MULTISCALE AND SPATIOTEMPORAL DYNAMICS OF SOCIOECONOMIC
AND ENVIRONMENTAL EFFECTS ON MENTAL ILLNESS MORTALITY
by
INSANG SONG
A DISSERTATION
Presented to the Department of Geography
and the Division of Graduate Studies of the University of Oregon
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
June 2023
DISSERTATION APPROVAL PAGE
Student: Insang Song
Title: Multiscale and Spatiotemporal Dynamics of Socioeconomic and
Environmental Effects on Mental Illness Mortality
This dissertation has been accepted and approved in partial fulfillment of the
requirements for the Doctor of Philosophy degree in the Department of Geography
by:
Hui Luan Chair
Amy Lobben Core Member
Mark Fonstad Core Member
Clare Rosenfeld-Evans Institutional Representative
and
Krista Chronister Vice Provost of Graduate Studies
Original approval signatures are on file with the University of Oregon Division of
Graduate Studies.
Degree awarded June 2023
ii
© 2023 Insang Song
This work, including text and images, is licensed under a Creative Commons
Attribution 4.0 International License.
iii
DISSERTATION ABSTRACT
Insang Song
Doctor of Philosophy
Department of Geography
June 2023
Title: Multiscale and Spatiotemporal Dynamics of Socioeconomic and
Environmental Effects on Mental Illness Mortality
Mental illness is a pressing global and national public health concern,
necessitating the identification of risk factors to develop effective prevention
measures. In this dissertation, I attempt to fill two research gaps by revealing the
spatial and/or temporal disparity in the impacts of unemployment and greenspace
on mental illness mortality with spatiotemporal modeling and a causal analysis
across three spatial scales.
In Chapter 2, the association between mental illness and substance use
mortality and unemployment was examined using Bayesian spatiotemporal
hierarchical models. The findings revealed heightened positive effects in rural
Appalachian and Midwestern counties. Overall mild effects were observed during
the Great Recession period. The patterns could be attributed to local contexts
such as the availability of healthcare supply and relative deprivation. Chapter 3
challenges the assumption of a spatially constant effect of greenspace exposure on
mental illness mortality, using census tract-level data from Oregon and Washington.
Results indicated that the impact of greenspace exposure on mental illness
mortality varies across census tracts, with protective effects more likely in areas
between Seattle and Portland. Protective effects were more likely observed in areas
iv
between Seattle and Portland. The contrast between urban and rural areas was
explained through factors such as patient preference and differential availability
and accessibility to greenspaces. Chapter 4 shed light on the spatial differences in
the causal effects of greenspace exposure on mental illness mortality using data
from the State of Washington. Dichotomized treatment settings and propensity
score matching methods were leveraged to examine the spatial disparity in causal
effects of greenspace exposure to mental illness mortality. The results elucidated
that the causal effect differed significantly across regions within Washington state,
emphasizing that spatial heterogeneity is a critical element when examining the
causal effects of greenspace exposure on mental illness mortality.
By highlighting the spatial and/or temporal disparity in socioeconomic and
physical environment factors’ effects, this dissertation provides new perspectives
to spatiotemporal mental health research and suggests a transition from disease
mapping to effect mapping. This transition offers evidence to devise locally-focused
measures that consider the spatial disparities of associative and causal effects.
This dissertation includes previously published and unpublished co-authored
materials.
v
CURRICULUM VITAE
NAME OF AUTHOR: Insang Song
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED:
University of Oregon, Eugene, OR, USA
Seoul National University, Seoul, Republic of Korea
DEGREES AWARDED:
Doctor of Philosophy, Geography, 2023, University of Oregon
Master of Arts, Geography, 2017, Seoul National University
Bachelor of Arts, Geography, 2015, Seoul National University
AREAS OF SPECIAL INTEREST:
Health & Medical Geography
Environmental Health
Spatiotemporal Analysis
Causal Inference
PROFESSIONAL EXPERIENCE:
Instructor, University of Oregon, 2023
Graduate Employee (Research and Teaching Assistant), University of
Oregon, 2019–2023
Researcher, National Cancer Center of Korea, 2018
Research Assistant, Seoul National University, 2015–2017
GRANTS, AWARDS AND HONORS:
Rippey Dissertation Writing Grant, Department of Geography, University of
Oregon, 2022
Sandra Pritchard Graduate Student Award, Department of Geography,
University of Oregon, 2022
vi
Raymund Fellowship, University of Oregon, 2019–2020
Lokey Graduate Science Award, University of Oregon, 2019
Excellent Poster Award, The Korean Society of Environmental Health and
Toxicology, 2016
Summa cum laude, Seoul National University, 2015
PUBLICATIONS:
Song, I., & Kim, D. (In press). Three common machine learning algorithms
neither enhance higher prediction accuracy nor reduce spatial
autocorrelation in residuals: An analysis of twenty-five socioeconomic
data sets. Geographical Analysis.
Taggart, T., Ransome, Y., Andreou, A., Song, I., Kershaw, T., &
Milburn, N. (2023). Utilizing activity space assessments to investigate
neighborhood exposure to racism-related stress and related substance
use risk among young Black men. American Journal of Public Health
113(S2), S136-S139.
Jun, Y.-B., Song, I., Kim, O.-J., & Kim, S.-Y. (2022). Impact of limited
residential address on health effect analysis of predicted air pollution
in a simulation study. Journal of Exposure Science and Environmental
Epidemiology 32, 637–643.
Song, I., & Luan, H. (2022). The spatially and temporally varying
association between mental illness and substance use mortality and
unemployment: a Bayesian analysis in the contiguous United States,
2001-2014. Applied Geography 140, 102664.
Ransome, Y., Luan, H., Song, I., Fiellin, D. A., & Galea, S. (2022). Poor
mental health days are associated with COVID-19 infection rates in the
USA. American Journal of Preventive Medicine 62(3), 326–332.
Luan, H., Song, I., Fiellin, D., & Ransome, Y. (2021). HIV infection
prevalence significantly intersects with COVID-19 infection at the
area-level: a USA county-level analysis. Journal of Acquired Immune
Deficiency Syndromes 88(2), 125–131.
Kim, D., & Song, I. (2021). Predicting model improvement by accounting
for spatial autocorrelation: A socio-economic perspective. The
Professional Geographer 73(1), 131–149.
vii
Song, I., Kim, O.-J., Choe, S.-A., & Kim S.-Y. (2020). Spatial heterogeneity
in the association between particulate matter air pollution and low birth
weight in South Korea. Environmental Research 191, 110096.
Park, Y., Song, I., Yi, J., Yi, S.-J., & Kim S.-Y. (2020). Web-based
visualization of scientific research findings: national-scale distribution
of air pollution in South Korea. International Journal of Environmental
Research and Public Health 17(7): 2230.
