0 30.0
in urban area
POVERTY—% population below official 0 57.2 15.2 7.0
poverty line
UNEMPLOYMENT—% population 0 23.9 5.0 2.1
unemployed
137. INCOME—Median household income 12,200 70,167 29,550
7,553
DIVORCE—% divorced population 1.8 16.1 8.2 1.8
RESTABLE—% in same house as 5 yrs. 14.4 81.3 58.8 7.7
earlier
AGE2534—% population aged 25-34 7.5 28.1 14.9 1.52
BLACK—% non-Hispanic Black 0 86.1 8.6 14.4
population
REGION—Region, Census classification 1 4 2.4 1.4
VIOLENT CRIME—Avg. no. of violent 0 125,918 534 3,798
crimes, 1994-1996
Note: Data on the 544 police killed feloniously in the line of
duty 1990-2000 are from the Federal Bureau
of Investigation; data on the number of full-time equivalent
(FTE) sworn law enforcement officers are from
the Bureau of Justice Statistics (1998); Census variables are
averages of 1990 and 2000 values; violent
crimes are mid-decade estimates based on the average number
of violent crimes 1994-1996 (excluding
rape) and are from the FBI’s Uniform Crime Report (UCR;
missing data were taken from adjacent years).
association between age structure and murders of police (Table
1). However, statis-
tics compiled by the FBI show that somewhat older offenders
tend to kill police. For
instance, of felons who murdered police between 1988 and
1997, 11.1% were under
18 years of age, 37.0% were aged between 18 and 24 years, and
another 51.9% were
138. aged 25 years or older (table 20 in Federal Bureau of
Investigation, 1997, p. 36).
Therefore, we include the percentage of the population aged 25-
34 years to control
for the potential effect of differences across counties in age
structure (we test alter-
native age groupings as well).
Indicators of region are included to control regional differences
in police homicide
risk. Kaminski et al. (2000) identified significant spatial
clustering of homicides of
police in the southeastern United States, and simple tabular
analyses adjusting for
levels of violent crime, arrests, population, or the number of
law enforcement officers
employed consistently show that police are at greater risk of
being murdered in the
South than in other areas (Cardarelli, 1968; Federal Bureau of
Investigation, 1997;
Fridell & Pate, 1997; Geller & Scott, 1992). Although
substantial theoretical and
empirical work has focused on cultural/subcultural differences
for explaining higher
levels of violence among Southerners and other groups
(Corzine, Huff-Corzine, &
Whitt, 1999; Ousey, 2000),7 other research suggests structural
poverty and economic
inequality account for the higher levels of homicide observed in
the South (Blau &
Blau, 1982; Loftin & Hill, 1974; Smith & Parker, 1980;
Williams, 1984). Regardless
of the causes, it is important to control for regional differences,
and we include indi-
cators of the South, West, and Midwest, with the Northeast
serving as the reference
139. category (Bureau of the Census classification).
Studies of whether police risk of homicide varies by type of law
enforcement
agency have not been conducted. We do not hypothesize a
direction for the effect of
agency type, but sheriff’s departments and other types of
agencies (municipal and
county police departments) can differ in function, geographic
coverage, or in other
ways that may affect risk (e.g., training, policies). To control
for this possibility, the
percentage of agencies that were sheriff’s offices in 1996
(agency) is included in the
analysis (Bureau of Justice Statistics, 1998). Thus, low values
on this measure indi-
cate counties with many municipal agencies, a value of 100%
indicates counties in
which the only law enforcement agency is a sheriff’s
department (7.9% of counties),
and a zero (7% of counties) represents counties in which there
is no sheriff’s agency
(e.g., a county police department has jurisdictional
responsibility).
A final variable included in our model, violent crime, is what
Kaminski, Jefferis,
and Gu (2003) referred to as propensity for violence. Using
Uniform Crime Report
(UCR) data (Federal Bureau of Investigation, 2001), this is the
average of the sum
of the number of homicides, aggravated assaults, and robberies
per county between
1994 and 1996 (rape is excluded because it is one of the least
reliably reported
crimes).8 To reduce collinearity with the other variables in the
140. model, we regress vio-
lent crime on three structural factors derived from a principal
components analysis
(discussed later), and use the residuals in the regression
(Roncek, 1997). The violent
362 Homicide Studies
crime residuals represent the level of violent crime in counties
not explained by their
structural characteristics (plus error). Previous research found
this measure was pos-
itively associated with serious but nonfatal assaults on police at
the block-group level
in Boston (Kaminski et al., 2003), and we anticipate that police
risk of being mur-
dered will be higher in counties that have a greater propensity
for violence, net of
structural conditions and other variables in our model.
