APPLICATION OF NEGATIVE BINOMIAL AND LINEAR REGRESSION ANALYSIS
IN ASSESSING SPATIAL AND TEMPORAL TRENDS OF ALCOHOL OUTLET
DENSITY AND AGGRAVATED ASSAULT IN THE CITY OF PITTSBURGH
BETWEEN 2000 AND 2012
by
Phyon K. Christopher
BS, Mathematics, University of the Virgin Islands, 2005
Submitted to the Graduate Faculty of
Epidemiology
Graduate School of Public Health in partial fulfillment
of the requirements for the degree of
Master of Public Health
University of Pittsburgh
2015
UNIVERSITY OF PITTSBURGH
GRADUATE SCHOOL OF PUBLIC HEALTH
This essay is submitted
by
Phyon K. Christopher
on
July 30, 2015
and approved by
Essay Advisor:
Anthony Fabio, PhD, MPH
Assistant Professor
Department of Epidemiology
Graduate School of Public Health
University of Pittsburgh
______________________________________
Essay Reader:
Tiffany L. Gary-Webb, PhD, MHS
______________________________________
Associate Professor
Department of Behavioral and Community Health Sciences
Graduate School of Public Health
University of Pittsburgh
ii
Copyright © by Phyon K. Christopher
2015
iii
Anthony Fabio, PhD, MPH
APPLICATION OF NEGATIVE BINOMIAL AND LINEAR REGRESSION
ANALYSIS IN ASSESSING SPATIAL AND TEMPORAL TRENDS OF ALCOHOL
OUTLET DENSITY AND AGGRAVATED ASSAULT IN THE CITY OF
PITTSBURGH BETWEEN 2000 AND 2012
Phyon Christopher, MPH
University of Pittsburgh, 2015
ABSTRACT
Objective: This study examines the public health significance of recent legislature change which
allows for the acquisition of a wider variety of alcohol retail licenses. The temporal trend in
alcohol retail density and its effect on aggravated assault in the city of Pittsburgh is assessed by
comparing data from 2000 and 2012. Previous studies have concluded that there is an association
between alcohol outlet density (AOD) and violence, but many of these studies are inconsistent
with some reporting an association between AOD and violence and others reporting no increase
in risk of violence.
Methods: Data for this study was geocoded to determine alcohol outlet density within Pittsburgh
from InfoUSA and Dun&Bradstreet; population and demographic data was geocoded from the
US Census Bureau; neighborhood level rates of violence were calculated from data provided by
the Pittsburgh police department; and data pertaining to 11 neighborhood characteristics were
extracted from Summary File 1 and Summary File 3 of the 2000 and 2010 US Census. The
association between AOD and violence was assessed using negative binomial regression; the
temporal relationship was assessed using linear regression modeling. As a proxy for commercial
activity, “restaurant outlet density” (restaurants) was added to the negative binomial models to
check for robustness.
iv
Results: The model building process produced 16 results: 8 for data where the rates were divided
per capita and 8 where the rates were divided per square miles. In 2000 all models produced the
same result. Initially they were significant and became non-significant once “restaurants” was
added to the model. In 2012 almost all models remained significant after adding restaurants
except for the off-premise alcohol retail density per square miles rates in 2012. In 2012 some of
the models also changed from positive to negative association after adding restaurants to the
models. The linear models all showed that there was no association between the change in AOD
and the change in aggravated assault.
Conclusions: The results of this study suggest a weak or no association between AOD and
aggravated assault. When models are created without “restaurants” added, all models produce
relative risk values approximately equal to 1 which shows that AOD does not impact the risk of
violence. After restaurants are added to the model almost all predictors of interest become nonsignificant. These two results confirm that the association either isn’t present or is not as strong
as previous literature reported.
v
TABLE OF CONTENTS
PREFACE .................................................................................................................................... XI
1.0
INTRODUCTION ........................................................................................................ 1
2.0
METHODS.................................................................................................................... 4
2.1
DATA SOURCES ................................................................................................ 4
2.2
DATA ANALYSIS ............................................................................................... 7
2.3
CONCEPTUAL FRAMEWORK....................................................................... 8
3.0
RESULTS ...................................................................................................................... 9
3.1
MODELS FOR POPULATION RATES 2000.................................................. 9
3.2
MODELS FOR POPULATION RATES 2012................................................ 11
3.3
MODELS FOR CHANGE IN POPULATION RATES................................. 13
3.4
MODELS FOR SQUARE MILES RATES 2000 ............................................ 15
3.5
MODELS FOR SQUARE MILES RATES 2012 ............................................ 17
3.6
MODELS FOR CHANGE IN SQUARE MILES RATES ............................. 19
4.0
5.0
DISCUSSION.............................................................................................................. 21
4.1
EFFECT SIZE ................................................................................................... 21
4.2
CONFOUNDING ............................................................................................... 22
4.3
TEMPORAL RELATIONSHIP....................................................................... 23
CONCLUSION ........................................................................................................... 25
vi
5.1
COMPARISON TO OTHER LITERATURE ................................................ 26
5.2
LIMITATIONS .................................................................................................. 27
APPENDIX: SUPPLEMENTARY TABLE ............................................................................. 29
BIBLIOGRAPHY ....................................................................................................................... 32
vii
LIST OF TABLES
Table 1. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Capita
to Predict Aggravated Assault in 2000 while Controlling for Socio Economic Covariates ......... 10
Table 2. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Capita
to Predict Aggravated Assault in 2000 while Controlling for Socio Economic Covariates ......... 11
Table 3. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Capita
to Predict Aggravated Assault in 2012 while Controlling for Socio Economic Covariates ......... 12
Table 4. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Capita
to Predict Aggravated Assault in 2012 while Controlling for Socio Economic Covariates ......... 13
Table 5. Linear Regression Using Change in Density of On-premise Alcohol Retail per Capita to
Predict Change in Aggravated Assault while Controlling for the Change in Socio Economic
Covariates ..................................................................................................................................... 14
Table 6. Linear Regression Using Change in Density of Off-premise Alcohol Retail per Capita to
