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Content uploaded by Alexander C Wagenaar
Author content
All content in this area was uploaded by Alexander C Wagenaar on May 12, 2015
Content may be subject to copyright.
Neighborhood level spatial analysis
of the relationship between alcohol outlet
density and criminal violence
HEATHER R. BRITT
1
, BRADLEY P. CARLIN
2
*,
TRACI L. TOOMEY
3
andALEXANDER C. WAGENAAR
4
1
Minnesota Department of Education, Safe and Healthy Learners Unit, Roseville, Minnesota
2
School of Public Health, Division of Biostatistics, University of Minnesota, MMC 303, Min-
neapolis, Minnesota, 55455-0392
E-mail: brad@biostat.umn.edu
3
School of Public Health, Division of Epidemiology, University of Minnesota, Minneapolis,
Minnesota
4
College of Medicine, Department of Epidemiology and Health Policy Research, University of
Florida, Gainesville, Florida
Misuse of alcohol is a significant public health problem, potentially resulting in unintentional
injuries, motor vehicle crashes, drownings, and, perhaps of greatest concern, serious acts of
violence, including assaults, rapes, suicides, and homicides. Although previous research
establishes a link between alcohol consumption increased levels of violence, studies relating the
density of alcohol outlets (e.g., restaurants, bars, liquor stores) and the likelihood of violent
crime have been less common. In this paper we test for such a relationship at the small area
level, using data from 79 neighborhoods in the city of Minneapolis, Minnesota. We adopt a
fully Bayesian point of view using Markov chain Monte Carlo (MCMC) computational
methods as available in the popular and freely available WinBUGS language. Our models
control for important covariates (e.g., neighborhood racial heterogeneity, age heterogeneity)
and also account for spatial association in unexplained variability using conditionally auto-
regressive (CAR) random effects. Our results indicate a significant positive relationship be-
tween alcohol outlet density and violent crime, while also permitting easy mapping of
neighborhood-level predicted and residual values, the former useful for intervention in the
most at-risk neighborhoods and the latter potentially useful in identifying covariates still
missing from the fixed effects portion of the model.
Keywords: Bayesian, Markov chain Monte Carlo, alcohol, criminal violence, neighborhood
1352-8505 Ó 2005 Springer Science+Business Media, Inc.
1. Background
Misuse of alcohol is a significant public health problem in the United States,
resulting in unintentional injuries, motor vehicle crashes, drownings, and – of special
*Corresponding author
Environmental and Ecological Statistics 12, 411–426, 2005
1352-8505 Ó 2005 Springer Science+Business Media, Inc.
concern–serious violence, including assaul ts, rapes, suicides and homicides (NIAAA,
2000; Edwards, 1997; Greenfeld, 1998). The alcohol establishment (e.g., restaurant,
bar, liquor store) is an important access point for the purchase and, for on-premise
outlets, the consumption of alcohol (Edwards, 1997). Although evidence exists
connecting alcohol consumption to levels of violence, a limited number of studies
have been conducted examining the specific relationship between alcohol availabil-
ity, as defined by alcohol establishment density, and violence (Scribner et al., 1995;
Gorman et al., 1998; Gorman et al., 1998; Speer et al., 1998; Alaniz et al., 1998;
Scribner et al., 1999; Stevenson et al., 1999, Gorman et al., 2001; Reid et al., 2003).
Scribner and co-authors conducted the first of these recent studies, examining the
risk of assaultive violence and alcohol ava ilability in cities within Los Angeles
County (Scribner et al., 1995). The authors discovered that after adjusting for so-
ciodemographic factors, higher levels of alcohol outlet density were significantly
associated with higher rates of assaultive violence (i.e., criminal homicide, forcible
rape, robbery, aggravated assault and domestic violence) within a geographic unit.
A subsequent replication study, examining the same relationship in New Jersey
municipalities, however, did not find that higher alcohol outlet density was associ-
ated with elevated rates of violence (Gorman et al., 1998), nor did a follow-up study
focusing only on domestic violence (Gorman et al., 1998).