Methods
There are three issues that deserve careful attention in the
analysis of homicides
of police across enumeration units; these are the rare-event–
count nature of police
killings, spatial autocorrelation, and multicollinearity among
the regressors. An
additional concern is the presence of within-unit heterogeneity
when analyzing large
spatial aggregates, such as states or counties (Bailey, 1984;
Osgood & Chambers,
2000). Each issue is discussed in turn.
141. As displayed in Figure 1, the distribution of the number of
murders of police
office across counties and county equivalents over the 11-year
period is extremely
skewed. No officers were murdered in 89% (2,776) of the 3,105
counties, one offi-
cer was slain in 8.1% (251) of the counties, and in only 2.5% of
the counties were
two or more officers murdered.
Two common strategies for dealing with skewed data are to
transform the dependent
variable to approximate normality and proceed with linear
regression, or to combine all
outcomes greater than zero into a single category and employ
binary logistic regression.
Transformations of these data, however, are unable to
approximate a normal distribu-
tion, and dichotomizing the dependent variable for use with
binary logistic regression
results in a loss of efficiency (Cameron & Trivedi, 1998). First
recommended by
Kaminski (1997) for analyzing police killings, a now common
strategy for analyzing
outcomes with many zeros and large positive skew is the use of
count regression mod-
els, such as the Poisson, which we employ for the analysis
(Cameron & Trivedi, 1998;
Long, 1997).9 Further, to control for unequal exposure, that is,
differences in the number
of law enforcement officers at risk across counties, we include
the number of FTE
sworn officers in 1996 as an offset in the regression (Long &
Freese, 2001).
A second major concern in studies using spatially contiguous
142. units such as coun-
ties or states is spatial autocorrelation, which when present can
lead to underestima-
tion of standard errors of parameter estimates (Odland, 1988).10
Tests for global and
local spatial autocorrelation on the dependent variable, without
regressors, were sta-
tistically significant (Anselin, 2003).11 Note, however, that the
spatial dependence
may be adequately accounted for with the introduction of
regressors (Baller et al.,
2001). Two procedures are used to test for residual spatial
dependence following the
introduction of the regressors. First, using the number of FTE
sworn officers per
county as the population at risk, we used SatScan’s spatial scan
statistic to test for
Kaminski / County-Level Covariates of Police Homicides 363
364 Homicide Studies
statically significant clustering of police homicides across
counties, with the
assumption that the number of murders in each county is
Poisson distributed
(Kulldorff, 1997, 2006). As anticipated (see, for example,
Kaminski et al., 2000),
this identified a large statistically significant cluster (p = .001)
in the southeastern
United States. Next, to adjust for covariates, we replaced the
number of FTE sworn
officers per county with the predicted values from our Poisson
regression model.12
143. No statistically significant clusters were detected with the
introduction of the pre-
dicted values, suggesting that spatial autocorrelation is no
longer problematic once
the regressors are in the model (Kulldorff, 2006).
Anselin’s alternative method was used as a second test for the
presence of spatial
dependence (Kubrin & Weitzer, 2003; Land & Deane, 1992).
This strategy involves
Figure 1
Frequency Distribution of 544 Law Enforcement Officers
Murdered Across 3,105 Counties, 1999-2000
1 2 3 4 5 6 7 11 12 14 16 20 26
Number of Officers Murdered
50
100
150
200
250
N
um
be
r o
144. f C
ou
nt
ie
s
Note: Counties with zero counts excluded.
a two-stage estimation procedure where the predicted values of
the dependent vari-
able from a regression model are multiplied by a spatial weights
matrix.13 The result-
ing product is then included as a variable in the final regression
model to adjust for
any remaining spatial dependence. This term was not nearly
statistically significant
(p = .62) and its inclusion had virtually no impact on the other
included regressors.
Given the negative results of both tests, we conclude that
spatial autocorrelation is
not problematic. (Complete results of the tests are available
upon request.)
A third major concern is collinearity among the regressors, an
apparent common
problem in early general homicide research (Land et al., 1990).
Diagnostic tests
were conducted using multiple linear regression, and the results
suggested problems
with multicollinearity. Although variance inflation factors were
not very high (four
145. regressors had values greater than 4.0 but less than 6.0), 5
condition indices were
greater than 15 (suggestive of a problem) and 2 were greater
than 30 with variance
proportions greater than .50, indicating a serious problem
(Belsley, Kuh, & Welsh,
1980; Myers & Well, 2003). Thus, we followed the example of
Land et al. (1990)
and conducted a principal components analysis on conceptually
similar regressors.
All regressors loaded into interpretable components at .80 or at
a higher level. Three
components were extracted, explaining 78.1% of the variance.
Component 1 is eco-
nomic disadvantage, which consists of poverty, unemployment,
and income.