Predict Change in Aggravated Assault while Controlling for the Change in Socio Economic
Covariates ..................................................................................................................................... 14
Table 7. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Square
Mile to Predict Aggravated Assault in 2000 while Controlling for Socio Economic Covariates 15
Table 8. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Square
Mile to Predict Aggravated Assault for 2000 while Controlling for Socio Economic Covariates 16
viii
Table 9. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Square
Mile to Predict Aggravated Assault in 2012 while Controlling for Socio Economic Covariates 17
Table 10. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per
Square Mile to Predict Aggravated Assault in 2012 while Controlling for Socio Economic
Covariates ..................................................................................................................................... 18
Table 11. : Linear Regression Using Change in Density of On-premise Alcohol Retail per Square
Mile to Predict Change in Aggravated Assault while Controlling for the Change in Socio
Economic Covariates .................................................................................................................... 19
Table 12. Linear Regression Using Change in Density of Off-premise Alcohol Retail per Square
Mile to Predict Change in Aggravated Assault while Controlling for the Change in Socio
Economic Covariates .................................................................................................................... 20
Table 13. Basic descriptive statistics for selected demographic characteristics at aggregate county
level ............................................................................................................................................... 30
ix
LIST OF FIGURES
Figure 1. Conceptual Framework Displaying Casual Pathway between Predictors, the
Confounder and the Outcome ......................................................................................................... 8
x
PREFACE
Working on this research has been a great experience and it couldn’t have been done without the
guidance and patience of my mentor and advisor Dr. Anthony Fabio. Even when I turned things
in late he was always positive and kept me motivated to finish. I would also like to take time to
thank my second reader Dr. Tiffany L. Gary-Webb for reading my paper on such short notices
and providing great feedback. I wouldn’t have been able to improve this document so drastically
without her help. Thank you both for your help and your patience.
xi
1.0
INTRODUCTION
Violence is not randomly distributed, but tends to cluster in certain neighborhoods with
certain characteristics such as high levels of unemployment, low levels of family income,
poverty, female headed households and low high school graduations rates – disadvantaged
neighborhoods
7-9,27,36
. Ecologic studies at the neighborhood level suggest that availability of
alcohol is related to violence, injury, traffic crashes, drunk-driving offenses, cirrhosis mortality,
assaultive violence, sexually transmitted diseases and liquor law violations
39
. Violence is
intimately linked with alcohol consumption. Studies have shown that “alcohol use directly
affects cognitive and physical functions” and can “reduce self-control, the ability to process
incoming information, assess risks, increase emotional liability, increase impulsivity, and certain
drinkers are more likely to resort to violence in confrontation”
42
. Every year about 3 million
violent crimes occur where the offender is perceived to be inebriated. These crimes include rape,
sexual assault, robbery, and aggravated and simple assault 8.
For years Pennsylvania has been very conservative with alcohol retail with licenses
limited based on county populations. State stores owned by the Pennsylvania Control Board were
the only places that sold wines and spirits while malt beverages and beer were sold in cases by
licensed beer retailors. In 2013 legislature passed which allows for the acquisition of a broader
range of alcohol retail license from a wider group of retailers2,3,26. Beer distributors are able to
acquire licenses to sell wines, spirits, and six pack beers in addition to the cases of beers which
1
were previously the only thing sold. New areas such as restaurants and supermarkets are now
allowed to sell beer and wine. Convenient stores with eat-in areas can also sell take-out beer 51.
This increase in alcohol retail has implications for an increase in violence with some studies
claiming alcohol outlet density (AOD) as a major contributor to violence while advocating for
limiting alcohol outlet density
47,48,49
. For this study, we define AOD as the number of liquor
licenses existing within an established geographic area and this includes on-premise alcohol
retailers (this includes taverns, nightclubs, hotels and theaters) and off-premise retailers (state
liquor stores and beer distributors).
One of the main theoretical hypotheses of the association between AOD and violence is
the routine activity theory
1,28
. The theory states that a crime occurs when there is an accessible
target, the absence of capable guardians (law enforcement) that could intervene and the presence
of a motivated offender. It is suggested that areas of high AOD attract motivated offenders, have
high rates of accessible targets, and lower rates of capable guardians. This, along with social
disorganization theory is thought to decrease social control in areas in which people congregate
to purchase alcohol
4,18,36
. Just as areas with high AOD attract motivated offenders, have high
rates of accessible targets, and lower rates of capable guardians, areas of high commercial
activity exhibit these same traits. Because both of these contribute to an increase in violent
crimes and because they are both related to one another it is important to evaluate how model
building is affected by the inclusion of commercial activity as a confounder. These theoretical
underpinnings are based on the geographic area in which these interactions can occur, in which
the location is where the incident took place and relies on accurate measurements and analysis of
the neighborhood.
2
There are a number of studies which examine whether AOD within or around a
neighborhood is related to higher rates of violence however the results are inconsistent across the
studies. Although some studies found an association 13,37,43, many did not find an association 12, 38
or mentioned it would take an unrealistic increase in alcohol retailers to see an effect
44
. There
was one study which reported finding an association within univariate models, but not within
multivariate models 25. Few studies assessed the temporal association, and limit any assessment
of causality. To understand the variations in the current available literature, this study was
constructed to assess the following specific aims: 1.) Assess the cross-sectional association with
AOD and violence within Pittsburgh during two time periods – 2000 and 2012; 2.) Evaluate the
temporal association of alcohol retail density on the incidence of violence as they change over
time; 3.) Assess the presence of confounding due to commercial activity and determine the effect
size of the results.