viii
To My Family
ix
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Aims and structure of the dissertation . . . . . . . . . . . . . . 5
II. THE SPATIALLY AND TEMPORALLY VARYING
ASSOCIATION BETWEEN MENTAL ILLNESS
AND SUBSTANCE USE MORTALITY AND
UNEMPLOYMENT: A BAYESIAN ANALYSIS IN THE
CONTIGUOUS UNITED STATES, 2001–2014 . . . . . . . . . . . . 9
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1.1. Mortality data . . . . . . . . . . . . . . . . . 11
2.2.1.2. Covariate data . . . . . . . . . . . . . . . . . 11
2.2.2. Statistical analysis . . . . . . . . . . . . . . . . . . . 13
2.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1. Descriptive analysis . . . . . . . . . . . . . . . . . . . 16
2.3.2. Spatiotemporal regression results . . . . . . . . . . . . . 17
2.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 26
III. LOCALIZED EFFECTS OF GREENSPACE EXPOSURE
ON MENTAL ILLNESS MORTALITY IN THE PACIFIC
NORTHWEST UNITED STATES . . . . . . . . . . . . . . . . . 28
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1. Study area . . . . . . . . . . . . . . . . . . . . . . . 31
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Chapter Page
3.2.2. Main outcome . . . . . . . . . . . . . . . . . . . . . 32
3.2.3. Greenspace exposure and covariates . . . . . . . . . . . . 33
3.2.3.1. Greenspace exposure assessment . . . . . . . . . 33
3.2.3.2. Covariates . . . . . . . . . . . . . . . . . . . 34
3.2.3.3. Spatial data integration . . . . . . . . . . . . . 36
3.2.4. Model formation . . . . . . . . . . . . . . . . . . . . 37
3.2.4.1. Spatiotemporal interaction model . . . . . . . . 37
3.2.5. Model fitting and sensitivity analysis . . . . . . . . . . . 39
3.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1. Descriptive results . . . . . . . . . . . . . . . . . . . 40
3.3.2. Model results . . . . . . . . . . . . . . . . . . . . . 41
3.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 51
IV. LOCALIZED CAUSAL EFFECTS OF GREENSPACE
EXPOSURE TO MENTAL ILLNESS MORTALITY:
A PIONEERING STUDY IN THE STATE OF
WASHINGTON, 2018 . . . . . . . . . . . . . . . . . . . . . . . 52
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2. Spatial Causal Inference and Statement of Problems . . . . . . . . 54
4.3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2. Exposure assessment . . . . . . . . . . . . . . . . . . 58
4.3.3. Covariates . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.4. Propensity score matching . . . . . . . . . . . . . . . . 60
4.3.5. Subregion definition . . . . . . . . . . . . . . . . . . . 61
4.3.6. Treatment setting with absolute and relative
greenspace exposure . . . . . . . . . . . . . . . . . . . 63
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Chapter Page
4.3.7. Examination of research questions . . . . . . . . . . . . 64
4.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.1. Descriptive analysis . . . . . . . . . . . . . . . . . . . 65
4.4.2. Dichotomization conditions . . . . . . . . . . . . . . . 66
4.4.3. Matching analysis results . . . . . . . . . . . . . . . . 66
4.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 73
V. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . 74
APPENDICES
A. CHAPTER 2 APPENDIX . . . . . . . . . . . . . . . . . . . . 78
A.1. Modeling spatiotemporal interaction . . . . . . . . . . . . . . . 78
B. CHAPTER 3 APPENDIX . . . . . . . . . . . . . . . . . . . . 88
B.1. Detailed descriptions on spatiotemporal models . . . . . . . . . . 88
B.1.1. Spatiotemporal areal model formulation . . . . . . . . . . 88
B.1.2. Description of hyperparameter estimates . . . . . . . . . . 91
B.2. Supplementary tables and figures . . . . . . . . . . . . . . . . 92
C. CHAPTER 4 APPENDIX . . . . . . . . . . . . . . . . . . . . 101
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LIST OF FIGURES
Figure Page
1. Research flow and organization of this dissertation . . . . . . . . . . 8
2. Maps of the coefficient of β1it from the mental illness and
substance use mortality model 5-IV . . . . . . . . . . . . . . . . . 21
3. Tract-level random slope relative risk (RRi1 = exp (βi1))
of one standard deviation increase of the park areas per
10,000 population to mental illness mortality and its
posterior probability of being smaller than one in Oregon
and Washington . . . . . . . . . . . . . . . . . . . . . . . . . 44
4. Data selection flowchart . . . . . . . . . . . . . . . . . . . . . . 58
5. Five subregions in State of Washington based on level 2
ecoregions and urban growth areas with the distribution of
five-year (2013-2017) average NDVI values (above) and the
distribution of average NDVI values in 15-minute walking
areas by subregions . . . . . . . . . . . . . . . . . . . . . . . . 62
6. Difference between treatment probability by
dichotomization (a) in the entire study population and
(b) among the five subregional populations at 2 percentile
intervals across 50-90 percentile thresholds . . . . . . . . . . . . . . 67
7. Average probability of mental illness mortality at 2
percentile intervals across 50-90 percentile greenspace
exposure thresholds from local (red) and global (orange)
data in the State of Washington . . . . . . . . . . . . . . . . . . 68
8. Causal effect estimates from the State of Washington
and three subregions by percentiles (a) and values (b) of
greenspace exposure thresholds . . . . . . . . . . . . . . . . . . . 70
A.1. Temporal trends of unemployment rates (grey lines) and
mental illness and substance use mortality rates (red lines)
in 3,108 contiguous US counties and the overall trends
(dashed bold lines) . . . . . . . . . . . . . . . . . . . . . . . . 82
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Figure Page
A.2. Spatiotemporal distribution of one-year lagged
unemployment rates in 3,108 contiguous US counties in
2001-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
A.3. Spatiotemporal distribution of mental illness and
substance-use mortality rates (per 100,000 people) in 3,108
contiguous US counties in 2001-2014 . . . . . . . . . . . . . . . . 84
A.4. Probability map of the random slope of unemployment
rates in Model 5-IV . . . . . . . . . . . . . . . . . . . . . . . . 85
A.5. Residual maps of Model 5-IV. . . . . . . . . . . . . . . . . . . . 86
A.6. Mental health and substance use treatment facility per
100,000 people in counties in the contiguous United States (2018) . . . 87
B.1. Map of state, county, and census tract boundary and
elevation in Oregon and Washington . . . . . . . . . . . . . . . . 99
B.2. One-year lagged annual mean normalized difference
vegetation index (NDVI) at each census tract by year
during the study period (2006–2018) from the moderate
resolution imaging spectrometer (MODIS) Terra sensor . . . . . . . . 100
C.1. Standardized difference of covariates in the treated and
controlled groups by five percentile thresholds for treatment
definition in the State of Washington . . . . . . . . . . . . . . . . 103
C.2. Standardized difference of covariates in the treated and
controlled groups by five percentile thresholds for treatment
definition in subregions . . . . . . . . . . . . . . . . . . . . . . 104
C.3. Effect estimates from matching analysis by five percentile
thresholds for treatment condition in five core-based
statistical areas where dichotomization conditions were
fulfilled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
xiv
LIST OF TABLES
Table Page
1. Model specifications of the baseline model (Model 1) and
random effects with and without spatiotemporal interaction
in random slopes (Models 2–5) . . . . . . . . . . . . . . . . . . . 14
2. Summary statistics of variables in 3,108 counties . . . . . . . . . . . 17
3. Model fit statistics . . . . . . . . . . . . . . . . . . . . . . . . 18
4. Regression coefficients and the 95 % credible intervals (CrI)
of fixed and random effects of Models 1 and 5-IV . . . . . . . . . . . 19
5. Annual rate of mental illness mortality per 10,000
population in Oregon and Washington in 2006–2018 . . . . . . . . . . 41
6. Deviance and Watanabe-Akaike information criteria of five
model settings with and without spatiotemporal interaction . . . . . . 43
7. Estimated relative risks of explanatory factors from Model 5 . . . . . . 46
8. Equivalence conditions for dichotomizing continuous
exposure variables from Stitelman et al. (2010) . . . . . . . . . . . . 64
A.1. Pearson correlation matrix of dependent and independent variables . . . 81
A.2. Variance inflation factor (VIF) of each variable . . . . . . . . . . . . 81
A.3. Summary of model hyperparameters of from Model 5-IV:
summary statistics of posterior marginals and 95 % credible
intervals of precisions for each model component . . . . . . . . . . . 82
B.1. List of North American Industry Classification System
(NAICS) codes for identifying care facilities . . . . . . . . . . . . . 92
B.2. Principal component analysis results for deriving
socioeconomic deprivation index . . . . . . . . . . . . . . . . . . 93
B.3. Correlation matrix of explanatory variables . . . . . . . . . . . . . 93
B.4. Variance inflation factors of explanatory variables . . . . . . . . . . . 94
xv
Table Page
B.5. List of twenty-eight excluded census tracts and the reasons
of exclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
B.6. Descriptive statistics of the data . . . . . . . . . . . . . . . . . . 96
B.7. Sensitivity analysis results . . . . . . . . . . . . . . . . . . . . . 97
B.8. Summary of hyperparameter estimates . . . . . . . . . . . . . . . 98
C.1. Descriptive statistics of the decedents who deceased in
natural manners in the State of Washington, 2018 . . . . . . . . . . . 101
xvi
CHAPTER I
INTRODUCTION
1.1 Background
Mental illness is a rising global public health problem. Studies reported
mental illness mortality as a major pressure to the increase in overall mortality
throughout the world (Campbell, 2010; GBD 2019 Mental Disorders Collaborators,
2022). In the United States, both the incidence and mortality of mental illness
have increased in the last two decades (Chang et al., 2010; Fekadu et al., 2015;
Jayatilleke et al., 2017; Walker et al., 2015). As a response, the mechanism and
etiology of mental illness have been transformed in the literature, where scholars
accounted for both compositional and contextual factors to explain mental health
outcomes across various spatial scales1.
Early literature suggested that the prevalence of mental illness notably
differs by individual traits. For instance, women were found to be more susceptible
to mental illness (Gove, 1972), and there was no evidence of racial differences
(Warheit et al., 1975). These studies suggested an alternative perspective for
the analysis of mental illness against perspectives emphasizing personal motives
alone, although they were based on empirical evidence rather than a theory.