Population size and density comprise component 2 (population
structure), and com-
ponent 3 is referred to as instability, which consists of the
percentage of the popula-
tion that is divorced and the percentage of the population still
residing in the same
household as 5 years earlier (inversely related).14 Regression
diagnostics after sub-
stituting these components for the original regressors showed
substantial improve-
ment in the collinearity diagnostics (no condition index greater
than 30 and only one
variance inflation factor greater than 4.0).
A final concern in the study is that spatially large aggregates
such as states or coun-
ties is the problem of within-unit heterogeneity (Bailey, 1984;
Osgood & Chambers,
2000). Osgood and Chambers (2000) warned, for example, that
analysis at the county
146. level treats a single value of each variable as being
characteristic of an entire county,
whereas communities within a county may deviate substantially
from the average. This
results in decreased variation in the independent variables,
thereby reducing the abil-
ity to detect statistical relationships. However, Osgood and
Chambers argued, “If a
meaningful level of variation occurs across counties, strong
relationships should be
apparent, and any lack of precision would not introduce
systematic biases” (p. 90).
Their county-level analysis provided substantial empirical
support for their position.
Findings
Table 3 presents the results from four Poisson regression
models. Model 1 shows
the initial estimates using all counties and all observations.
Model 2 excludes three
Kaminski / County-Level Covariates of Police Homicides 365
366 Homicide Studies
potentially high-leverage counties (New York, Los Angeles, and
Cook counties).15
Model 3 excludes counties with populations less than 50,000
residents to determine
whether the obtained estimates are affected by the extreme
variability in county pop-
ulation size (see, for example, Loftin & McDowall, 2003).
147. Finally, Model 4 excludes
both the three high-leverage counties and counties with
populations less than 50,000.
To conserve space, only exponentiated coefficients and
indicators of statistical sig-
nificance are presented (the full results are available upon
request).
As shown in Model 1, economic disadvantage is strongly
associated with
increased risk of police homicide (β = 1.31; p ≤ .000). The
model suggests that each
unit increase in the economic disadvantage component is
associated with a 31%
increase in the expected mean number of murders of police,
controlling for other fac-
tors in the model. The impact of economic conditions is nearly
identical when New
York, Los Angeles, and Cook Counties are excluded (Model 2).
Although the magni-
tude of the effect is attenuated somewhat when excluding the
smaller counties (Model
3), and when both smaller counties and the three outliers are
excluded (Model 4), it
remains statistically significant and substantive. Therefore, we
conclude that adverse
economic conditions are related to police risk of homicide at the
county level.
Table 3
Poisson Regression Models for All Counties, Counties With
Populations
>> 49,999, and After Removal of Three Influential Counties
Model
148. 1 2 3 4
Population Pop. > 49,999 &
Variable All Counties –3 Counties > 49,999 –3 Counties
Economic disadvantage 1.314*** 1.289*** 1.186** 1.159*
Population structure 0.961** 0.999 0.961* 0.970
Instability 0.993 0.975 0.958 0.919
Black 1.010** 1.010** 1.017*** 1.016***
South 1.609* 1.668** 1.634* 1.703*
West 1.739* 1.717* 1.986** 2.027*
Midwest 1.574* 1.711** 1.523* 1.769**
Urban 0.994*** 0.994*** 0.997 0.997
Age 25-34 1.073** 1.067* 1.062* 1.064.097
Violent crime (residual) 1.008 1.029 1.006 1.028
Agency 1.000 1.001 0.991* 0.992.102
Sworn (offset) 2.718 2.718 2.718 2.718
Constant –8.148 –8.097 –8.207 –8.286
McFadden’s Pseudo R2 0.4570 0.3787 0.4878 0.3907
Note: Coefficients are exponentiated incidence rate ratios;
significance tests are based on robust standard
errors; constants are not exponentiated.
*p ≤ .05. **p ≤ .01. ***p ≤ .001.
Kaminski / County-Level Covariates of Police Homicides 367
Population structure is significant in Model 1 (β = .961; p =
.007) and Model 3
(β = .961; p = .022); however, unexpectedly, it is inversely
related to killings of
149. police. Thus, this model suggests that the risk of being killed
feloniously in the line
of duty is lower in counties characterized by large and dense
populations. However,
population structure is not nearly statistically significant in
Model 2 (β = .999; p =
.975) or Model 4 (β = .980; p = .616). Therefore, its impact in
Models 1 and 2 is
dependent on the inclusion of Los Angeles, New York, and
Cook Counties. This is
not surprising, as these counties have the largest police and
civilian populations in
the United States, and New York County/City ranks highest in
population density.
Interestingly, urbanicity affects the risk of police being killed
feloniously in the
line of duty independently of population size and density, with
the risk being lower
in counties with larger urban populations (β = .994; p ≤ .000).