In an attempt to clarify the inconsistency regarding the relationship of density to
violence, researchers in New Jersey decided to focus on one city, Newark, and to
geographically link violence rates to outlet density in census tracts and census block
groups, rather than using larger city or municipality definitions of geographic areas.
In doing so, the regression models revealed that alcohol outlet densities were sig-
nificant predicto rs of rates of violent crime at both the census tract level and the
census block group level (Speer et al., 1998). Similar analyses conducted on census
tracts in New Orleans, block groups in Califo rnia and Camden, New Jersey, and
census tracts in Kansas City, Missouri, revealed that outlet density (whether defined
as outlets per square mile or outlets per person) was strongly associated with rates of
various types of assaultive violence (Alaniz et al., 1998; Scribner et al., 1999; Gorman
et al., 2001; Reid et al., 2003).
In the current study we attempt to address limitations of earlier research. Previous
studies have used various units of analysis (i.e., counties, cities, census tracts and
block groups) as the geographic area within which to assess the effect of outlet
density, some of which may not be appropriate due to the nature of alcohol outlet
density. In beginning our analysis, we sought a theoretical perspective to inform our
choice of geographic unit. Skog (1985) suggests that our drinking culture is a system
of interdependent actors – the density of outlets in a neighborhood is linked to the
social network in which these actors live and carry out their daily activities. From
that perspective, analyzing outlet density from the level of individual outlets is
inappropriate, as the effect of density is a summed effect across a geographic area.
We believe that a unit of analysis most appropriately reflecting neighborhoods would
best estimate the effect of density, rather than a larger unit of analysis, such as a city
or county. Parker and Wolz (1979) have noted that density is related to locations
small enough to be influenced by a varying population structure and a stratification
that exists within certain geography. Using larger geographic units may result in a
loss of focus on the fundamental nature of outlet density (Parker and Wolz, 1979).
Britt et al.412
In addition, most previous studies have lacked a solid theoretical model upon which
to base analysis. As a result, we sought an appropriate theoretical perspective to inform
our choice of covariates. Sampson, Raudenbush and Earls, in their work examining
neighborhoods and viole nt crime, have suggested that collective efficacy (cohesion and
trust within a community coupled with expectations for intervening when necessary) is
an informative social theory upon which to base analysis at the neighborhood level
(Sampson et al., 1997). Communities with greater collective efficacy may be able to
better accommodate behaviors of alcohol establishment patrons and may be able to
provide some social control restricting violent behavior within and outside establish-
ments (Sampson and Raudenbush, 1999). Communities with less collective efficacy and
facing greater structural constraints (including heterogeneity in a community, chal-
lenging economic situations, family disruption and heavy urbanization) may be less
able to cope with alcohol establishments and patrons with problems (Sampson and
Raudenbush, 1999). This theoretical perspective suggests a set of covariates reflecting
collective efficacy and structural constraints should make up our analysis model.
Finally, much of the research into the connection between outlet density and
violence has utilized multiple regression, controlling for sociodemographic variables
(Gorman et al., 1998; Gorman et al., 1998; Speer et al., 1998; Stevenson et al., 1999;
Reid et al., 2003). In evaluating spatially related data, however, problems arise
because geographic units are not necessarily independent of one another (Cliff and
Ord, 1981; Upton and Fingleton, 1985; Banerjee et al., 2004). In fact, researchers
would expect that the density of outlets in one neighborhood would be likely to
influence health outcomes in an adjacent neighborhood. Not controlling for spatial
autocorrelation may result in a false positive, i.e., concluding that outlet density has
a significant effect on violence, when it fact it does not. It appears that an analysis
that controls for spatial autocorrelation is necessary in evaluating whether outlet
density is related to violence (Millar and Gruenewald, 1997).
In an effort to address each of the aforementioned limitations, we cond ucted a
cross-sectional ecologic analysis, using spatial smoothing, to evaluate the relation-
ship between alcohol establishment density and criminal violence using neighbor-
hood level data from Minneapolis, Minnesota. We use alcohol outlet density as our
measure of collective efficacy, based upon the notion that organiz ed communities are
able to influence this density. Covariates from the U.S. Census serve as our structural
constraint variables.
2. Methods
We needed to obtain neighborhood level data about alcohol establishments, criminal
violence, and structural constraint variables to perform our analysis. In this section
we review data sources and discuss analysis steps.