3
2.0
METHODS
2.1
DATA SOURCES
The sample for this study consisted of 91 well-defined neighborhood tracts with stable
boundaries defined by mixture of historical ward boundaries and boundaries decided by the City
Planning Commission. Each neighborhood consists of either one or two census tracts. Census
tracts have been used as the unit of analysis in previous studies in this area of research 20, and are
considered by some to be the most appropriate administrative boundary to use in assessing such
neighborhood effects
22
therefore for this study census tracts were used for analysis. The change
in geography of census tracts between successive censuses is a major barrier for longitudinal
analysis as during each successive census, tracts may be split or consolidated from the previous
boundaries. Census tracts boundaries were therefore standardized to the 2000 census.
The primary exposure was AOD at the neighborhood level. Part of the study evaluated
AOD as a rate calculated by summing the number of establishments within each census tract for
each category of alcohol establishment and dividing based on per capita (per 10,000 residents)
based on data generated from the US census. Using the same data, AOD rates were also
calculated by summing the number of establishments within each census tract for each category
of alcohol establishment and dividing based on square miles (per 10 square miles). On-premise
outlets were defined as drinking places and included the standard industrial classification (SIC)
4
code of 5183 and off-premise the SIC code of 5181 (wholesale beer) and 5181 (Wholesale wines
and distilled alcoholic beverages).
Two commercial databases were used, InfoUSA (http://www.infousa.com/) and
Dun&Bradstreet (D&B) (http://www.dnb.com/), based on data generated in 2009 and 2003 for
Allegheny county, PA to measure and calculate AOD. Details for this process have been
described elsewhere 29. InfoUSA and D&B are sales and marketing companies that provide data
of businesses in the USA and Canada. In order to standardize the neighborhood boundaries as
mentioned above, the Longitudinal Tract Data Base (LTDB) was used, which provides a
backwards LTDB in which data provided in 2010 tract boundaries can be estimated within 2000
boundaries (Russel Sage Foundation, 2010). Types of establishments and associated
classifications are based on the standard industrial classification and North American Industry
Classification (NAICS) taxonomy.
The 2000 (the average of the data from 2000 to 2003) and the 2012 (the average of the
data from 2009 to 2012) US Census population and demographic data included the number of
residents per census tract to calculate density measures (e.g. density of grocery stores within a
geographic region) were also used. All establishments were geocoded based on local data
provided by the Allegheny County Geographic Information System (GIS) department. The local,
reference database included a combination of streets and rooftops, which produce higher match
rates and positional accuracy (Roongpiboonsopit and Karimi, 2010). ArcGIS version 10 (ESRI,
Redlands, USA) was used to geocode establishments. Spelling sensitivity was set at 70,
minimum candidate score at 10 and minimum match score at 60. Output included XY
coordinates, which were spatially matched to census tracts using year 2000 government census
shape files. The 2003 data was successfully geocode at 87.2% (n = 6,849; 1,008 were unmatched
5
to address points in the geocoding reference file) of the establishments from and 83.1% (n =
3,316; 672 were unmatched) for InfoUSA. The data from 2012 was successfully geocoded at
86.1% (n = 5,073; 817 were unmatched) of the D&B establishments and 84.9% (n = 3,679; 656
were unmatched) from InfoUSA.
Neighborhood outcome rates of violence for 2000 and 2012 were calculated from data
provided by the Pittsburgh police department. All aggravated assaults and robberies reported to
the police are geocoded to a Pittsburgh neighborhood. For police data, definitions were based on
the FBI’s Uniform Crime Reporting (UCR) Programs definition. Violent crimes are defined in
the UCR Program as those offenses that involve force or threat of force. The primary outcome of
interest for this study was aggravated assault as determined by the police report. In the analysis,
the neighborhood-level violent crime rate was calculated as crimes per 10,000 persons and per
10 square miles.
Finally, data pertaining to 11 neighborhood characteristics were extracted from Summary
File 1 and Summary File 3 of the 2000 and 2012 US Census (US Census Bureau, 2003). These
variables were chosen as they had been used in previous studies of alcohol availability and
violent crime
11, 22, 24
, as well as studies of violent crime in urban neighborhoods7-10, 43. These
data included racial composition (total population that was non-White), total population size, sex
(total population that was male), unemployment (total population 16 years and over in labor
force who were unemployed), median family income, median home income, poverty (percentage
of households who made an income below the poverty level in 1999 and percentage of
households with public assistance income), family instability (percentage of female-headed
households), and education (percentage of the population older than 25 years with at least a high
school diploma and percentage of the population older than 25 years with a Bachelor's degree).
6
2.2
DATA ANALYSIS
All analyses were conducted using SAS 9.4 and began with summary and descriptive
statistics which can be found in Table 1. Initially the data was acquired as counts, but were
transformed to rates for analysis. In order to evaluate the differences between 2000 and 2012 two
techniques were executed: first, cross-sectional models were created for the two time periods;
second, change variables were created by taking the difference between 2012 and 2000 for each
predictor and from these predictors linear regression models were created. For the cross-sectional
models, negative binomial regression with a log link was used in order to protect against the
effect of excessive zeroes in the data. Following the example of previous studies, backward
stepwise selection regression was used to remove variables that did not fit a predetermined pvalue of <0.2; the predictor of interest remained in the model regardless of its p-value and was
controlled for by 11 demographic variables which were mentioned previously 5,43.