Specifically, each
additional percentage of the population residing in an urban
area is associated with
a 6% decrease in the risk of officer homicide. The estimates are
virtually identical in
Models 1 and 2; thus, the effect of urbanicity is insensitive to
removal of the high-
leverage counties. However, urbanicity is statistically
insignificant in Models 3 and
4, suggesting it is important only when many, largely rural
counties are included.16
The third component, residential and family instability, is
unrelated to homicides
in Model 1 (β = .993; p = .915), and it remains statistically
insignificant in the remain-
150. ing models. The bivariate analysis described earlier (see Note
14) suggested that per-
cent divorced, but not percent still residing in the same
household as 5 years earlier,
was related to murders of police. To assess their independent
effects, Models 1-4 were
reestimated using the original variables one at a time in place of
the component. In no
instance was either of the variables related to police killings (all
p > .15).17
Model 1 suggests that each one unit increase across counties in
the percentage of
the population that is non-Hispanic Black is associated with a
1% increase in risk of
police homicide (β = 1.01; p = .002). The effect of race is
virtually unchanged with
the removal of New York, Los Angeles, and Cook Counties
(Model 2), whereas it
increases somewhat in magnitude in Models 3 and 4 (β = 1.017
and 1.016, respec-
tively). Thus, the risk of police being killed feloniously appears
to be higher in coun-
ties with larger proportions of Black residents.
The three regional indicators in Model 1 show that the risk of
homicide is sub-
stantially and significantly lower in the Northeast than in the
other three regions.
County location in the South, for example, is associated with a
61% increase in the
expected number of police homicides. To test whether risk in
the West and Midwest
regions is significantly different than in the South, we
reestimated Model 1 using the
South as the reference category. The results (not displayed)
151. indicate that neither the
West (β = 1.08; p = .621) nor the Midwest (β = 0.98; p = .859)
are significantly dif-
ferent from the South regarding police homicide victimization
risk. Although we
observe some variation in the magnitudes of the estimates and
levels of significance
across the four models, the conclusion remains the same; the
risk of homicide is
significantly higher in the South, the Midwest, and the West
than in the Northeast,
but the South is no riskier than the West or Midwest.
As expected, police risk of being killed feloniously is greater in
counties with
larger percentages of persons aged 25-34 years. In Model 1,
each one unit increase
in the age variable is associated with 7.3% increase in the
expected number of police
homicides (β = 1.073; p = .006). The magnitude of the effect is
similar across all
models, but in Model 4 it is statistically significant at the .10
level only (β = 1.06;
p = .097). We find a similar impact when substituting the
percentage of persons aged
35-44 years in Model 1 (not shown), but it is significant only at
the .10 level
(β = 1.09; p = .081). However, this age group does not approach
statistical signifi-
cance when the high-leverage counties are removed and/or when
smaller population
counties are excluded. Estimates for the percentages of persons
aged 14-17, 18-24,
152. and 45-54 years are unrelated to murders of police in all models
(results not shown).
In Model 1, the violent crime residuals and the percentage of
law enforcement agen-
cies that were sheriff’s offices are unrelated to murders of
police (both p > .24). The vio-
lent crime residuals remain insignificant in Models 2-4, but the
percentage of sheriff’s
agencies is statistically significant in Model 3 (β = 0.991; p =
.039), perhaps due to
greater variability in the mix of agency types in the larger
counties. Although limited to
larger population counties, this suggests that police homicide
risk may be higher in
counties that contain greater proportions of non-sheriff’s
agencies. Note, however, that
in Model 4 the effect is not quite significant at the .10 level (β
= 0.992; p = .102).
The models explain substantial amounts of the variance
(McFadden’s R2 ranges
from .36 to .49). To further assess model fit, deviance residuals
were plotted against
observation numbers (Hardin & Hilbe, 2001, p. 43), both before
and after removal
of the three high-leverage counties and counties with
populations less than 50,000
(see Figure 1A in Appendix). In the top graph, we observe two
counties for which
Model 1 does a particularly poor job predicting police
homicides. These are
Jennings County, Indiana, (population 25,608; two murders) and
Powell County,
Kentucky (population 12,467; two murders). The largest
negative residual is for San
153. Bernardino County, California (population = 1,563,907; zero
murders). The pattern
of the residuals improve somewhat with removal of the small
population counties
and the three influential cases, but clearly the models have a
tendency to underpre-
dict police homicide counts. Generally, however, the residuals
appear reasonable.
In summary, the analysis provides strong support for the effects
of adverse eco-
nomic conditions, the percentage of the non-Hispanic Black
population, and region
on the geographic patterning of police homicides in the
contiguous United States.