2.1 Neighborhoods
The City of Minneapolis is unique in that it contains 84 self-identified neighborhoods
with distinctive geographic borders. Most of these neighborhoods have a
Neighborhood level spatial analysis 413
neighborhood association, street signs identifying the neighborhood, and represent a
combination of census tracts and block groups. Rather than selecting zip codes,
census tracts, or block groups for the geographic unit of analysis for our study, we
were fortunate to be able to use neighborhoods, units that we believe best represent a
geographic location for the activation of collective efficacy (i.e., geograp hic regions
whose residents can unite in an effort to change alcohol outlet density through
common action). Thes e neighborhoods are probably most similar to the ‘‘neigh-
borhood clust ers’’ identified by Sampson and his co-authors in their Project on
Human Development in Chicago Neighborhoods (Sampson et al., 1997). More
specifically, each neighborhood in Minneapolis is a unique combination of census
tracts and block groups (i.e., self identified areas that align well with Census data).
The City of Minneapolis Planning Department provided us with geographic
boundaries of the neighborhoods. Of the 84 neighborhoods initially identifi ed, we
used 79 neighborhoods for the current study, as five of the neighborhoods were
highly industrial areas with few residents and few alcohol establishments. The total
population of the City of Minneapolis, according to the 2000 Census, was 382,618.
The city is 7.6% Hispanic/Latino, 18% African American/Black, 2% American In-
dian, 6% Asian, and 4% two or more races. The remainder of the community is
white/Caucasian. Minneapolis is 55 square miles and has an overall population
density of 6970 residents per square mile.
2.2 Alcohol establishments
We obtained a list of all licensed alcohol outlets in 2000 in Minneapolis using two
sources. Lists of all ‘‘intoxicating liquor’’ establishments (including name, address,
phone and liquor license type) were obtained from the state Liquor Control Division.
Similar lists of all low-alcohol (3.2%) beer (‘‘non-intoxicating liquor’’) establishments
were obtained from the City of Minneapolis. Across the 79 neighborhoods included
in the study, 446 on-premise (i.e., bars, restaurants) establishments and 129 off-
premise (i.e., liquor stores, convenience stores) establishments were included in the
study. Staff from the City of Minneapolis GIS Unit geocoded each alcohol estab-
lishment to one of the 79 neighborhoods. The number of establishments per neigh-
borhood ranged from 0 to 129, with a mean of 7.28 and a median of 3. We calculated
alcohol establishment density (our collective efficacy variable) by taking the total
number of outlets in each neighborhood divided by the total population in that
neighborhood. The skewed nature of the resulting alcohol establishment density
variable suggested a natural log transformation, but because there were neighbor-
hoods without bars (n=9), we first added e =0.00001 to the density in each neigh-
borhood. The resulting log transformed alcohol establishment density has a minimum
of )11.51, maximum of )3.461, mean of )7.447, and median of )7.182.
2.3 Criminal violence data
The second set of data, criminal violence, was obtained from the City of Minneapolis
Police Department (PD). The PD provides crime data by neighborhood by month
Britt et al.414
through its public website. These data are initially collected as part of the PD’s
Computer Optimized DEployment – Focus On Results (CODEFOR) strategy.
CODEFOR data uses the same crime categories as the FBI’s Uniform Crime Report
(UCR) Part I offenses, but counts crimes differently (i.e., CODEFOR counts all
offenses in a multiple offense scenario, as opposed to just the most serious event, as
in the FBI’s UCR). Offenses included in the CODEFOR data include: homicide,
rape, robbery, aggravated assaul t, burglary, motor vehicle theft and arson. Because
crime rates vary dramatically over the course of a year (with seasonal highs and
lows) and can be subject to rapid changes year-by-year (Sherman et al., 1989), we
collected crime data for three years (2000, 2001 and 2002) and created an average of
the total number of crimes per neighborhood. Total average yearly criminal violence
per neighborhood has a minimum of 48 incidents, maximum of 2448 incidents, mean
of 328 and median of 196.