Income, sex/gender, and race/ethnicity are often linked to mental illness in the
literature (McGilloway et al., 2010; Ridley et al., 2020). Contextual factors have
been extensively accounted for by early scholars in ecological studies. These factors
are thought to influence personal factors on the onset of mental illness. The list
of contextual variables has been expanded, which encompasses residential and
1Scale here refers to as a term that includes a nested hierarchy of geographic units.
1
built environments (Goldsmith et al., 1986), crime (M. White et al., 1987), and
socioeconomic status (Gruebner et al., 2017; Leventhal & Brooks-Gunn, 2003).
The spatial and temporal dimensions of emerging compositional and
contextual factors have been emphasized in the literature. Processual or
incidental factors like events in a life course (e.g., post-stress trauma) highlight
the significance of accounting for the temporality to understand mental illness.
For instance, longitudinal study designs are usually employed to trace the
changing relationship between outcomes and explanatory factors over time.
Spatially, collective effects, which include the social network (the impact of the
relationship with other people) and social grouping effect (the impact of group
identification in individuals), are hypothesized to mediate other factors of mental
illness. Environmental factors are actively explored in addition to neighborhood
socioeconomic status in mental illness studies. As a surrogate of a specific or
an integrated physical environmental feature, environmental factors have been
gradually integrated into conceptual frameworks in mental health research
(Bratman et al., 2019; Dzhambov, Markevych, Hartig, et al., 2018; Helbich, 2018b;
Markevych et al., 2017), and numerous empirical studies supported the integration
(Oh et al., 2020; Speldewinde et al., 2009; Van Haaften & Van de Vijver, 1999;
F. Wang et al., 2018). Greenspace (e.g., parks and vegetation) and bluespace
(e.g., rivers and lakes) exposures are pronounced as the major factors of interest in
contemporary mental health research (Bratman et al., 2019; Helbich, 2018a; Labib
et al., 2020; Su et al., 2019; M. P. White et al., 2021; World Health Organization,
2021).
The emergence of spatiality as a key element in the study of mental
illness risk factors raised a crucial question: What role does geography play in
2
our understanding of mental illness? The answer to this question hinges on two
fundamental insights offered by geography. First, geography underscores that the
majority of factors influencing mental health–including the physical environment
and almost all contextual factors–vary across space. These factors are therefore
spatially organized. Examples of such factors include neighborhood-level income
and ethnic composition, which are subject to spatial segregation (Bettencourt et al.,
2019; Reardon & Bischoff, 2011). This variability across spatial scales (Catney,
2018) highlights the need of conducting mental health research with different
spatial frameworks.
The second insight offered by geography lies in the spatial disparities in
mental illness incidence and mortality rates. Such disparities, demarcated by
jurisdictional or natural boundaries, bring geographic disparity to the forefront
of mental health studies. Understanding these disparities not only helps explain
the prevalence of mental illness across various regions but also guides the design of
proactive, geographically tailored interventions. Such interventions are important
given the growing burden of adverse mental health outcomes and the limited
resources available for addressing them.
In recent years, mental health research has shifted from a focus on the
spatial disparity in the outcomes (i.e., disease mapping) to an understanding of
the spatial disparity in environment factors’ impacts on mental health (i.e., effect
mapping). This transition enables stakeholders in public mental health policies
to identify risk factors specific to certain geographic areas. It has been widely
accepted that spatial disparities in mental health outcomes exist at both national
and subnational levels, often mirroring socioeconomic gradients (Griffith & Jones,
2020; Philo, 2005). Comparative studies have also demonstrated spatial differences
3
in mental health outcomes and explanatory factors across countries (Gissler et al.,
2013) and subnational regions (Andrilla et al., 2018; Charlesworth et al., 2023;
Cortina & Hardin, 2023; Gorski-Steiner et al., 2022; Hudson, 2012; Ma et al., 2009;
Maas et al., 2019; Rodero-Cosano et al., 2016; Ryan et al., 2023; Sutarsa et al.,
2021). Given this context, it becomes imperative to ask whether spatial disparities
in the impacts of risk factors on mental illness remain consistent over time. This
question is especially relevant for factors exhibiting high temporal volatility or
variation. Exploring the spatial patterns in mental illness has been common in
research, employing measures such as spatial autocorrelation indices and spatial
clustering analyses (Grigoroglou et al., 2020; Ngui et al., 2013). However, the
research is noticeably sparse on investigations of spatial disparities in the effect
of risk factors across different spatial scales. Only a few studies hypothesized
the spatially varying effects of selected factors including mental health service
utilization (Law & Perlman, 2018), poverty, insufficient sleep, marital status
(Yankey et al., 2021), and health behavior (Choi & Kim, 2017), where the first
two studies were done at a small area level in a city scale, underscoring the need for
further evidence on spatial disparity at larger spatial scales.
Regarding the spatiotemporal analysis of mental illness, two significant
research gaps stand out. The first is the lack of attention given to the interaction
between spatial and temporal dimensions in effects. While recent years have seen
an increased availability of longitudinal data on mental health outcomes and
explanatory factors, researchers have yet to fully leverage this data to understand
the spatiotemporal interaction that affect mental health outcomes. There is a
pressing need for modeling approaches that capture spatially varying effects of
contributing factors (Janko et al., 2019; Labib et al., 2020; Shin et al., 2020). The
4
second gap lies in our understanding of the spatiality of causal effects in mental
illness research. While there has been growing interest in establishing causal
relationships between different factors and mental illness incidence and mortality
(Ridley et al., 2020; Uher & Zwicker, 2017), the role of spatial variations in these
effects remains largely unexplored. Thus, future research must aim to bridge these
gaps by focusing on the spatiotemporal interplay of factors influencing mental
health outcomes and investigating the spatially varying causal effects on mental
illness. Such studies will contribute to expanding our understanding of mental
illness, providing valuable insights to design effective interventions.
1.2 Aims and structure of the dissertation
The primary goal of this dissertation is to address two crucial gaps identified
in current mental health research. I attempt to accomplish the goals by three
approaches: scrutinizing the spatial and temporal disparities in the influence of
unemployment and greenspace exposure on mental illness mortality, performing
this analysis at different spatial scales, and extending the analysis to infer causal
effects beyond mere associations. The dissertation can be conceptualized as an
exploration of the spatiotemporal dynamics of socio-environmental factors and
their associations and causal impacts on mental illness mortality through three
case studies across different spatial scales: counties, census tracts, and individual
residential locations. This approach offers an integrated and comprehensive
understanding of the relationship between mental health outcomes and socio-
environmental factors.
Unemployment rates and greenspace exposure, the primary factors of
interest of this dissertation, are considered significant contributing factors of mental
health outcomes (Bartley, 1994; Barton & Rogerson, 2017; Collins et al., 2020;
5
Marazziti et al., 2021; Uutela, 2010; Virgolino et al., 2022; Wan et al., 2022). The
effects of these variables have been assumed to be constant across spatial entities
within a single spatial framework. I challenge this assumption by proposing that
these variables have spatially and temporally varying effects on mental illness. To
reveal the spatial disparity in these associative and causal effects, the scope of the
investigation is progressively narrowed down to focus on finer levels of spatial scale.
Chapter 2 presents a nationwide, county-level analysis of mental illness and
substance abuse mortality rates, with a particular focus on the spatiotemporally
varying effects of unemployment rates from 2001 to 2014. This fourteen-year
span, encompassing two significant economic recessions including the Great
Recession, provides a good case to trace the temporal shift in the spatial pattern
of unemployment’s impact on mental illness mortality. In Chapter 3, the analysis
narrows down to a regional level, where I will examine the impact of greenspace
exposure on mental illness mortality in the States of Oregon and Washington at the
census tract level. This chapter employs spatiotemporal hierarchical linear models
to analyze spatial variation in the effects of greenspace exposure, accounting for
excess zeros in the aggregated mental illness mortality dataset. Chapter 4 takes
the analysis a step further by attempting to estimate causal effects. It focuses on
individual-level mental illness mortality data, using observational causal inference
approaches (i.e., matching methods) to explore the spatial difference in the causal
effect of greenspace exposure (defined as the average vegetation index value in a
15-minute walking area along the road network) on mental illness mortality. This
chapter also uncovers challenges associated with estimating causal effects across
multiple regions, particularly regarding the conditions for dichotomization to
define the treated and controlled group from continuous greenspace exposure. The
6
diagnosis is conducted based on the theoretical conditions of equivalence suggested
by Stitelman et al. (2010) (Stitelman et al., 2010).