There is also substantial support for the impact of urbanicity
(when all counties are
included) and the percentage of the population aged 25-34
years. The effect of the
proportion of non-sheriff’s agencies appears to be important
only for larger popula-
tion counties, whereas the effect of population structure is
conditional on the inclu-
sion of the three high-leverage counties. We find no evidence
that residential
instability, divorce, or the violent crime residuals are related to
police homicides.
368 Homicide Studies
Discussion
One of the more robust findings of the analysis is the effect of
adverse economic
154. conditions on police risk of homicide victimization, and we
conclude that local police
are significantly more likely to be murdered in counties
characterized by low levels of
income and high levels of poverty and unemployment.
Economic strains increase
motivations for crime, weaken formal and informal social
controls, and generate
frustrations leading to diffuse hostility and aggression
(Brantingham & Brantingham,
1984; Bursik & Grasmick, 1993; Krivo & Peterson, 1996;
Parker & McCall, 1999;
Sampson et al., 1999; Sampson & Raudenbush, 1999; South &
Cohen, 1985), which
arguably increase police officer proximity and exposure to
motivated offenders.
Although this finding is consistent with some previous research
on police killings
(Batton & Wilson, 2006; Chamlin, 1989; Kaminski, 2002, 2004;
Kaminski & Marvell,
2002) and research on serious but nonlethal violence directed
against police (Kaminski
et al., 2003), evidence for the impact of economic conditions on
officer homicide vic-
timization has largely been mixed (see Table 1). This
inconsistency, however, may be
due to methodological shortcomings or other differences among
studies. In any case,
this study provides strong support for the effects of economic
conditions.
Because residential mobility, family disruption, and large and
dense populations
have been associated with weak, formal and informal social
controls and higher
levels of crime (Bursik & Grasmick, 1993; Kornhauser, 1978;
155. Krivo & Peterson,
1996; Sampson et al., 1999; Sampson & Raudenbush, 1999;
Shaw & McKay, 1969),
we expected these factors to be positively associated with
homicides of police.
Residential stability and divorce, whether entered individually
or as a combined
component, were unrelated to police homicides. Most studies
have not included
measures of population mobility, but the limited evidence to
date also suggests that
it is unrelated to murders of police (Kaminski, 2002, 2004).
Several previous stud-
ies examined the impact of divorce, but with mixed results
(Table 1).
Previous research on the effects of urbanicity and population
size and density on
police homicide risk almost universally failed to find a
relationship (see Table 1).
Interestingly, although we predicted a positive association
between these factors and
murders of police, our analysis found that the risk of homicide
is actually lower in more
urbanized counties and in counties with large and dense
populations (though the impact
of population size/density is dependent on the inclusion of the
high-leverage counties).
Although only speculation, a possible explanation may be found
in differences in the
availability and quality of emergency trauma care between rural
or largely rural counties
and their more urban counterparts (Kaminski et al., 2000;
Kaminski & Marvell, 2002).
For example, in urban areas transport times are faster, high
patient volume helps main-
156. tain provider skills, and greater population density increases
local public financing
(Bonnie, Fulco, & Livermore, 1999). Although research shows
significant differences
between rural and urban areas in mortality rates from traumatic
injury (Bonnie, Fulco, &
Livermore, 1999), research on general homicides and medical
resources is less conclu-
sive (Doerner, 1988; Hanke & Gundlach, 1995; Giacopossi,
Sparger, & Stein, 1992;
Kaminski / County-Level Covariates of Police Homicides 369
Long-Onnen & Cheatwood, 1992). Kaminski and Marvell (2002)
tested the effect of the
adoption of statewide trauma care systems on police homicides,
but found no evidence
of a relationship. Addressing the role of trauma care is beyond
the scope of this study,
but future work should examine its potential impact using
improved measures.
The analysis found that police were significantly more likely to
be killed felo-
niously in counties with larger Black populations. One
explanation for this finding
is that the high rates of violent crime in Black communities
(Blau & Blau, 1982;
Parker, 2001; Wilson, 1987) increase police proximity and
exposure to offenders
who are willing to resort to violence to avoid arrest and
punishment, including vio-
lence against the police (Kaminski, 2002, 2004). If this were
true, we would expect
157. the effect of race to diminish once we controlled for levels of
violent crime and other
conditions (e.g., economic deprivation, and residential and
family instability).
However, percentage Black remained statistically significant
even with these vari-
ables in the model. Other recent research also found that the
effect of percentage
Black persisted, despite the inclusion of large numbers of
regressors (Jacobs &
Carmichael, 2002; Kaminski & Stucky, 2005). Additional
research is needed to
explain the persistence of percentage Black in studies of
violence against the police.