2.4 Structural constraints
We obtained structural constraint data from the City of Minneapolis Planning
Department that specially generates Census data aligning to Minneapolis neigh-
borhoods. Research has demonstrated that a number of neighborhood sociodemo-
graphic characteristics (i.e., structural constraints) are related to rates of violence,
including economic structure of a community, ethnicity, age structure, level of
urbanicity and social structure (Scribner et al., 1995; Gorman et al., 1998). Specifi-
cally, the covariates used include:
a) Heterogeneity in race . This covariate, which represents the percentage of neigh-
borhood residents that are non-white, was calculated by dividing the total of
(black or African American alone; American Indian and Alaska native alone;
Asian, Native Hawaiian and other Pacific Islander alone; some other race
alone; and two or more races) by the total neighborhood population.
b) Heterogeneity in age. This covariate, which represents the ratio of younger
residents to middle age residents, was calculated by dividing the total num-
ber of 15–24 year olds in a neighborhood by the number of 25–44 year olds.
c) Heterogeneity in home ownershi p . This covariate, which represents the per-
centage of housing that is rented in the neighborhood, was calculated by
dividing the total number of renter occupied housing units by the number of
all occupied units in the neighborhood.
d) Ratio of single headed households to family households. This covariate, which
represents the ratio of single headed households to two parent households,
was calculated by dividing the sum of (female headed households; male
headed households) by family households for each neighborhood.
e) Size of households. Thi s covariate represents the average size of households
in the neighborhood.
Due to the count nature of the independent variable, we also include the total
population of each neighborhood in our models. This value ranges from 828 to
19,805, with a mean of 4839 and a median of 4335.
Neighborhood level spatial analysis 415
Sociodemographic information assessed at a small geographic unit is likely to more
accurately reflect community composition than more aggregate measures at the
municipality or city level. Assessment of these measures at the neighbo rhood level will
provide for more heterogeneity in covariates than assessment at a larger geographic
level. Recent research also suggests that aggregate census information is a relatively
accurate predictor of the true sociodemographic characteristics of a geographic unit
(Geronimus and Bound, 1998). Census data are unlikely to accurately refl ect individual
level characteristics, but for the purposes of this study, aggregate data are more
appropriate. Because our interest is in investigating the alcohol-crime link at the
neighborhood level, as opposed to individual level, and our results will only be inter-
preted at the neighborhood level, we do not risk producing an ecologic fallacy.
2.4 Analysis
Because of the potential for spatial similarity across neighborhoods, a spatial
smoothing analysis is warranted. We used Bayesian methods implemented via
Markov chain Monte Carlo (MCMC) algorithms to obtain a full posterior distri-
bution on the true crim e level in neighborhoods and to estimate the relationship
between alcohol establishment density and crime, controlling for structural con-
straints. To perform this analysis, we used WinBUGS 1.4 software that executes
Bayesian inference using Gibbs sampling (see e.g., Section 5.4 Carlin and Louis,
2000). This software is available for free download and was developed by the MRC
Biostatistics Unit in Cambridge and the Imperial College School of Medicine in
London (Spiegelhalter et al., 1995).
We base our analysis on empirical Bayes approaches to aerial count data,
following the seminal work of Clayton and Kaldor (1987), who demonstrated
spatial smoothing with lip cancer rates for Scotland counties, and the celebrated
conditionally autogregressive (CAR) spatial random effect models of Besag et al.
(1991). We apply this approach to criminal violence levels and the impact of
alcohol outlet density on these levels. We include neighborhood-level spatially
smoothed random effects because we anticipate that crime levels in adjacent
neighborhoods will be similar. Usi ng O
i
to represent the observed numbers of
crimes in the ith neighborhood and urbanpop
i
to represent the population in the
ith neighborhood, our basic model is:
O
i
Poisson ðl
i
Þ
log l
i
¼ logðurbanpop
i
Þþa
0
þ b
i
b
i
Normal ðb
i
; 1= ðn
i
sÞÞ
n
i
¼ Number of neighbors of neighborhood i
b
i
¼ 1 =n
i
R
j¼neighborðiÞ
b
j
In this model, a
0
is given a non-informative normal prior distribution (with mean 0 and
precision equal to 0.00001) and s (the precision parameter controlling the degree of
spatial smoothing) is given a gamma prior distribution with mean 10 and precision 1.