In sum, this dissertation provides a comprehensive examination of the
spatial disparities in the associative and causal effects of unemployment and
greenspace exposure on mental illness mortality. Such examination enriches,
corroborates, and challenges existing theories seeking a universal explanation
for the effects of these factors on mental health (Figure 1). By investigating
the local contexts that shape these effects, the dissertation contributes to a
deeper understanding of the interplay between mental health outcome and socio-
environmental factors.
7
Figure 1. Research flow and organization of this dissertation
Outcome Mental illness – Mortality 
Main theme Spatiotemporal disparity and difference in effects of—
Chapter 2 Chapter 3 Chapter 4
Main factor 
of interest Unemployment Greenspace Greenspace
Contiguous U.S. Pacific Northwest State of Washington
Cases
Counties Census tracts Individuals
“Multi-scale”
Analytic frameworks Spatiotemporal analysis Causal analysis
“Associative to causal” Bayesian hierarchical models Matching models
Local explanation of disparity
Contribution Theory-engaging
Expanding conventional theories and pathways
8
CHAPTER II
THE SPATIALLY AND TEMPORALLY VARYING ASSOCIATION BETWEEN
MENTAL ILLNESS AND SUBSTANCE USE MORTALITY AND
UNEMPLOYMENT: A BAYESIAN ANALYSIS IN THE CONTIGUOUS UNITED
STATES, 2001–2014
This chapter is based on the published work in volume 140 of the journal Applied
Geography in March 2022. I chose the topic, collected data, conducted statistical
analysis, and wrote the draft; Dr. Hui Luan, the dissertation chair and my advisor,
supervised the statistical analysis and revised the draft. This chapter is a revision
of the original work.
2.1 Introduction
The Great Recession led to a global deterioration of mental health status
(Bacigalupe et al., 2016; Margerison-Zilko et al., 2016). During this time, mental
illness mortality rates increased the United States, reaching a peak of 49.5 per
100,000 population in 2013 (CDC, 2021). The unemployment surge during the
Great Recession reignited a broad scholarly inquiry to examine the impact of
unemployment on mental health with its variable relationship during economic
recessions (De Vogli et al., 2014; Frasquilho et al., 2015; Haaland & Telle, 2015;
Norström & Grönqvist, 2015). Evidence suggested a clear negative association
between mental health and unemployment, leading to increased substance use
mortality and decreased life quality and satisfaction (Bartelink et al., 2020; Junna
et al., 2020; Mousteri et al., 2018; Murphy & Athanasou, 1999; Paul & Moser,
2009). These effects seem more profound in early life stages, where unemployment
9
has been linked to heightened cigarette use (Lee et al., 2015), high-risk alcohol use
(Henkel, 2011), and general substance use (Compton et al., 2014).
Few large-scale ecological studies have accounted for spatial variations in
these associations, while an extensive number of individual-level studies indicated
variability in the impact of unemployment on mortality across countries. The
ecological studies attributed such variability to the difference in labor policy and
workforce skills (McLeod et al., 2012; Norström & Grönqvist, 2015; van Lenthe,
2005). Despite suggesting spatial difference in the impacts, these studies assumed
a spatially constant impact of unemployment on mental health outcomes, which
may overlook the spatial autocorrelation of both mortality and unemployment rates
(Halliday, 2014; Lorant et al., 2001; Molho, 1995; Patacchini & Zenou, 2007). Given
these disparities, a spatially explicit approach is required to fully understand how
local contexts may influence the unemployment and mental health relationship
(Heutel & Ruhm, 2016; Sameem & Sylwester, 2017; Shoff et al., 2012; Trgovac
et al., 2015)
Informed by these gaps in the literature, this chapter poses two key research
questions. First, how does the relationship between mental illness, substance use
(MISU) mortality, and unemployment vary across U.S. counties over time? Second,
how has unemployment impacted MISU mortality spatiotemporally during the
2001 and 2008 economic recessions? By utilizing a multilevel regression model
with spatiotemporal components, I seek to demonstrate how this relationship
evolves across space and time. These research questions not only address the
ongoing debate about the effect of economic recessions on MISU mortality rates,
but also explore whether these impacts manifest differently at a county level given
spatiotemporal variations in both mortality and unemployment rates. Furthermore,
10
this study revisits the claim that mortality rates decrease during recessions while
shifting the focus from the mortality rates to the effect of unemployment rates
on them. The study period, encompassing two economic recessions of 2001 and
2007, provides good cases to answer the research questions (Ariizumi & Schirle,
2012; Haaland & Telle, 2015; Miller et al., 2009; Neumayer, 2004; Ruhm, 2000; The
National Bureau of Economic Research, 2020).
2.2 Methods
2.2.1 Data.
2.2.1.1 Mortality data. The primary outcome of interest is the county-level
Mental Illness and Substance Use (MISU) mortality rates provided by the Institute
for Health Metrics and Evaluation (IHME) (Institute for Health Metrics and
Evaluation, 2016). These rates are cause-specific and age-standardized from 1980 to
2014 across twenty-one categories. The original work’s authors categorized the raw
mortality data by reclassifying codes in the International Classification of Diseases
9th and 10th (Dwyer-Lindgren et al., 2016). Given the consistency of county-level
boundaries in the contiguous United States throughout the study period, the use of
this dataset avoids potential misalignment problems (Gryparis et al., 2009). MISU
were grouped into a single category due to confidentiality constraints associated
with the small number of MISU deaths in this dataset.
2.2.1.2 Covariate data. The key explanatory variable is the unemployment
rate, which is operationalized as the one-year lagged annual average unemployment
rate. This one-year lag was chosen to assess the short-term impact of
unemployment on MISU mortality rates. The unemployment data was sourced
from the Local Area Unemployment dataset, which has been tracking monthly
11
unemployment rates for all U.S. counties since 1976 (U.S. Bureau of Labor
Statistics, 2019).
Eight covariates were collected from the IPUMS National Historical
Geographical Information System to control for potential confounding factors
affecting MISU mortality (Manson et al., 2019; Ruggles, 2014). These were selected
based on their relevance to MISU mortality as identified in previous ecological
studies and other research that linked neighborhood socioeconomic status to MISU
(Ballester et al., 2019; Catalano et al., 2011; Goldsmith et al., 1998; Jia et al.,
2009; Kloos & Townley, 2011; Monnat, 2018; Moortel et al., 2018; Ridley et al.,
2020; Silver et al., 2002; van den Berg et al., 2017). The covariates represent three
indicators representing county-level economic status: median household income
(adjusted to the year 2000 values using the consumer price index for consistency),
renter-occupied housing ratios, and the ratio of households under the poverty
line. Factors were included such as the elderly population, considered protective
against MISU disorders (Silver et al., 2002), higher educational attainment, often
associated with a protective effect against MISU (Goldsmith et al., 1998; Melchior
et al., 2015; Seabury et al., 2019), ethnic composition represented by the ratio of
the non-white population, and other demographic conditions like the ratio of the
rural population and the ratio of single-person households (Solmi et al., 2017).
Since each year’s data contained eight variables from two decennial census during
the study period, the 2001-2009 mortality rates were matched to the covariates of
the 2000 Census and the 2010-2014 rates to the 2010 Census covariates.
It was found that the pairwise correlations of the covariates range between
−0.727–−0.670, with only 5 (out of 36) having absolute values greater than
0.5. The variance inflation factors were well below 10, indicating no severe
12
multicollinearity (James et al., 2021). Thus, there was no need to compute a
composite socioeconomic index using these covarites. County boundaries in
2014 were collected from the Census Bureau (U.S. Census Bureau, 2015). Some
covariates, however, were incomplete due to small population sizes or confidentiality
issues. Literature suggests that when the missing rate is less than 3 %, the
imputation accuracy is acceptable even when employing a simple imputation
method (Harrell, 2015). As such, I imputed missing values with the global median,
given all the covariates had missing rates less than 1 %.
2.2.2 Statistical analysis. A set of spatiotemporal regression models were
implemented to explore the spatial variation in the impact of unemployment rates
on MISU mortality over time. The set was identified by adapting a hierarchical
linear model with a spatiotemporal interaction component (Blangiardo &
Cameletti, 2015, p. 240). Among four types of spatiotemporal interactions (often
expressed with roman numerals I–IV), the interaction with the higher type
order reflects the more complex relationship between the spatial and temporal
components than the lower ones. I compared four types of spatiotemporal
interaction terms in the random slope (Banerjee et al., 2015; Blangiardo &
Cameletti, 2015; Haining & Li, 2020; Knorr-Held, 2000). The type-IV interaction
models that the impact of the unemployment rate on MISU mortality rate in
one county is similar to its spatial and temporal neighbors. Thus, the present
year’s MISU mortality rate is explained by the unemployment rates of neighboring
counties and the previous year (Khana et al., 2018). The spatial, temporal, and
spatiotemporal interaction terms were incrementally included in the random slope
of unemployment rates, which is numbered from Model 1 to 5 (Table 1). Model 5
includes all components in the model, where the spatiotemporal interaction term
13
has four types, which were numbered with Models 5-I to Model 5-IV. The most
comprehensive model, Model 5-IV, is specified in Formula 2.1.