None of the previous studies using cities or states as the unit of
analysis found
strong support for regional differences in police homicide risk
(with all but one study
using simple South vs. non-South comparisons), but the
regional indicators in our
analysis showed that police risk of being murdered was
significantly lower in coun-
ties located in the Northeast. Because our models controlled for
the number of police
at risk, the types of law enforcement agencies within counties,
and a variety of social
and economic conditions, we are unable to explain the
persistence of the regional
effects. Interestingly, although the South typically has been
characterized as being
particularly risky for police relative to other regions (Kaminski
et al., 2000), our
results show that Southern counties were no riskier for police
than counties located in
the West or the Midwest, seemingly negating Southern
158. subculture of violence expla-
nations for the high rate of police homicide victimization
observed in the South.
We found that police risk of being killed was higher in counties
with larger per-
centages of residents aged 25-34 years. The effect is significant
across all models
except for the last (large population counties without outliers),
where the effect is
significant at the .10 level. Estimates for older age groups are
similar (age range of
35-44 years and 45-54 years), but not statistically significant in
most models,
whereas younger-age categories are unrelated to police killings
(age ranges of 14-17
years and 18-24 years). Perhaps this finding can be explained by
greater police expo-
sure to somewhat older, violent offenders. For example, violent
crime index arrest
statistics compiled by the FBI show that the modal age category
of arrestees in 1995
was 25-34 years (Federal Bureau of Investigation, 1995: table
39, pp. 218-219).
Although previous studies found virtually no association
between age structure and
police killings, our results suggest that it may be premature to
dismiss age effects in
macrolevel studies of violence against police.
370 Homicide Studies
The analysis controlled for variation in the types of law
enforcement agencies across
159. counties (percentage of sheriff’s agencies) because the risk of
officer victimization may
be related in unknown ways to differences among them (e.g.,
function, geographical
coverage). The results suggest it may be important to do so in
county-level analyses.
Although not statistically significant when small population
counties are included, there
is evidence of an effect when analyzing larger population
counties. This is probably
because smaller population counties are less likely than larger
population counties to
contain many municipal police departments.18 In any case,
when restricted to larger
population counties, the analysis suggests that police homicide
risk increases with
increases in the proportion of non-sheriff’s agencies. Further
study of violence against
police by agency type or function may be an interesting topic
for future research.
One previous study found that variation in levels of violent
crime was predictive
of serious but nonfatal attacks on police, even when various
structural conditions
were controlled (Kaminski et al., 2003). However, despite the
use of various mea-
sures of violent crime (violent crime residuals, violent crime
count, violent crime
rate, violent crime rate residuals, and general homicide rate),
we find no evidence of
an effect at the county level. It may be that the propensity for
violence measure oper-
ates only at a local level of spatial aggregation. Another
possible explanation for the
lack of an effect is measurement error associated with county-
160. level UCR data (see
Maltz & Targonski, 2002), and an appropriate assessment of the
impact of violent
crime at the county level may need to await corrections to those
data.
To summarize, previous studies of homicides of police across
enumerations units
have been limited to analyses using cities or states, and we
believe our findings
demonstrate the utility of using county-level data to explain the
patterning of killings
of police across the contiguous United States. We employed
regression models appro-
priate for the analysis of rare-event counts; controlled the
underlying population at
risk; and checked for overdispersion, spatial autocorrelation,
multicollinearity, and
the influence of high-leverage counties. The models appear
adequate, and the
included regressors explain substantial amounts of the
“variance” in police killings.
The results show that police homicide risk is higher in
economically depressed
counties, in less urbanized counties, in counties with larger
percentages of Black resi-
dents, and in counties located in the South, West, and Midwest.
Although less consis-
tent, there is some evidence that police homicide risk is higher
in counties with larger
percentages of non-sheriff’s agencies and persons aged 25-34
years. Population struc-
ture (size and density) was inversely related to murders of
police, though its impact is
dependent on the inclusion of three high-leverage counties. We
161. found no evidence that
police killings are related to two traditional measures of social
disorganization—
population mobility and divorce rates. Finally, various measures
of violent crime were
unrelated to police homicides. Although this study helps explain
the patterning of
murders of police across the United States, given the overall
lack of consistency of
findings in the extant research, we encourage further study of
the causes and correlates
of violence against the police at multiple levels of areal
aggregation using additional
and improved measures.