It was suspected that there was some confounding with the increase in commercial
activity in Pittsburgh so after final models were built; the covariate “restaurant outlet density”
was added to the model to check for the robustness of the predictor of interest
45
. It was
suspected that if the Routine Activities Theory is taken into account the increase in commercial
activity fits well for explaining the presence of crime in many areas of Pittsburgh as focus on
infrastructure is encouraging growth in commercial activity 1, 28. With this in mind, the presence
of AOD is expected to increase in areas where commercial activity has increased and along with
this, likely offenders are presented with suitable targets in areas where people are more likely to
congregate.
7
As mentioned previously, change variables were calculated by subtracting their 2000
values from their 2012 values; the change for the outcome of interest was also calculated in the
same way and backward stepwise selection linear regression was used. After the final models
were produced influential points were identified using Cook’s distance
21, 46
. Each identified
point was considered for removal and if removed was replaced with a missing value. This was
done one influential point at a time stepwise between each replacement. Two census tracts were
highly influential and were determined to be mostly commercialized with little to no residential
areas and thus were different from the other neighborhoods in the data set; because of this they
were removed from the model so that the data was reflected in a more accurate way
21
. After
influential points were removed, models were created again using backward stepwise selection
regression starting from the full model.
2.3
CONCEPTUAL FRAMEWORK
Alcohol Outlet Density
Commercial Activity
Aggravated Assault
Demographic Variables
Figure 1. Conceptual Framework Displaying Casual Pathway between Predictors, the Confounder and the
Outcome
8
3.0
RESULTS
There were 91 tracts in this study for which summery statistics were generated as seen in
Table 1. The average population across all tracts was 3,717 in 2000 and 3,405 in 2012. There
was an increase in median family and home income from 2000 to 2012, which indicates positive
economic development across all census tracts. The number of high school graduates and
population with at least a bachelor’s degree increased slightly from 2000 to 2012. The mean total
population using public assistance income decreased from 211 in 2000 to 178 in 2012. The
average total population below the poverty level decreased from 560 in 2000 to 521 in 2012.
Unemployment also decreased from 180 in 2000 to 166 in 2012. The average on-premise AOD
increased from 2000 to 2012 (31 to 40). Once rates were created by dividing per square miles
there were differences in the average on-premise AOD which decreased slightly from 2000 to
2012 (16 to 10). The average and minimum off-premise alcohol retail density decreased, but not
significantly from 2000 to 2012 and the maximum decreased slightly from 23 to 16.
3.1
MODELS FOR POPULATION RATES 2000
The negative binomial regression model for predicting aggravated assault in 2000
revealed that on-premise alcohol retail density (β= 0.0062; p-value< 0.0001), female headed
households (β= 0.0243; p-value= 0.0016), having an income below the poverty level (β= 9
0.0258; p-value= 0.0003) and households on public assistance (β= 0.0961; p-value< 0.0001) are
all significant predictors. The predictor of interest was significant before restaurant density was
added to the model, but became not significant after it was added to the model (β= 0.0021; pvalue< 0.2006).
Table 1. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Capita to Predict
Aggravated Assault in 2000 while Controlling for Socio Economic Covariates
Model for On-Premise
Restaurant Outlet Density Added
with On-Premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
3.1245
<0.0001
2.9297
<0.0001
Density of On-Premise Alcohol
Establishments
0.0062
<0.0001
0.0021
0.2006
Female householder, No Husband Present
(%)
0.0243
0.0016
0.0410
<0.0001
Income Below Poverty Level (%)
-0.0258
0.0003
-0.0060
0.4557
Households with Public Assistance Income
(%)
0.0961
<0.0001
0.0183
0.3737
Restaurant Establishment
-
-
0.0020
<0.0001
The negative binomial regression model for predicting aggravated assault in 2000
revealed that off-premise alcohol retail density (β= 0.0207; p-value< 0.0001), total population
(β= -0.0002; p-value< 0.0001), population which identify as black (β= -0.0002; p-value=
0.0019), having an income below the poverty level (β= -0.0206; p-value= 0.0033) and
households on public assistance (β= 0.0722; p-value< 0.0001) are all significant predictors. The
10
predictor of interest was significant before restaurant density was added to the model, but
became not significant after it was added to the model (β= -0.0031; p-value< 0.6352).
Table 2. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Capita to Predict
Aggravated Assault in 2000 while Controlling for Socio Economic Covariates
Model for OffPremise
Restaurant Outlet Density Added
with Off-Premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
4.2017
<0.0001
3.9372
<0.0001
Density of Off-Premise Alcohol
Establishments
0.0207
<0.0001
-0.0031
0.6352
Total Population
-0.0002
<0.0001
-0.0001
<0.0001
Black or African American Alone
0.0002
0.0019
0.0003
<0.0001
Income Below Poverty Level (%)
-0.0206
0.0033
0.0017
0.8251
Households with Public Assistance Income
(%)
0.0722
<0.0001
0.0155
0.3584
Restaurant Establishment
-
-
0.0017
<0.0001
3.2
MODELS FOR POPULATION RATES 2012
The negative binomial regression model for predicting aggravated assault in 2012
revealed that on-premise alcohol retail density (β= 0.0044; p-value< 0.0001), total population
(β= -0.0001; p-value< 0.0001), population which identify as black (β= 0.0003; p-value= 0.0009),
female headed households (β= -0.0317; p-value= 0.0223), having an income below the poverty
level (β= 0.0161; p-value= 0.0414) and households on public assistance (β= 0.0529; p-value=
11
0.0114) are all significant predictors. The predictor of interest was significant before and after
restaurant density was added to the model (β= -0.0019; p-value= 0.0243).