Table 1. Model specifications of the baseline model (Model 1) and random effects
with and without spatiotemporal interaction in random slopes (Models 2–5)
Model Fixed and random main effects Random slope components in β1it
Spatial Temporal Spatiotemporal*
1
2 ∑ u1i·
3 β 90 + k=1 βkxkit + ui + vi + γt + εit γ1·t
4 u1i· γ1·t
5 u1i· γ1·t I–IV (RW(1)**)
* Interaction type (assumption for temporal grouping). ** First-order random walk.
∑
yit = β0 + β1itx
9
1it + k=1 βkxkit + ui + vi + γt + εit
βk ∼ N (0, τ−1β )k
ui ∼ ICAR(WS, τ−1u ), vi ∼ N (0, τ−1v ), εit ∼ N (0, τ−1ε )
γt = ρ0γt−1 + εt0, ρ0 ∼ N (0, 0.15), εt0 ∼ N (0, τ−1ε )0 (2.1)
β1it = u1i· + γ1·t + δ1it
u1i· ∼ ICAR(WS, τ−1u )1
(γ − γ ) ∼ N (0, τ−11·t 1·(t−1) γ )1
∆ ∼ N (0, τ−1δ [(D−WS)⊗WT ])
yit denotes the MISU mortality rate in county i and year t by including
a spatiotemporal random slope of one-year lagged unemployment rate at each
county i and year t, β1it. The mortality rates were log-transformed for assuming the
Gaussian likelihood. Thus, β1it is exponentiated for interpretation. For example,
14
when a model yields β1it = 0.05, it means that one standard deviation (2.78 %)
increase of one-year lagged unemployment rate is associated with 5.1 % increase
in MISU mortality rate (exp(0.05) − 1 = 1.051 − 1 = 0.051). The county-level
unemployment rate effect is modeled to have a random slope coefficient, that is,
the sum of a spatiotemporally structured part δ1it. The type-IV spatiotemporal
interaction (δ1it, ∆ in Formula 2.1 denotes the vector of δ1it) is expressed in
Formula 2.1. It models the spatiotemporal interaction by computing a Kronecker
product of (D −WS) and the temporal weight matrix WT to integrate the spatial
intrinsic conditional autoregressive (ICAR) and temporal first-order random walk
(RW1) processes (see Appendix A for an example) (Vicente et al., 2020; Williams
et al., 2019). Th∑e term D denotes a diagonal matrix with the sum of each row’s
elements (diag( j wSij)), where wSij is the (i, j) element of WS. The fixed effects
of other covariates are denoted as βk (k = 2, · · · , 9).
Known as the Besag-York-Mollié (BYM) model (Besag et al., 1991), ui and
vi separate spatially structured (i.e., ICAR) and exchangeable effects for every
county. The spatially structured effect depends on the distribution of adjacent
spatial units. For the spatial structure, counties sharing at least a vertex are
considered as neighbors (i.e., first-order Queen’s contiguity). γt is the temporal
effect that incorporates temporally autocorrelated functions by specifying a RW1
structure. The random slope term β1it consists of the spatially structured u1i·, the
temporally structured γ1·t, and the spatiotemporal interaction term δ1it.
Four types of spatiotemporal interactions in β1it were compared to identify
the term that fits the dataset best (Blangiardo & Cameletti, 2015; Haining &
Li, 2020). The models were implemented with the Integrated Nested Laplace
Approximation (INLA) approach. The INLA method assumes the latent Gaussian
15
distributions to estimate marginal posteriors, which is known to be effective in
large data analysis (Rue et al., 2017). Models were compared with the Deviation
Information Criterion (DIC) (Spiegelhalter et al., 2002) and the Watanabe-Akaike
Information Criterion (WAIC) (Watanabe, 2009). The best-fitting model is the one
with the lowest DIC and WAIC values. For hyperpriors, a weakly informative prior,
logΓ(1, 0.00005), was used for the log-precision hyperparameters ui, vi and γt. A
prior logΓ(100, 0.5) was applied to u1i· and γ1·t based on the assumption that the
precision of the random slopes is larger than that of fixed and main random effects.
All statistical analyses were performed with R 4.1.2 and R package INLA version
2021.11.01 (R Core Team, 2021; Rue et al., 2009; Verbosio et al., 2017).
2.3 Results
2.3.1 Descriptive analysis. The MISU mortality rates steadily increased
during the study period, while unemployment rates exhibited higher variability
than mortality rates, with a pronounced increase during the Great Recession
(2007–2009). The county-to-county variation in mortality rates was greater than
that of unemployment rates, as the county-specific mortality trends diverged from
the median trend (Figures A.1–A.3). The temporal trends in MISU highly varied
across counties, where some stagnated and others increased rapidly. Given the
disparate scales of the covariates, the coefficient of variation (CV) was employed
for comparative purposes. The ratios of the non-white and rural population showed
the highest CVs, whereas variables such as median household income, the ratio of
renter-occupied housing, and the ratio of the elderly population displayed relatively
lower CVs (Table 2).
16
2.3.2 Spatiotemporal regression results. The best-performing model
incorporated a type-IV interaction term, yielding the best goodness-of-fit metrics.
Among all models with random effects, the full model (5-IV) had the lowest
DIC and WAIC values (Table 3). Models incorporating only spatial random
effects (Model 2) showed better fit than those including temporal random effects
(Model 3). The global impact of the one-year lagged unemployment rate on
MISU mortality gradually strengthened from Model 1 to Model 5-IV, with the
impact increasing from 0.010 to 0.014. Notably, two covariates changed their
coefficient directions: ratios of renter-occupied housing (from -0.004 in Model
1 to 0.008 in Model 5-IV) and single-person households (from -0.025 to 0.005).
Meanwhile, two other variables exhibited diminishing impacts on MISU mortality:
the coefficients for median household income shifted from -0.036 to -0.019, and the
ratio of the elderly population moved from 0.018 to 0.009. The remaining variables
Table 2. Summary statistics of variables in 3,108 counties
Variable Mean Median SD 1 (CV 2)
One-year lagged unemployment rate (%) 6.57 6.00 2.78 (0.42)
Median household income
35563.51 34085.42 9032.27 (0.25)
(Inflation-adjusted as of 2000)
Ratio of non-white population (%) 15.76 9.42 16.17 (1.03)
Ratio of the population with or
17.56 15.44 8.28 (0.47)
higher than bachelor’s degree (%)
Ratio of the population below the poverty level 14.39 13.41 6.31 (0.44)
(%)
Ratio of the rural population (%) 49.67 42.87 33.73 (0.68)
Ratio of renter-occupied housing (%) 26.52 25.22 7.60 (0.29)
Ratio of single-person households (%) 25.94 26.03 3.95 (0.15)
Ratio of the elderly population
15.22 14.85 4.15 (0.27)
(65 years old or older, %)
1 Standard deviation; 2 Coefficient of variation.
17
demonstrated consistent coefficients. The results reported in the next section are
derived from the best-fitting model, Model 5-IV.
Table 3. Model fit statistics
Model DIC WAIC
1 -96382.50 -96295.92
2 -105528.97 -105591.72
3 -96539.23 -96450.34
4 -105680.51 -105735.67
5-I -105633.44 -105678.01
5-II -115598.62 -117514.14
5-III -105657.35 -105700.21
5-IV -119361.94 -120751.66
Note: the lowest value is highlighted.
Three key findings emerge regarding the random slope coefficients of
unemployment rates in the spatiotemporal interaction term. First, the random
slopes (β1it) displayed the clear spatial variation (Figure 2), contrasting with the
spatially constant coefficient of unemployment rates in Model 1 (the base model).