Britt et al.416
Next, we extend this model to include covariates. We reflect the effect of a co-
variate x
i
simply by modifying the log crime density to:
log l
i
¼ log ðurbanpop
i
Þþa
0
þ a
1
x
i
þ b
i
;
where a
1
is given a non-informative normal prior distribution (again, having mean 0
and precision 0.00001). We evaluate an extremely simplified model with no random
effects, as well as a model with only the natural log of alcohol outlet density as a
covariate and our spatial random effects. Finally, we consider a ‘‘full’’ model with
the natural log of alcohol outlet density, all of our covariates (z
i
) at once, and our
spatial random effects:
log l
i
¼ log ðurbanpop
i
Þþa
0
þ a
1
x
i
þ R
p¼6
k¼2
a
k
z
ik
þ b
i
;
where k=2 .... p indexes the covariates. We also consider non-spatial smoothing with
the last two models, by letting the b
i
’s be independently and identically distributed as
Normal (0, s) random variables, with the precision s given the same distribution as
above. We attempted to fit a model with both spatial and nonspatial random effects,
but in the absence of very informative prior distributions, our data were not rich
enough to separately identify the resulting very large collection of parameters,
resulting in MCMC convergence failure.
To compare models, we used the deviance information criterion (DI C), and an
associated measure, p
D
, which assesses the effective number of model parameters
(Spiegelhalter et al., 2002). The latter quantity offers insight into the amount of
Bayesian shrinkage of a model’s random effects toward their grand mean. The DIC
is a hierarchical modeling generalization of the Akaike information criterion (AIC)
defined as:
DIC ¼
D þ p
D
;
where
D is the posterior expectation of the deviance function, or minus twice the log of
the Poisson likelihood. Spiegelhalter et al. (2002) show that a reasonable definition of
p
D
turns out to be the posterior expectation of the deviance minus the deviance eval-
uated at the posterior mean of the model parameters. Since small
D values correspond
to good model fit, DIC (like AIC) represents a tradeoff between fit and complexity, with
smaller values indicating preferred models . While DIC can be us ed to rank models, the
DIC score by itself has no intrinsic meaning. Further, DIC values are only one measure
of the appropriateness of a model. We also assessed each model by performing a
collinearity analysis on all covariates, to ensure uniqueness of our structural con-
straints and satisfactory convergence and stability of our MCMC algorithms.
3. Results
We completed five separate WinBUG S runs for each model, allowing 50,000 iterations
for MCMC burn-in in each case, and 50,000 further iterations to determine the
posterior estimates. In our first model, we include only urban population, an intercept
term, and our collective efficacy variable, the natural log of alcohol outlet density, with
no random effects. In our second model, we test this same simplified model but add
Neighborhood level spatial analysis 417
independently and identically distributed normal random effects, a
i
. In our third
model, we test the simplified model with moderate spatial clustering in the random
effects, b
i
. Our fourth and fifth models include the addition of our structural constraint
covariates, with independent and spatially correlated random effects, respectively.
Table 1 presents the posterior means and standard distributions of the effect a
1
that corresponds to our collective efficacy variable, the natural log-transformed
alcohol outlet density. Also included in Table 1 are the DIC and p
D
values for each
of the five models.
With the exception of the first model with no error terms (and an extremely high
DIC), we find that the DIC and p
D
values remain fairly constant. The theoretical
perspective used to infor m this analysis suggests that either Model 4 or 5 would be
the most sensible to use in evaluating the impact of alcohol outlet density on criminal
violence rates. Examination of the effect of interest reveals that in each of these
models, the effect remains significant despite the inclusion of the other fixed effects,
with an increase in alcohol outlet density corresponding to an increase in criminal
violence. The effect in Model 5 is the smallest and most conservative, but with a
correspondingly small standard deviation. Based upon the intuitive appeal of
including a spatial smoothing term in our model, we select Model 5 as the final
model for our subsequent investigation.