Kaminski / County-Level Covariates of Police Homicides 371
372 Homicide Studies
Figure 1A
Index Plots of Hat Diagonals Before & After Removal
of Los Angeles, New York, & Cook Counties
ha
t d
iag
on
al
Observation Number
162. 0 500 1000 1500 2000 2500 3000
0
.25
.5
.75
1
1.25
LA NY
Cook
ha
t d
iag
on
al
Observation Number
0 500 1000 1500 2000 2500 3000
0
.25
.5
.75
163. 1
1.25
Appendix
Kaminski / County-Level Covariates of Police Homicides 373
Figure 2A
Index Plots of Deviance Residuals Using All Counties, and
Minus Los
Angeles, New York, & Cook Counties & Counties With
Populations << 50,000
de
via
nc
e r
es
idu
al
Observation Number
0 500 1000 1500 2000 2500 3000
–3
–2
164. 0
2
3
4
San Bernardino County, CA; pop = 1,563,907; 0 killed
Jennings County, IN; pop = 25,608; 2 killed
Powell County, KY; pop = 12,467; 2 killed
de
via
nc
e r
es
idu
al
Observation Number
0 500 1000 1500 2000 2500 3000
–3
–2
0
2
165. 3
4
Appendix (continued)
Notes
1. One previous study used counties as the unit of analysis to
test for statistically significant spatial clus-
tering of police homicides, but that study controlled only for the
underlying civilian population to estimate
risk (Kaminski, Jefferis, & Chanhatasilpa, 2000). Because the
current study uses multiple regression to
explain the variation of murders of police across the United
States, it represents a substantial improvement.
2. Attractiveness also is a major component of opportunity
theory and is typically conceptualized as
the symbolic or economic value of targets to offenders
(Garofalo, 1987, pp. 38-39; Miethe, Hughes, &
McDowall, 1991, p. 166; Miethe & McDowall, 1993, p. 749).
However, the concept of attractiveness as
applied to the victimization of police officers requires
substantial redefinition. Although some police offi-
cers may be sought out and murdered because of their
“symbolic” value (e.g., killed because they are per-
ceived as being representatives of a repressive government),
because most officers are murdered by
offenders engaged in serious crime who wish to escape and
avoid punishment (Cardarelli, 1968; Creamer
& Robin, 1970; Margarita, 1980b), it is arguable that
instrumental rather than expressive motives can be
attributed to most offenders’ decisions to kill police:
166. The motivation is not to harm police because they are despised
or because officers do something
to anger offenders. Rather, most offenders are motivated to kill
or seriously injure police because
the potential opportunity costs associated with their current
and/or past criminal activities are high
(e.g., safety, loss of freedom, reduced future income). Further,
most active criminals wish to avoid
police, and are unlikely to seek officers out as “attractive”
targets. (Kaminski, 2004, pp. 23-24)
3. African Americans are vastly overrepresented among those
who kill law enforcement officers.
Specifically, though they represent only about 13% of the
population, they constitute about 43% of the
felons who kill police (Brown & Langan, 2001).
4. Data on murders of police are considered to be highly
reliable and valid (Chapman, 1998, p. 8;
Margarita, 1980a, p. 16), and they do not suffer from data
problems typically associated with the Uniform
Crime Report (Maltz & Targonski, 2002). Homicides of police
are the most widely publicized events in
law enforcement, and when assailants remain at large all law
enforcement agencies are notified, includ-
ing the FBI, with the hope that the perpetrator will be
apprehended. When local police apprehend a sus-
pect, at a minimum the FBI is notified to access the suspect’s
criminal history file prior to trial (Chapman,
1998, p. 8; Konstantin, 1984, p. 34). In addition to receiving
notification of duty-related deaths directly
from state and local law enforcement agencies, the FBI receives
notification from its field divisions and
legal attaché officers, and from the Public Safety Officers’
Benefits Program (administered by the Bureau
167. of Justice Assistance). Once notification has been made, the FBI
obtains additional details concerning the
circumstances surrounding the death from the victim officer’s
employing agency. The primary source of
error is the rare incident where the cause of death is not clearly
identified (Konstantin, 1984, p. 34).
5. The five New York City Counties (Richmond, Queens, Kings,
Bronx, and New York) were merged
into a single polygon and treated as a single entity because the
data did not allow for the apportioning of
New York City police officers killed to their respective
boroughs. Other adjustments also were made in
merging the county-level data, such as deleting South Boston
County, Massachusetts (because of a
merger), counties in Alaska and Hawaii, and Yellowstone
National Park. The final number of counties
used in the analysis is 3,105.
6. The subculture-of-violence thesis also has been employed as
an explanation for the high Black
crime rates in urban areas (Wolfgang & Ferracuti, 1967), which
essentially posits that some subcultures
provide greater normative support for violence in upholding
values such as honor, courage, and manli-
ness. Although measurement and design issues leave the debate
unsettled, there appears to be more
research support for theoretical perspectives emphasizing
structural rather then cultural explanations
(Parker et al., 1999, p. 109).
7. Cultural/subcultural explanations for the observed high levels
of homicide in the South essentially
posit that the Southern subculture provides greater normative
support for violence in upholding values
168. 374 Homicide Studies
such as honor, courage, and manliness, though not necessarily a
culture that condones violence (Corzine
et al., 1999; Gastil, 1971; Hackney, 1969). Cultures more
supportive of expressions of physical aggres-
sion and combat in response to threats to one’s honor or as a
measure of daring and courage increase the
likelihood of violence and homicide (Wolfgang & Ferracuti,
1967).