Table 3. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Capita to Predict
Aggravated Assault in 2012 while Controlling for Socio Economic Covariates
Model for On-Premise
Restaurant Outlet Density Added
with On-Premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
3.9644
<0.0001
3.7157
<0.0001
Density of On-Premise Alcohol
Establishments
0.0044
<0.0001
-0.0019
0.0243
Total Population
-0.0001
<0.0001
-0.0001
<0.0001
Black or African American Alone
0.0003
0.0009
0.0003
<0.0001
Female householder, No Husband Present
(%)
-0.0317
0.0223
-0.0231
0.0410
Income Below Poverty Level (%)
0.0161
0.0414
0.0165
0.0088
Households with Public Assistance Income
(%)
0.0529
0.0114
0.0477
0.0041
Restaurant Establishments
-
-
0.0025
<0.0001
The negative binomial regression model for predicting aggravated assault in 2012
revealed that off-premise alcohol retail density (β= 0.0188; p-value< 0.0001), total population
(β= -0.0002; p-value< 0.0001), population which identify as black (β= 0.0003; p-value= 0.0017),
female headed households (β= -0.0331; p-value= 0.0228) and households on public assistance
(β= 0.0494; p-value= 0.0259) are all significant predictors. The predictor of interest was
12
significant before and after restaurant density was added to the model (β= -0.0224; p-value=
0.0001).
Table 4. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Capita to Predict
Aggravated Assault in 2012 while Controlling for Socio Economic Covariates
Model for OffPremise
Restaurant Outlet Density Added
with Off-Premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
4.2735
<0.0001
3.6011
<0.0001
Density of Off-Premise Alcohol
Establishments
0.0188
<0.0001
-0.0224
<0.0001
Total Population
-0.0002
<0.0001
-0.0001
<0.0001
Black or African American Alone
0.0003
0.0017
0.0003
<0.0001
Female householder, No Husband Present
(%)
-0.0331
0.0228
-0.0224
0.0332
Income Below Poverty Level (%)
0.0129
0.1174
0.0189
0.0015
Households with Public Assistance Income
(%)
0.0494
0.0259
0.0477
0.0020
Restaurant Establishments
-
-
0.0030
<0.0001
3.3
MODELS FOR CHANGE IN POPULATION RATES
From the linear regression models, the values for on-premise and off-premise alcohol
retail density were not significant with values β= 0.03761, p-value= 0.8311 and β= 1.87664, pvalue= 0.0893 respectively. In regards to the temporal relationship between the predictors and
13
the outcome, these values indicate that there is no significant association between the change in
the predictors of interest and the change in the outcome.
Table 5. Linear Regression Using Change in Density of On-premise Alcohol Retail per Capita to Predict
Change in Aggravated Assault while Controlling for the Change in Socio Economic Covariates
Variable
Estimate (β)
P Value
Intercept
-2.03949
0.7517
Change in Density of On-Premise Alcohol Establishments
0.03761
0.8311
Change in Total Population
-0.01227
0.1931
Change in Black or African American Alone
0.01251
0.1805
Change in Female householder, No Husband Present (%)
-0.98752
0.1457
Change in Population 25 years and over who are High School Graduate or
more (%)
0.94768
0.0413
Change in Population 25 Years and Over with Bachelor's Degree (%)
-1.29794
0.1042
Table 6. Linear Regression Using Change in Density of Off-premise Alcohol Retail per Capita to Predict
Change in Aggravated Assault while Controlling for the Change in Socio Economic Covariates
Variable
Estimate
(β)
P Value
Intercept
1.9438
0.7426
Change in Density of Off-Premise Alcohol Establishments
1.87664
0.0893
Change in Population 25 years and over who are High School Graduate or more
(%)
1.15797
0.0062
Change in Population 25 Years and Over with Bachelor's Degree (%)
-1.06289
0.1538
14
3.4
MODELS FOR SQUARE MILES RATES 2000
The negative binomial regression model for predicting aggravated assault in 2000
revealed that on-premise alcohol retail density (β= 0.0138; p-value= 0.0002), total population
(β= -0.0002; p-value< 0.0001), population which identify as black (β= 0.0002; p-value= 0.0145),
population over 16 years old who are unemployed (β= -0.0007; p-value= 0.0588 [marginally
significant]), population who at least hold a high school diploma (β= 0.0296; p-value= 0.0008)
and households on public assistance (β= 0.0670; p-value< 0.0001) are all significant predictors.
The predictor of interest was significant before restaurant density was added to the model, but
became not significant after it was added to the model (β= 0.0034; p-value= 0.2037).
Table 7. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Square Mile to
Predict Aggravated Assault in 2000 while Controlling for Socio Economic Covariates
Model for On-premise
Restaurant Outlet Density Added
with On-premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
1.6801
0.0285
5.1259
<0.0001
Density of On-premise Alcohol
Establishments (per square mile)
0.0138
0.0002
0.0034
0.2037
Total Population
-0.0002
<0.0001
-0.0001
<0.0001
Black or African American Alone
0.0002
0.0145
0.0003
<0.0001
Population 16 Years and Older
Unemployed
-0.0007
0.0588
-0.0003
0.3063
Populations 25 years and over whom are
High School Graduate or more (%)
0.0296
0.0008
-0.0149
0.1414
Households with Public Assistance Income
(%)
0.0670
<0.0001
0.0096
0.4638
Restaurant Establishment
-
-
0.0017
<0.0001
15
The binomial regression model for predicting aggravated assault in 2000 revealed that
off-premise alcohol retail density (β= 0.0672; p-value= 0.0049), total population (β= -0.0002; pvalue< 0.0001), population which identify as black (β= 0.0002; p-value= 0.0158), population
who at least hold a high school diploma (β= 0.0242; p-value= 0.0055) and households on public
assistance (β= 0.0592; p-value< 0.0001) are all significant predictors The predictor of interest
was significant before restaurant density was added to the model, but became not significant
after it was added to the model (β= 0.0098; p-value= 0.5393).