The coefficient of one-year lagged unemployment rate in Model 1 was significantly
positive (1.01 %, 95 % credible interval: [0.80 %, 1.21 %]) and invariant across
all counties, while β1it from Model 5-IV was between -0.666 and 0.479, which
are equivalent to -47.63 % and 61.45 % change in MISU mortality rates by one
standard deviation (2.78 %) increase of one-year lagged unemployment rate (Table
4). The positive random slope coefficients were found in the counties in Missouri,
Illinois, Indiana, Ohio, and Pennsylvania in 2001–2004, among which counties near
Cincinnati gradually shifted to the border of West Virginia and Kentucky after
18
Table 4. Regression coefficients and the 95 % credible intervals (CrI) of fixed and
random effects of Models 1 and 5-IV
Model 1 Model 5-IV
2.268* 2.272
Intercept
(2.265, 2.272)** (2.270, 2.275)
0.010 0.014
One-year lagged unemployment rate
(%) (0.008, 0.012) (0.011, 0.017)
−0.666 (minimum)
(-0.774, -0.557)
Random slopes of one-year lagged
unemployment rate –−0.479 (maximum)
(0.374, 0.583)
Median household income -0.036 -0.019
(Inflation-adjusted as of 2000) (-0.041, -0.031) (-0.024, -0.012)
0.042 0.044
Ratio of non-white population (%)
(0.034, 0.050) (0.035, 0.052)
-0.007 -0.019
Ratio of the population with or higher
than bachelor’s degree (%) (-0.012, -0.002) (-0.025, -0.014)
0.026 0.028
Ratio of the population below the
poverty level (%) (0.022, 0.029) (0.023, 0.032)
-0.015 -0.015
Ratio of the rural population (%)
(-0.020, -0.008) (-0.021, -0.008)
-0.004 0.008
Ratio of renter-occupied housing (%)
(-0.009, 0.001) (0.001, 0.014)
-0.025 0.005
Ratio of single-person households (%)
(-0.030, -0.020) (-0.001, 0.010)
Ratio of the elderly population 0.018 0.009
(65 years old or older, %) (0.013, 0.022) (0.003, 0.015)
* Mean, ** 95 % CrI; Note: All explanatory variables were standardized.
19
the Great Recession. Second, regions with strong positive correlations between
MISU mortality and unemployment expanded geographically throughout the study
period. After Great Recession, an increase in counties with higher positive β1it
values was primarily observed in South and North Dakotas. Lastly, the association
between MISU mortality and unemployment generally contracted during and in
the wake of the Great Recession (2007–2010, between -0.1 and 0.1), compared to
other study years (Figure 2). Summary statistics for the posterior distributions of
hyperparameters are detailed in Table A.3.
2.4 Discussion
MISU mortality’s association with unemployment varied both spatially and
temporally. The results demonstrated that the association was dynamic rather
than static (Towne et al., 2017). Considering that the study period spanned from
2001 to 2014, it becomes evident that this association underwent considerable
changes, adapting and evolving with time and location. Through the period of
2002 to 2003, immediately after the 2001 recession, and again during 2009 to 2011,
corresponding with the Great Recession, the unemployment rates rose consistently
in most counties (Figure A.2). The manifestation of this trend was evident in the
striking shifts seen in the coefficients of some covariates. In comparison to the
base model, the best-fitting model yielded significant transformations in both the
magnitude and direction of these coefficients. Such alterations in the coefficients
underscore the crucial need to take into account spatiotemporal dependencies
when analyzing multi-year, areal MISU mortality data. The shift observed in the
spatiotemporal random slopes emphasized the significant impact of aligning the
spatial and temporal resolution between the MISU mortality rates and one-year
20
Figure 2. Maps of the coefficient of β1it from the mental illness and substance use
mortality model 5-IV
21
lagged unemployment rates. The inversion of the coefficients of the two covariates
is intriguing. The alteration in coefficients can potentially be ascribed to the
impacts arising from resolution mismatches (Cross et al., 2019) and the mediating
effects brought about by the spatiotemporal interaction.
The results of the study reinforce the importance of considering the role
of spatiotemporal resolution in covariates when implementing spatiotemporal
areal disease modeling. The evidence strongly suggests that such an approach is
necessary for comprehending the complex interplay of factors contributing to the
spatial and temporal changes in MISU mortality rates in relation to unemployment.
Consequently, a more detailed and careful investigation into this matter is called
for, promising to enhance our understanding of these dynamics.
Three primary patterns emerged from the analysis. First, a consistent
positive correlation was found in rural Appalachia, potentially attributed to
marginalized living conditions and economic hardship prevalent in these regions
(Moody et al., 2017; Shamblin et al., 2012). Additionally, the economic stagnation
in these areas, compounded by rising unemployment rates, might have contributed
to increased MISU mortality levels. Limited access to psychiatric clinics or
rehabilitation facilities could be another factor contributing to this correlation
in these regions (Rural Health Information Hub, 2021). For instance, MISU
care facilities are particularly sparse in the Midwest, central South, and western
Appalachian regions. Most counties in these areas exhibit lower access to MISU
care facilities compared to the national average (13.73 facilities per 100,000
population) (Figure A.6). This pattern can be further elucidated by socio-
psychological deprivation impacting youth groups (Alcántara & Gone, 2007;
Brockie et al., 2015).
22
Second, the influence of unemployment on mental health appears to have
grown stronger in the Mountain West following the Great Recession. However,
this observation warrants a measured interpretation due to the relatively low
unemployment and mortality rates these counties maintained throughout the
entire study period. The high sensitivity of mortality rates to fluctuations in
unemployment rates indicates the existence of internal or endogenous factors,
such as social interaction dynamics and local responses to economic recession. The
relative deprivation hypothesis could offer a possible explanation (Wilkinson &
Pickett, 2007). This theory suggests that deprivation arises not from an individual’s
absolute social status, but rather from their relative social circumstances.
Therefore, individuals who become unemployed in areas with low unemployment
rates may experience heightened adverse mental health outcomes due to a stronger
sense of relative deprivation. This aligns with previous research that underscores
the relationship between relative deprivation and mental health outcomes (Beshai
et al., 2017; Kondo et al., 2008; Mishra & Carleton, 2015; Saito et al., 2014;
Salti, 2010). Beyond this, it’s important to recognize that policy responses to
unemployment may vary across counties, which could influence the observed
associations (Thiede & Monnat, 2016). The delayed response to the impact of
the Great Recession could be one of the contributing factors to the increased
association between MISU mortality and unemployment observed in the Mountain
West. Should a definitive relationship between relative deprivation and the onset
of mental illness be established, it would further substantiate this explanation. The
examination of such internal dynamics and regional policy responses forms a critical
part of understanding the intricate ways in which unemployment affects mental
health outcomes.
23
Finally, in an intriguing pattern, virtually all counties exhibited a diminished
influence of the unemployment rate on MISU mortality during the Great Recession
compared to periods before and after. Additionally, there was a smaller disparity
in these effects across counties during the recession years than in non-recession
years. This suggests that the impact of economic recessions might actually reduce
the detrimental effects of unemployment on MISU mortality, supporting the
relative deprivation hypothesis. Interestingly, these findings align with the notion
of spatiotemporally heterogeneous impacts of unemployment on MISU mortality,
as well as the counter-intuitive idea that recessions may be associated with benefits
for mortality rates (Ariizumi & Schirle, 2012; Miller et al., 2009; Neumayer, 2004;
Ruhm, 2000). The key takeaway from this study is that this benefit of recession
is not universal but is locally evident in the impact of unemployment on MISU
mortality at the county level, and moreover, this county-level effect fluctuated
over time. This understanding has crucial policy implications. It suggests that
policy interventions need to be tailored to the specific needs of different counties.
By identifying counties where the effect of unemployment on MISU mortality is
particularly pronounced, resources can be allocated more effectively. Prioritizing
these areas for intervention can enhance state-level unemployment benefits, which
in turn could serve to alleviate the adverse health impacts of unemployment
(Cylus et al., 2015). Thus, understanding the spatial and temporal dynamics of
unemployment effects can guide more targeted and effective public health policies.
This chapter contributes to the existing literature in two significant
ways. Firstly, it underscores the necessity for locally-tailored intervention
policies to address areas with positive associations between MISU mortality
and unemployment. If unemployment is considered an external factor, local
24
health policymakers can respond to the increased impact of unemployment on
mortality by identifying areas experiencing the abrupt unemployment increase.
Additionally, by considering individual-level factors like subjective health evaluation
or behavioral adjustment post-unemployment, the findings can inform proactive
policies aimed at weakening the link between increased MISU mortality and local
unemployment. Secondly, this chapter offered a methodological contribution by
comparing various spatiotemporal interaction terms in models for the association
between MISU mortality and unemployment–an area rarely explored. I found that
the type-IV interaction term best fits the data, suggesting that the association
between mortality and unemployment in one area is correlated with associations
in neighboring areas and times.