The raw data are mapped in Fig. 1, with the corresponding fitted values from
Model 5 mapped in Fig. 2. Both maps depict, for each Minneapolis neighborhood
included in this analysis, the density of crimes: the number of acts of criminal vio-
lence per 1000 neighborhood residents in one year. Unshaded neighborhoods cor-
respond to those having so few residents that they were excluded from the analysis.
The visual similarity of the maps indicates excellent fit of the spatial random effects
model. The maps reveal a concentration of violence in the central and northeastern
neighborhoods in the city, wi th less criminal violence in the southern and outer
neighborhoods. A map of the spatial random effects (b
i
in Model 5 above) in Fig. 3
reveals that a few key neighborhoods (in dark gray) absorb much of the spatial error,
indicating that those neighborhoods have unusually different criminal violence levels
in comparison to their neighbors – ‘‘hot spots’’ of activity. A map of the fitted
Table 1. Model fitting results.
Effect of alcohol outlet density, a
1
Model
a
Mean
Standard
deviation
Mean/Standard
deviation
DIC p
D
1. log outlet density 0.2797 0.00500 56.01 8794.98 2.49
2. log outlet density, a 0.1602 0.03119 5.14 729.20 77.15
3. log outlet density, b 0.1041 0.02432 5.12 731.42 77.70
4. log outlet density, other
fixed covariate effects, a
0.1244 0.04201 2.96 728.78 76.53
5. log outlet density, other
fixed covariate effects, b
0.0827 0.02896 2.86 730.92 77.12
a
Here we use a to signify the vector of i.i.d random effects, and b to signify the vector of
spatially associated random effects.
Britt et al.418
random effects (a
i
in Model 4 above) is similar, but reveals somewhat less spatial
pattern. Since the DIC scores of the two models are equal up to MCMC error, we
prefer the spatial model, since greater smoothness in the random effects map should
assist somewhat in any search for missing spatial covariates.
As expected, an examination of the residuals from the final model, depicted in
Fig. 4, reveals a reasonably normal distribution, though with three outliers. The
smaller two outliers, neighborhoods 59 and 45, are both neighborhoods with
unusually low bar density and number of residents for their high criminal violence
rates. These two neighborhoods are both transition neighborhoods – the first (59) is
going through housing and resident income improvements and the second (45) is a
declining industrial area with a much larger daytime employment population than its
Figure 1. Raw crime density (per 1000 Residents).
g y( )
Neighborhood level spatial analysis 419
nighttime residential population. The bigges t outlier, neighborhood 45, is located in
the centra l part of the city and is the city’s downtown busines s corridor. This
neighborhood has an incredibly large number of on-premise and off-premise alcohol
establishments serving as the social center for Minneapolis on evenings and week-
ends. Again, this neighborhood sees a much greater daytime employment and
nighttime visitor population than its nighttime residential populati on.
The final model includes an intercept, the natural log of alcohol outlet density, and
a number of structural constraints we believe important for this analysis. In Table 2
we present the posterior means and standard distributions of each of the final model
effects. We also include the posterior summaries for the spatial variance parameter s.
While the DIC scores in Table 1 did not indicate a data-based preference for the
Figure 2. Fitted Crime Denity (Per 1,00 Residents).
Britt et al.420
spatial model over the nonspatial, the 95% pos terior confidence interval for s does
indicate significant Bayesian learning about this parameter: its prior mean was as-
signed to be 10, which lies far from this interval.
As noted previously, the natural log of alcohol outlet density is significan tly re-
lated to criminal violence, although the significance of this effect is not overwhelming
for our chosen model. Of the covariates included in the final model, only hetero-
geneity in race and household head ratio are statistically significant. Those neigh-
borhoods with a greater heterogeneity in the race of their residents are associated
with greater criminal violence, and this relationship appears strong. Neighborh oods
with a greater percentage of families with single heads of household, either males or
Figure 3. Values for spatial random effects, Model 5.
Neighborhood level spatial analysis 421
females, in comparison to households with two heads of household, are associated
with less criminal violence, although the significance of this relationship is marginal.
Heterogeneity in age, heterogeneity in homeownership, and household size do not
appear to be significantly related to criminal violence.