Table 8. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Square Mile to
Predict Aggravated Assault for 2000 while Controlling for Socio Economic Covariates
Model for Off-premise
Restaurant Outlet Density Added
with Off-premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
2.2586
0.0029
5.4030
<0.0001
Density of Off-premise Alcohol
Establishments
0.0672
0.0049
0.0098
0.5393
Total Population
-0.0002
<0.0001
-0.0001
<0.0001
Black or African American Alone
0.0002
0.0158
0.0003
<0.0001
Population 16 Years and Older
Unemployed
-0.0007
0.0676
-0.0003
0.3417
Populations 25 years and over whom are
High School Graduate or more (%)
0.0242
0.0055
-0.0181
0.0646
Households with Public Assistance Income
(%)
0.0592
<0.0001
0.0061
0.6306
Restaurant Establishment
-
-
0.0018
<0.0001
16
3.5
MODELS FOR SQUARE MILES RATES 2012
The negative binomial regression model for predicting aggravated assault in 2012
revealed that on-premise alcohol retail density (β= 0.0317; p-value< 0.0001), total population
(β= -0.0002; p-value< 0.0001), population which identify as black (β= 0.0002; p-value= 0.0236),
population who hold a bachelor’s degree (β= -0.0435; p-value< 0.0001) and households on
public assistance (β= 0.0570; p-value= 0.0151) are all significant predictors. The predictor of
interest was significant before restaurant density was added to the model and remained
significant after restaurant was added to the model (β= 0.0107; p-value= 0.0104).
Table 9. Negative Binomial Regression Using Density of On-premise Alcohol Retail per Square Mile to
Predict Aggravated Assault in 2012 while Controlling for Socio Economic Covariates
Model for On-premise
Restaurant Outlet Density Added
with On-premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
3.6914
0.0008
3.8567
<0.0001
Density of On-premise Alcohol
Establishments
0.0317
<0.0001
0.0107
0.0104
Total Population
-0.0002
<0.0001
-0.0002
<0.0001
Black or African American Alone
0.0002
0.0236
0.0003
0.0017
Female householder, No Husband Present
(%)
-0.0277
0.0749
-0.0078
0.5070
Populations 25 years and over whom are
High School Graduate or more (%)
0.0169
0.1162
0.0034
0.7232
Total Population 25 Years and Over with
Bachelor's Degree
-0.0435
<0.0001
-0.0159
0.1075
Households with Public Assistance Income
(%)
0.0570
0.0151
0.0485
0.0034
Restaurant Establishments
-
-
0.0014
<0.0001
17
The negative binomial regression model for predicting aggravated assault in 2012
revealed that off-premise alcohol retail density (β= 0.1167; p-value= 0.0023), total population
(β= -0.0003; p-value< 0.0001), population which identify as black (β= 0.0003; p-value= 0.0364),
female headed households (β= -0.0371; p-value= 0.0222), population who hold a bachelor’s
degree (β= -0.0438; p-value< 0.0001) and households on public assistance (β= 0.0581; p-value=
0.0245) are all significant predictors. The predictor of interest was significant before restaurant
density was added to the model, but became not significant after it was added to the model (β=
0.0192; p-value= 0.4625).
Table 10. Negative Binomial Regression Using Density of Off-premise Alcohol Retail per Square Mile to
Predict Aggravated Assault in 2012 while Controlling for Socio Economic Covariates
Model for Offpremise
Restaurant Outlet Density Added
with Off-premise
Variable
Estimate
(β)
P Value
Estimate (β)
P Value
Intercept
4.2118
0.0003
4.0724
<0.0001
Density of Off-premise Alcohol
Establishments
0.1167
0.0023
0.0192
0.4625
Total Population
-0.0003
<0.0001
-0.0002
<0.0001
Black or African American Alone
0.0003
0.0364
0.0003
0.0045
Female householder, No Husband Present
(%)
-0.0371
0.0222
-0.0087
0.4710
Populations 25 years and over whom are
High School Graduate or more (%)
0.0155
0.1714
0.0009
0.9262
Total Population 25 Years and Over with
Bachelor's Degree
-0.0438
<0.0001
-0.0122
0.2339
Households with Public Assistance Income
(%)
0.0581
0.0245
0.0476
0.0056
Restaurant Establishments
-
-
0.0016
<0.0001
18
3.6
MODELS FOR CHANGE IN SQUARE MILES RATES
The values produced from the linear regression models show that both on-premise and
off-premise alcohol retail density were not significant with values β= 0.32286, p-value= 0.2017
and β= 2.47946; p-value= 0.1075 respectively. Exactly like the models created using the percapita data, the values in the next two tables indicate that there is no significant association
between the change in the predictors of interest and the change in the outcome.