Several limitations of this study must be acknowledged. First, although a
spatially varying relationship between MISU mortality and unemployment was
observed, individual studies have shown that an explicit non-linear relationship
(e.g., squared term of unemployment rates on mortality rates) might exist
(Bonamore et al., 2015; Garcy & Vågerö, 2012). The model developed in this study
can be adapted to incorporate a nonlinear term (e.g., Generalized Additive Model)
to control the complex effect of unemployment rates. Second, future research need
to consider the impacts of long-term unemployment, extending one-year lagged
unemployment rate. It can reveal the impacts of long-term unemployment on MISU
mortality by including multiple lags or cumulatively weighted unemployment rates
in the model (Tapia Granados et al., 2014; Zheng, 2012). Third, I only considered
mortality rates of both genders and all races/ethnicities in the model. This is
largely due to the high missing rates or unavailability of gender- and race/ethnicity-
specific mortality rates and covariates. The issue can be addressed by introducing
25
advanced imputation methods (for example, H. Quick, 2019) and by examining the
impact of unemployment rates on gender-specific mortality rates (Dagher et al.,
2015). Finally, residuals in several counties are particularly high, which indicates
that there could be uncontrolled and mediating factors that could improve the
model. Future research can account for additional spatial and spatiotemporal
factors in the analysis, for example, the regime and the policy stance that affect
the elasticity of unemployment (Norström & Grönqvist, 2015), the liberalization of
trades (Pierce & Schott, 2016), and the economic diversity in the composition of
industries and businesses (Farré et al., 2018; van den Berg et al., 2017; Watson &
Deller, 2017).
2.5 Conclusion
This chapter provided insights into the spatiotemporal variation of the
association between MISU mortality and unemployment at the county level in
the contiguous United States between 2001 and 2014. I found that the impact of
unemployment on MISU mortality weakened during the Great Recession period.
High positive associations were observed in counties within Ohio, Kentucky, and
West Virginia, while moderate positive associations emerged in counties within
North and South Dakotas post-Great Recession. Negative associations were
concurrently prevalent in southeastern counties. Such heterogeneity reflected the
regional contexts such as the shortage of medical services, economic depression, and
other local processes. These findings add to the literature by indicating that the
impact of unemployment on mortality decreased during recession periods as well as
support the prevailing view that economic recession might be negatively associated
with MISU mortality. Future studies are warranted to examine the consistency of
26
these findings across different gender, race/ethnicity, age groups, and more recent
data at various spatial scales.
27
CHAPTER III
LOCALIZED EFFECTS OF GREENSPACE EXPOSURE ON MENTAL ILLNESS
MORTALITY IN THE PACIFIC NORTHWEST UNITED STATES
This chapter is under review for publication in Applied Geography. I conceived
research questions, collected data, conducted statistical analysis, and wrote and
edited the entire draft. Dr. Hui Luan advised to edit the draft.
3.1 Introduction
Mental illness is a leading contributor to the worldwide increase in overall
mortality, thus became a global public health issue (GBD 2019 Mental Disorders
Collaborators, 2022; Lawrence, 2015; Vigo et al., 2016; Walker et al., 2015). This
trend is notably prominent in the United States, where incidence and mortality
rates have surged over the past two decades (Chang et al., 2010; Fekadu et al.,
2015; Jayatilleke et al., 2017; Zheng & Echave, 2021). Therefore, it is crucial
to identify factors beneficial to promoting mental health. Recent research is
increasingly focusing on the protective impacts of greenspace (e.g., parks and
vegetation) and blue space (e.g., rivers and lakes) exposure on mental health
outcomes (Bratman et al., 2019; Labib et al., 2020; Pearson et al., 2019; Su et al.,
2019).
According to Wilson’s biophilia hypothesis, human beings innately incline
toward natural environments (Wilson, 1984). Expanding on this idea, Hartig et
al. (2011) proposed that exposure to nature, including forests and greenspaces,
is beneficial to human health and expanded this concept to mental illness by
incorporating ecosystem services (Hartig et al., 2011). Empirical studies have
28
also documented the protective effect of residential proximity to greenspaces on
mental health status, leveraging data from various study designs including cross-
sectional, longitudinal, panel, randomized trials, twin studies, and ecological studies
(Gascon et al., 2016; M. P. White et al., 2021). Theoretical underpinnings and
empirical findings have informed the development of frameworks that consider
the effects of greenspace and its potential confounding and mediating effects
(Dzhambov, Markevych, Hartig, et al., 2018; Hartig et al., 2014; Markevych et al.,
2017; R. Zhang et al., 2021). For instance, Markevych et al. (2017) presented
a framework for examining the influence of greenspace to health and well-
being outcomes, which are mediated by three functions of greenspace exposure
including reducing harm, restoring capacities, and building capacities (Markevych
et al., 2017). Another framework suggested by Dzhambov et al. (2018) included
annoyance that is a response of perceived greenspace, noise, and air pollution, and
they assumed that perceived greenspace takes effect in poor mental health status
via restorative quality (Dzhambov, Markevych, Hartig, et al., 2018).
Most existing research on the relationship between mental health outcomes
and greenspace relies on individual-level data. These studies often utilize mental
health status or surrogate indicators such as antidepressant prescriptions (Helbich
et al., 2018; McDougall et al., 2021; Reeves et al., 2011). While small-scale and
individual-level studies provide valuable insights, their findings cannot readily be
generalized to the broader population (Yoo et al., 2021). Conversely, data from
population-scale sources such as death registers can inform universally applicable
mental health measures at the population level. Death registers, which record
deaths attributable to mental illness, offer opportunities for spatial analyses and
the integration of neighborhood contexts (Flores et al., 2020). However, the lack
29
of control populations in these datasets hinders the examination of associations
between mental illness mortality and greenspace exposures. Nevertheless, spatial-
ecological data can still inform public health policies at administrative levels
(e.g., county or state in the United States), providing valuable insights for public
health professionals and urban planners to devise effective greenspace strategies for
reducing mental illness mortality at the population level, for example, prioritizing
the improvement of accessibility to greenspace for vulnerable population.
Few studies have empirically examined greenspace exposure may be either a
mediating or a mediated factor in mental health outcomes (Engemann et al., 2019;
Klompmaker et al., 2019; McDougall et al., 2021; Vries et al., 2016), even though
the conceptual frameworks proposed by Markevych et al. (2017) and Dzhambov et
al. (2018) suggest these relationships (Dzhambov, Markevych, Hartig, et al., 2018;
Markevych et al., 2017). Recent research has started to incorporate greenspace
and bluespace exposures into investigations of associations between mental health
outcomes and the physical environment while accounting for socioeconomic factors
(Labib et al., 2020; McDougall et al., 2021). However, comprehensive frameworks
integrating these environmental factors have not yet been examined to generate
reliable estimates of the effect of greenspace exposure on mental illness mortality,
despite its having potentials to provide additional knowledge on the relationship
between mental health outcomes and greenspace exposure.
Spatial disparity is another important consideration when examining the
effect of greenspace on mental illness mortality. It is well-documented that access
to greenspace is not evenly distributed across geographic units or socio-economic
and ethnic/racial groups within a city (Boulton et al., 2018; Chen et al., 2022; Dai,
2011; Gruebner et al., 2017; H. Ha, 2019; I. Song & Luan, 2022; Y. Song et al.,
30
2021; Wolch et al., 2014). Therefore, another research question arises: do the effects
of greenspace exposure on mental illness mortality vary spatially? This inquiry
may provide insights into how spatial disparities in greenspace can explain mental
illness mortality and expand our understanding of where greenspace exposure can
effectively reduce (or even exacerbate) the risk of mental illness mortality. Also,
revealing the spatial disparity in the greenspace effect is a means of discovery to
new hypotheses of explaining such disparity.
Given these concerns and observations from the literature, I hypothesize
a spatially varying effect of greenspace exposure on mental illness mortality. The
research questions I seek to answer are: (1) does the effect of greenspace exposure
on mental illness mortality differ across small areas (specifically, census tracts
in this case)? (2) what is the general relationship between socioeconomic and
environmental factors and mental illness? Using a Bayesian spatiotemporal model
on data from the Pacific Northwest of the United States (comprising Oregon
and Washington), I aim to address these research questions and draw related
implications.
3.2 Methods
3.2.1 Study area. The study area is the northwestern region of the
contiguous United States (42°–49° N, 125°–116° W), specifically the states of
Oregon and Washington, which, as of 2020, had populations of 4,237,256 and
7,705,281 respectively. The terrain of these states is divided into the temperate
western Cascades and the drier eastern Cascades by the Cascade Range (Figure
B.1). Major cities such as Seattle, Washington, and Portland, Oregon, are situated
in the western region, which is also home to the majority of the population. The
31
Columbia River serves as a boundary between the two states, shaping a basin
that includes the central and eastern regions of these states and is surrounded by
mountainous areas in southeastern Oregon and northwestern Washington. These
two states are known for their equitable mental healthcare into legislation before
the federal enactment of parity in mental health services (Brodey et al., 1995;
Wallace & McConnell, 2013).