4. Discussion
In this study we have analyzed the relationship between alcohol outlet density and
criminal violence in the neighborhoods of a large Midwestern city (Minneapolis,
Minnesota) controlling for structural constraints and using spatial random effects.
Our analysis revealed a statistically significant relationship between outlet density
and criminal violence at the neighborhood level, in the presence of the fixed effects
0
1
2
3
4
5
6
7
8
-0.8 -0.55 -0.3 -0.05 0.2 0.45 0.7 0.95 1.2 1.45
Resi dual
Count
Figure 4. Final model residuals histogram.
Table 2. Final model covariates.
Covariate effects, a
j
Covariate Mean
Standard
deviation
Mean/Standard
deviation
95% Confidence
interval
Intercept (a
0
) )1.958 0.39100 )5.01 ()2.74, )1.18)
LN outlet density (a
1
) 0.08269 0.02896 2.86 (0.025, 0.141)
Heterogeneity in race (a
2
) 2.083 0.45000 4.63 (1.18, 2.98)
Heterogeneity in age (a
3
) )0.001071 0.00826 )0.13 ()0.018, 0.015)
Heterogeneity in homeownership
(a
4
)
0.4706 0.32690 1.44 ()0.183, 1.12)
Household head ratio (a
5
) )1.436 0.67070 )2.14 ()2.78, )0.095)
Household size (a
6
) )0.2826 0.17310 )1.63 ()0.629, 0.064)
s 1.807 0.27800 – (1.25, 2.36)
Britt et al.422
and a moderate degree of spatial smoothing. Central and north central neighbor-
hoods in the city have the highest density of criminal violence, and correspond to
areas with high densities of alcohol outlets, while south and outer ring neighbor-
hoods have the lowest density of criminal violence, and correspond to areas with
lower densities of alcohol outlets. In addition, two structural constraints included in
the model, heterogeneity in race of neighborhood residents and ratio of single head
households to two head households, were significantly related to criminal violence.
Translation of this study’s findings into magnitude of effect reveals that an
addition of one alcohol establishment to a neighborhood having the average ob-
served value of alcohol outlet density would result in an increase in the number of
criminal violence acts in that neighborhood by 5 crimes per 1000 individuals per
year. Although a seemingly small increase in crime, recall that we focus on criminal
violence in this study, not all crimes. For the purposes of our investigation, we
included only severe crimes: homicide, rape, robbery, aggravated assault, burglary,
motor vehicle theft and arson. Controlling for the spatial autocorrelation that exists
between neighborhoods yielded a more conservative, but also more precise, estimate
of effect than when we included independently and identically distributed normal
random varia bles, or when we did not include substantively important fixed effects.
Previous research in this area has resulted in a call for examination of the spatial
effects of neighborhood characteristics and alcohol outlet densities from a more
theoretically informed perspective, and in a more diverse array of settings (Gorman
et al., 2001). The current study offers a unique contribution to the research on
alcohol outlet density, analyzing relationships based upon the theoretical concepts of
collective efficacy and structural constraints, appropriately controlling for spatial
autocorrelation, and at an especially appropriate unit of analysis – the self-identified
neighborhood unit. It is at this geographic level that we are likely to see neighbors
come together in an effort to address alcohol outlet density issues and criminal
violence problems.
Although unique in some ways, the current study is not without limitations. First,
our measures of population are based on home residence data from the U.S. Census,
and are thus not measures of daytime neighborhood populations, or, perhaps more
importantly, non- residential neighborhood populations at night. This issue is espe-
cially important for those ‘‘hot spot’’ areas of concentrated alcohol outlet density,
where evening populations frequenting alcohol establishments may differ dramati-
cally from residential populations. To address this issue in future research, we sug-
gest use of better Census data (i.e., a ‘‘night’’ Census).
In addition, the current study does not include other aspects of community life
that may influence criminal violence, including location of other spots where crime
may concentrate (e.g., bus depots, nighttime business centers, major street inter-
sections) (Roncek and Maier, 1991). Further, this study does not include other
assessments of neighborhood collective efficacy aside from outlet density (Sampson
et al., 1997). Future studies could include a broader array of each of these variables.