Table 11. Linear Regression Using Change in Density of On-premise Alcohol Retail per Square Mile to
Predict Change in Aggravated Assault while Controlling for the Change in Socio Economic Covariates
Variable
Estimate (β)
P Value
Intercept
-0.98213
0.8761
Change in Density of On-premise Alcohol Establishments
0.32286
0.2017
Change in Total Population
-0.01263
0.1745
Change in Black or African American Alone
0.01154
0.2123
Change in Female householder, No Husband Present (%)
-0.94901
0.1561
Change in Population 25 years and over who are High School Graduate or more
(%)
1.00769
0.0272
Change in Population 25 Years and Over with Bachelor's Degree (%)
-1.31914
0.0954
19
Table 12. Linear Regression Using Change in Density of Off-premise Alcohol Retail per Square Mile to
Predict Change in Aggravated Assault while Controlling for the Change in Socio Economic Covariates
Variable
Estimate (β)
P Value
Intercept
-0.30326
0.9616
Change in Density of Off-premise Alcohol Establishments
2.47946
0.1075
Change in Total Population
-0.01410
0.1301
Change in Black or African American Alone
0.01138
0.2156
Change in Female householder, No Husband Present (%)
-0.93249
0.1609
Change in Population 25 years and over who are High School Graduate or
more (%)
0.96243
0.0322
Change in Population 25 Years and Over with Bachelor's Degree (%)
-1.30389
0.0971
20
4.0
DISCUSSION
4.1
EFFECT SIZE
Of the studies found during the literature review there were only 5 which reported an
effect size
12,25,37,43,44
. Of those five, three used R2 as their measure while the other two used
relative risk and Akaike information criterion (AIC). Of the different methods used to describe
the effect size, the most useful measure is relative risk because R2 and AIC are not real measures
of effect since they only describe how much variability in the outcome is predicted by the model.
R2 and AIC don’t describe the magnitude of the relationship between the predictor(s) of interest
and the outcome. Relative risk however is a well-documented method for measuring the
magnitude of an association between an exposed and non-exposed group 52-56.
For comparison reasons, relative risk (RR) was calculated for the predictors of interest
by exponentiation of their beta values (exponential formula being eβ). From this study’s
population based rates in 2000 it was found that the RR of aggravated assault occurring in an
area with on-premise outlet density was 1.006 which indicates that there is almost no association.
After commercial activity was added to the model the predictor of interest became not
significant. This result indicates that when not taking the confounding factor into consideration,
the effect of AOD in an area does not have a meaningful effect.
21
Similar results were found for all models in 2000 where the largest relative risk was
1.069 from the off-premise model for square mile rates. This result indicates that an area with
off-premise AOD would have an approximately 7% higher risk of aggravated assaults than an
area without AOD. Even as the largest relative risk value, the magnitude of this effect is not very
large and once adjusted for commercial activity became non-significant. In 2012, the largest
relative risk was 1.124 from the off-premise model for square mile rates. This indicates that an
area with off-premise AOD would have a 12% higher risk of aggravated assault than an area
without AOD. This value might indicate a meaningful effect depending on how risky a safe
neighborhood is expected to be. With that said, after adding commercial activity to the model
this value is no longer significant. Compared to the paper with relative risk, this result appears to
be consistent as Zhu Li, et al. found similar results in their paper and concluded that alcohol
outlet density is not strongly associated with violent crime, but rather activity around illicit drug
markets presents a much stronger association 44.
4.2
CONFOUNDING
As with previous studies the results from this study show positive associations when
commercial activity is initially ignored. However, taking into account a potential confounder had
a major impact on the results. The results discussed in the previous section briefly describes
some of the effects of adjusting for commercial activity as a potential confounder on the results
with many of the models showing AOD as significant before commercial activity is included, but
not significant once commercial activity is included. In 2000 the results of the all the models 22
whether they are based on population rates or square mile rates - show that once commercial
activity is adjusted for, AOD is not a significant predictor for aggravated assault. In 2012 the
potential confounding affects the results in a different way. Every model in 2012 (except one)
remains significant and showed a positive association before adding restaurants to the models,
but the models for population rates showed a change in the direction of association once
commercial activity was adjusted for. Possible confounding in the 2000 data was confirmed
when the predictors of interest changed from significant to non-significant; in 2012 instead of a
change in significance, there were changes in direction of association. These changes all seem to
confirm that commercial activity was a potential confounder. Many previous studies found a
positive association between AOD and violence, but failed to take any confounding factors into
consideration. It is possible that other potential confounders exist and should be considered for
model building.
4.3
TEMPORAL RELATIONSHIP
To understand the temporal relationship of AOD it was important to evaluate the change
in AOD as it related to the change in aggravated assault while controlling for the change in other
factors. During the linear model building process, change in AOD remained non-significant.
What was found was that as AOD changed over time, it did not significantly influence the
change in aggravated assault over time as the p-value remained greater than 0.05. This is
important to note since as mentioned previously some studies suggested that reducing AOD will
reduce violence rates in an area over time. Based on the comparison of results from the cross
sectional portion of this study to the temporal portion, cross sectional models are not fair
23
assessments of AODs effect on violence over time as there may be a significant positive
association within every time period, but using a change over time model it’s possible that those
same studies would find that those associations aren’t significantly related to a change in
violence over time. With that said, showing cross-sectional analysis of the association of AOD
on violence is not enough to make a decision about reducing violence over crime by reducing
AOD.
24
5.0
CONCLUSION
Although there are many studies that concluded that there is an association between AOD
and violence, this study was not able to find a significant association. Three key aspects were
discussed: effect size, potential confounding and the temporal relationship between AOD and
violence. Looking at effect size, it was noted that the majority of risk ratios were approximately
equal to 1 which indicates that there is approximately no association between AOD and violence.
Even if the models produced larger relative risk values, the majority of models produced a
predictor of interest that was no longer significant once commercial activity was added to the
model. With this in mind it might be possible that there are other confounding factors that were
unaccounted for or that may be present in other areas that are not present in Pittsburgh and vice
versa. For example, commercial activity might not act as a confounder in more rural areas where
AOD is present. Future studies should try to consider the possibility of confounding and adjust
for it. The reporting of effect size in a standardized way is also important. It was difficult to
compare the effect size found in this study with other studies because the majority used Rsquared which is not a very useful indicator of effect size. There was only one study that reported
relative risk which is a great indicator. This study could have gone further by comparing the
effect sizes found here to other studies in order to assess how much of an impact AOD has on
violence, but with the current information available this task may be conducted in the future.