8. Crime data were not available for 128 counties. Also, we
advise readers that county-level crime
data suffer from a number of limitations, and thus caution must
be used when interpreting the effects of
this regressor (for details, see Maltz & Targonski, 2002).
9. In practice, count data are frequently overdispersed; that is,
the variance is greater than the mean,
which violates the Poisson assumption of equidispersion (the
mean and variance of the event counts are
equal). In this case, the Poisson regression model can produce
inefficient (though consistent) estimates,
and z tests may overestimate the significance of variables
(Long, 1997, p. 230). An alternative to the
Poisson under these conditions is the negative binomial
regression model. However, a likelihood-ratio test
of the overdispersion parameter from a negative binomial
regression suggests our model is not overdis-
persed, and a comparison of estimates and standard errors
across models shows virtually no differences.
These results are available on request. Note further that given
the large number of zero values a zero-
inflated Poisson (ZIP) model is arguably more appropriate for
169. the analysis (Long, 1997). We attempted
to estimate a ZIP model, but for reasons unclear we were unable
to get the model to converge.
10. Spatial autocorrelation can occur when the enumeration
units being analyzed share boundaries
that result in a structure to the data. Units that share physical
boundaries or are closer to each other are
likely more similar than units not sharing physical boundaries
or those that are farther away from one
another. Thus, geographic data may often fail to meet the
assumption that observations are independent.
The consequence is that the errors will not be independent—a
condition necessary for valid hypothesis
tests. The consequences of spatial autocorrelation are the same
as in temporal autocorrelation, that is, the
standard errors will be biased, and t statistics used to test the
null hypothesis may seriously overstate the
statistical significance of an effect. This can lead to the
mistaken conclusion that variables are related
when they are not (Odland, 1988).
11. Global Moran’s I = .0907 (p = .0020) with 999
permutations; local Moran statistics indicate sig-
nificant clustering for 312 observations (p ≤ .05) with 999
permutations.
12. Although SatScan allows the introduction of categorical
covariates, it cannot handle continuous
covariates; hence, Kulldorff’s recommendation to use the
predicted values from a regression model.
13. Our spatial weights matrix consisted of a first-order spatial
lag of the dependent variable using the
queen criterion. All calculations were carried out with GeoDa
(version 9.5-i; Anselin, 2003).
170. 14. We examined each individual regressor’s relationship to
police killings by entering each into
bivariate Poisson model using the number of full-time
equivalent (FTE) sworn officers as the offset.
Poverty, unemployment, and income were all highly significant
(all p ≤ .000) and in the expected direc-
tion. Percent divorced also was highly significant (p ≤ .000) and
positive, but percent still residing in the
same house as 5 years earlier was not significant (p = .902), and
it was in the opposite direction expected.
Population size (logged, as the model using the raw metric
failed to properly converge) and population
density also were both highly significant (p ≤ .000) but
inversely related.
15. Diagonal entries from the regression model’s hat matrix, hii,
are useful for detecting influential
observations (Cameron & Trivedi, 1998, p. 150) and are
presented in Figure 2A in the Appendix. The top
graph suggests that New York City (all five boroughs
combined), Los Angeles County, and Cook County
exert a strong influence on the estimates in Model 1. The
bottom graph in Figure 1A in the Appendix
displays the results after removal of these three counties.
16. Counties with populations less than 50,000 had on average
only 1.9% of the population residing
within urbanized areas (93% had no residents living in
urbanized areas), whereas counties with popula-
tions of 50,000 or more had on average 48.7% of the population
residing within urbanized areas (23%
had no residents living in urbanized areas).
17. We also tested the effect of an interaction term between the
two original variables, but the inter-
171. action term did not even approach statistical significance in any
model.
Kaminski / County-Level Covariates of Police Homicides 375
18. Sheriff’s departments accounted for a third of the agencies
in 21.1% of the small population coun-
ties (SPCs), for half in 24.5%, and they were the sole local law
enforcement agency in 10.7% of the SPCs.
Conversely, sheriff’s departments accounted for a third of
agencies in only 7.8% of the large population
counties (LPCs), for half in 5.7%, and they were the sole local
agency in only 7 counties (0.8%). Thus,
sheriff’s departments accounted for a third or more of the law
enforcement agencies in more than half of
the SPCs (56.3%), but did so in only 14.3% of the LPCs.
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Robert J. Kaminski is an assistant professor in the Department
of Criminology and Criminal Justice,
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public perceptions of the police, police use
of force, violence against the police, less lethal technology,
crime mapping and spatial analysis, and
applied quantitative methods.
380 Homicide Studies
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