Future studies might also include an aggrega te measure of alcohol consumption in
order to better link alcohol outlet density and resulting criminal violence (Reid et al.,
2003). Finally, the current study is cross-sectional in nature and does not explore the
spatio-temporal nature of the relationship between outlet density and crime. W e are
unable to assess a causal relationship between density and criminal violence using
Neighborhood level spatial analysis 423
our study design; assistance in this regard might come from analyzing more years of
data (Waller et al., 1997). One difficulty with this approach, however, is the fact that
outlet density is slow in changing, so a lengthy time period would be necessary to
follow a change in outlet density and to evaluate whether this leads to a detectable
change in criminal violence (Edwards, 1997).
Despite these shortcomings, the current study is congruent with other small area
analysis research, revealing that areas with higher outlet density experience more
criminal viole nce than areas with lower outlet density, even when controlling for a
number of structural constraints including heterogeneity in a community, chal-
lenging economic situations, family disruption and heavy urbanization (Scribner et
al., 1995; Speer et al., 1998; Alaniz et al., 1998; Scribner et al., 1999; Gorman et al.,
2001; Reid et al., 2003). Further, the current study extends the geographic area,
demographic diversity, and unit of analysis where this relationship is found. The
study’s fully Bayesian approach also accounts for spatial correlation in the data, and
permits full posterior and predictive inference (e.g., the probability that l
i
exceeds
some threshold c in some unmeasured or unmeasurable neighborhood i) unavailable
using traditional statistical methods.
Finally, we comment on limitations and possible extens ions of our statistical
methods. The simple CAR model we have used is often called an intrinsic CAR
(IAR), and includes only one parameter (s) to control both spatial smoothing and
the overall scale of the random effects b
i
. Thus, it is difficult to infer the amount of
‘‘spatial story’’ in our data simply by looking at the posterior distribution of s.
However, a slightly more general version of the CAR model (see car.proper in
WinBUGS) includes two parameters to separately regulate these two aspects, and
thus allows (to some extent) the data to determine the appropriate degree of spatial
smoothing. Replacing
b
i
with a weighted average is also possible, thus allowi ng
certain neighborhoods to play larger or smaller roles in the final, spatially smoothed
rates. In fact, these weights can be estimated if relevant covariate data are available –
say, allowing regions with similar racial, age, or income distributions to have greater
influence on ea ch other’s fitted rates (see Lu and Carlin, 2005). While our current
data set was not rich enough to support these model enhancements, they may well
prove valuable in future, similar investigations.
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Geographical Analysis.
Biographical sketches
Heather Britt is a Prevention Researcher with the Safe and Healthy Learners Unit at
the Minnesota Depart ment of Education (MDE). Her work at MDE focuses on
alcohol, tobacco and other drug research for the Safe and Drug Free Schools pro-
gram, evaluation of the 21
st
Century Community Learning Centers program, as well
as implementation of the triennial Minnesota Student Survey. She has an MPH in
health behavior and health education from UNC-Chapel Hill and a recent PhD in
epidemiology from the University of Minnesota.
Brad Carlin is Professor of Biostatistics and Mayo Professor in Public Health at
the University of Minnesota. His teaching and research interests focus on the
development of hierarchical Bayesian methods for spatial and spatiotemporal data,
especially techniques that take advantage of modern computing power. He is the
author of two recent texts – Hierarchical Modeling and Analysis for Spatial Data
(with colleagues Sudipto Banerjee and Alan Gelfand) and Bayes and Empirical Bayes
Methods for Data Analysis (with colleague Tom Louis). He has a PhD in statistics
from the University of Connecticut.
Traci Toomey is Assistant Professor of Epidemiology at the University of
Minnesota. Her teaching and research interests focus on the use of policy and
community organizing as tools to improve the public’s health, prevention of
alcohol and tobacco-related problems, and intentional and unintentional injury
prevention. She has an MPH and PhD in epidemiology from the University of
Minnesota.
Alex Wagenaar is Professor of Epidemiology at the University of Florida. His
teaching and research interests focus on health behavior and social change, alcohol
and dru g problem s, and evaluation of public policy changes and community-level
interventions. He has an MSW in program evaluation and research and a PhD in
health behavior and health education from the University of Michigan.
Britt et al.426