25
Another important study design future papers should consider is the temporal relationship
of AOD on violence. There were only a few papers that took the temporal relationship into
consideration. As policy aimed at reducing violence is developed, it is important to guide
decisions using the results of research. As it stands, most research provides cross sectional results
which isn’t as useful as temporal results such as those produced from models containing change
variables. It might be possible to reduce violence from alcohol consumption in a more fruitful
way if future research also concluded that AOD is not a major contributor. As AOD increases in
Pittsburgh the results of this study may change in the future, but this study must conclude that it
is not significantly nor practically related to aggravated assault.
5.1
COMPARISON TO OTHER LITERATURE
Previous studies applied various model building methods to evaluate the effects of
alcohol density on violence. Many focused on the geographic association of violence and the
environmental context that drinking occurred in such as demographic factors and types of
alcohol retail establishments. The common theme shared within the literature was the evaluation
of the spatial relationship between AOD and violence. The conclusion of these research varied
depending on what other factors were considered as the data was evaluated. In the Brower et al.
paper, the relationship between the congregation of students and the time of day was considered
for evaluation 57. In the paper by Graham et al. they looked at sexual activity and bar location as
it factored into the relationship between AOD and violence 14. Zhu et al. looked at the association
between illicit drug markets and violence and compared that to AOD and violence 44. What most
26
of these papers concluded is that other factors play a larger role in the incidence of violent
activity than alcohol outlet density. For instance, Graham et al. found that aggression was more
severe at suburban locations rather than locations where there was a lot of entertainment such as
clubs and bars (commercial activity). Comparing this result to the results of this paper, it appears
that social constructs in an area do indeed influence the way AOD relates to violence. In this
research we evaluated commercial activity as a potential confounder and believe that although
it’s not a direct confirmation, this research supports their findings that areas where there are
entertainment such as clubs, bars or restaurants (commercial activities) there is an interaction
between those and AOD which simultaneously impact violence.
5.2
LIMITATIONS
There were several study limitations. Population density and square miles were not
evenly distributed and so some areas had more of an influence on the outcome than others. There
are some areas in Pittsburgh that have almost no residential areas and so for model building two
of those areas were removed. The points removed were not only influential points with a lot of
leverage; they were also areas with no residential areas, but a lot of alcohol outlet retail and
commercial activity. The approach to interpreting the longitudinal effect of AOD on violence
was also a major limitation. Actual longitudinal data was not used for model building so instead
the difference between the two years was taken and modeled. The use of change variables can
only act as a slight description of the temporal relationship between AOD and violence. It tells us
that there is no significant association between the change in the predictor as it relates to the
change in the outcome. If there was a significant association, it would be impossible to describe
27
what the change meant; as AOD increased we wouldn’t be able to tell if violence increased or
decreased – we would only be able to say that it changed over time along with AOD.
28
APPENDIX: SUPPLEMENTARY TABLE
29
Table 13. Basic descriptive statistics for selected demographic characteristics at aggregate county level
2000
2012
Change
Variable
Min
Max
Mean
SD
Min
Max
Mean
SD
Min
Max
Mean
SD
Median Household Income
7,440
642,660
12,1117
13,3326
9,375
831,268
160,701
17,5017
24,5901
38,306
57,982
Median Family Income
0
991,320
161,323
187,538
10,148
1,524,784
234,268
290,686
14,7422
-34,213
752,168
69,406
121,263
Populations 25 years and over whom are
High School Graduate or more (%)
28
100
78
11
0
100
87
13
-100
72
8
17
Total Populations 25 years and over whom
are High School Graduate or more
20
13,489
3,017
2,924
0
14,426
3,053
3,070
-712
1,776
36
475
Population 25 Years and Over with
Bachelor's Degree (%)
0
34
11
7
0
49
15
9
-20
24
3
6
Total Population 25 Years and Over with
Bachelor's Degree
0
4,097
508
765
0
4,671
598
834
-566
863
90
211
Total Population
41
14,507
3,717
3,272
0
14,826
3,405
3,247
-1,418
1,117
-313
488
Male Population
20
6,923
1,768
1,607
0
7,340
1,636
1,622
-848
1,119
-132
308
Black or African American Alone
1
4,980
1,008
1,193
0
4,368
876
937
-1,640
1,419
-132
516
Households with Public Assistance Income
(%)
0
57
8
9
0
36
7
8
-57
30
1
9
Total Households with Public Assistance
Income
0
917
211
191
0
607
178
167
-430
272
-33
125
Income Below Poverty Level (%)
0
100
19
18
0
100
19
18
-100
92
0.1746
18
Total with Income Below Poverty Level
0
1,967
560
492
0
1,967
521
486
-1417
1182
-39
364
30
Table 13 continued
Population 16 Years and Older
Unemployed
0
2,283
180
294
0
591
166
146
-1880
385
-14
250
Female householder, No Husband Present
(%)
2
71
20
13
0
71
18
14
-37
29
-2
8
Total Female householder, No Husband
Present
5
2,154
634
518
0
1,725
502
448
-974
364
-133
230
Density of On-Premise Alcohol
Establishments (per capita)
0
902
31
100
0
2,105
40
227
-472
2,105
8
231
Density of Off-Premise Alcohol
Establishments (per capita)
0
150
5
16
0
263
5
29
-68
263
0.5660
29
Density of On Premise Alcohol
Establishments (per square mile)
0
227
16
32
0
142
10
21
.93
36
-6
17
Density of Off Premise Alcohol
Establishments (per square mile)
0
23
3
5
0
16
2
3
-11
6
-1
3
Total Restaurant Establishments
0
2,068
100
317
0
2,857
106
400
-
-
-
-
31
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