3.2.2 Main outcome. I obtained individual death registers from 2006 to
2018, courtesy of the Oregon Health Authority and the Washington Department
of Health. These registers contain detailed information about the deceased, such
as birth and death dates, sex, marital status, underlying and contributing causes
of death (up to twenty), education attainment, and residential locations. Mental
illness mortality was defined by examining the causes of death in selected F
(Behavioral and Mental Disorders) sub-chapters of the International Classification
of Disease 10th revision. The included sub-chapter codes of causes of death were
F20–29 (Schizophrenia, schizotypal, delusional, and non-mood psychotic disorders),
F30–39 (Mood or affective disorders), F40–48 (Anxiety, dissociative, stress-related,
somatoform and nonpsychotic mental disorders), F50–59 (Behavioral symptoms
associated with physiological disturbances and physical factors), F60–69 (Disorders
of adult personality and behavior), F70–F79 (Intellectual disabilities), F80–F89
(Pervasive and specific developmental disorders), F90–F98 (Behavioral and
emotional disorders with onset usually occurring in childhood and adolescence), and
F99 (Unspecified mental disorder), based on the literature (Engemann et al., 2019;
Lundin et al., 2016; Yoo et al., 2021). Substance use disorders were excluded due to
their unique association with greenspace exposure (Engemann et al., 2019; Weeland
et al., 2019; Wiley et al., 2022). I incorporated decedents with determinable, non-
32
homicide related causes of death into the study. After integrating the attribute
and location tables and cleaning the location data, I aggregated the number of
decedents in each census tract. During the study period, Oregon and Washington
reported 6,020 and 5,859 decedents respectively. The data was collected under the
exemption approval of the Institutional Review Board at the University of Oregon
(protocol number: 12212020.026).
3.2.3 Greenspace exposure and covariates.
3.2.3.1 Greenspace exposure assessment. I considered the total area of
parks per 10,000 population in the study area to assess greenspace exposure. Parks
that are accessible and free of charge were deemed available to the population,
while larger areas like national parks and national/state forests were included
separately as a binary variable in the model. This choice aligns with the goal of
examining residential greenspace exposure at the census tract level, as vast parks
and forests have limited spatial (e.g., entrance) and temporal (seasonal opening
or prohibited access) availability. Notably, in Oregon and Washington, greenness
measured with the normalized difference vegetation index, which is often used in
the literature to assess greenspace exposure (Astell-Burt & Feng, 2019; Nutsford
et al., 2013; Ribeiro et al., 2021; Wood et al., 2017; R. Zhang et al., 2021), presents
a clear contrast between the west and east sides of the Cascade Range (Figure B.1).
This difference could lead to misclassification and inflated estimates of greenspace
exposure’s effect in areas in the western Cascade Range, where most of the study
area’s population resides. Consequently, assessing greenspace exposure via parks
can help avoid potential bias. This method is consistent with previous studies on
the relationship between greenspace and mental health (Dzhambov, Markevych,
Hartig, et al., 2018; Labib et al., 2020; Wood et al., 2017). The base population for
33
calculating the mortality rates is collected from the American Community Survey
(ACS) five-year data tables for the years 2009–2018, adjusted with the non-prisoned
population rate in the 2010 Census to account for the population who are not
limited for daily activities.
Spatial datasets of parks were collected from both governmental and non-
governmental sources, including the Protected Areas Database (PAD-US) 3.0
from the United States Geological Survey (U.S. Geological Survey Gap Analysis
Project, 2022), state park databases, the ParkServe database from the Trust for
Public Land (Trust for Public Land, 2022), and OpenStreetMap. PAD-US is a
comprehensive database of protected areas in the US, while ParkServe encompasses
local parks across 14,000 communities in the US and classifies park management
agencies into private, public (federal, state, and city), and non-profit organizations.
By utilizing PAD-US and ParkServe, I first combined unique park polygons data,
then supplemented missing parks with auxiliary data like state park datasets
and OpenStreetMap. Certain tracts have large expanse of national parks, forests,
wilderness areas, preservation areas, and state forests, leaving little potential for
accessible parks. To account for such mutually exclusive characteristics between
park types, I controlled tracts located in and around large greenspace with a binary
variable, indicating whether a census tract intersects with large greenspace. I
performed spatial data operations using the R package sf (Pebesma, 2018).
3.2.3.2 Covariates. In addition to greenspace exposure, I accounted for ten
census tract level covariates potentially associated with mental illness mortality.
These covariates were divided into three categories: environmental, demographic,
and socioeconomic, which were selected based on the local characteristics of mental
illness mortality and the mechanisms. I considered the temporal availability of all
34
covariate data either to match the yearly mental illness mortality data or to avoid
temporal misalignment issues (Hund et al., 2012).
First, environmental confounders, including air pollution and bluespace,
were controlled (Labib et al., 2020; McDougall et al., 2021; Nutsford et al.,
2016; Pearson et al., 2019; Triguero-Mas et al., 2015). I obtained high spatial
resolution (0.01 by 0.01 decimal degrees) datasets of predicted surface particulate
matter with an aerodynamic diameter less than 2.5 micrometers (PM2.5) from the
Atmospheric Composition Analysis Group at Washington University in Saint Louis
(van Donkelaar et al., 2021) to calculate the average concentration. Bluespace data
was collected from the United States Geological Survey National Hydrography Data
(U.S. Geological Survey, 2019), from which only perennial freshwater features were
selected to calculate the proportion of waterbodies to each census tract’s total area.
Second, I controlled demographic covariates, including age structure and
the residential characteristics of decedents. Given that raw counts are used, I
considered the percentage of the senior (65 or older) population to account for
the age structure. I also considered care facilities and retirement homes (“care
facilities” onwards), which have a high prevalence of psychiatric disorders (Seitz
et al., 2010). Care facility locations in the study area were collected from DataAxle
using the ArcGIS Business Analyst and the North American Industry Classification
System (NAICS) codes (Table B.1 for details). Ethnic or racial composition,
accounted for by the percentage of non-white population, served as a proxy for
the sociodemographic context in each census tract. Additionally, the marital
trajectory and the presence of significant others, which could potentially associate
with the severity of mental illness (Barrett, 2000; Vaingankar et al., 2020), were
35
accounted for with the percentage of negative marital status (separated, divorced,
and widowed) from the ACS data.
Finally, socioeconomic factors were considered as contextual factors in
the model. The five-year ACS estimates were assigned to the period’s final year
(e.g., 2014–2018 estimates were matched to the 2018 mental illness mortality and
covariates). Socioeconomic deprivation was proxied by variables such as median
household income, educational attainment higher than the bachelor’s degree,
unemployment rates, and the percentage of households below the poverty line.
The deprivation index was derived from the principal component analysis of these
four variables, with the first component used (Table B.2). Before calculating the
deprivation index, median household income values were adjusted to 2010 dollar
values using the consumer price index from the U.S. Bureau of Labor Statistics
(U.S. Bureau of Labor Statistics, 2022). All variables were standardized to reduce
skewness. The correlation matrix of eleven explanatory variables shows the Pearson
correlation coefficient between any pair of variables ranges between -0.700 and
0.656, and the variance inflation factors are between 1.059 and 3.713, indicating
that the data does not have severe multicollinearity (Tables B.3–B.4).
3.2.3.3 Spatial data integration. Given that the boundaries of census
tracts in Oregon and Washington were adjusted in each census year, I utilized the
crosswalk tables provided by the US Census Bureau to tackle the spatiotemporal
misalignment issue in the dataset. These tables, which account for all possible
matches of geographic areas between the origin and the destination census years,
enabled the integration of the dataset spanning the 2000 and 2010 Censuses (U.S.
Census Bureau, 2021b). Utilizing the area and population fractions for each 2000
Census tract, I computed the population-weighted mean of the covariates at the
36
2010 census tracts for the 5-year ACS estimates from 2005 to 2009. For the period
2006–2008, the data values from the 2005–2009 dataset were assigned, given the
availability of 5-year ACS estimates only after 2009.
Twenty-eight census tracts–nine in Oregon and nineteen in Washington–were
excluded upon examination of the ACS data. This exclusion was driven by various
factors. Eighteen tracts were essentially water areas, while ten were excluded due
to the fulfillment of the spatial model assumption and the need for a sufficient
population size. An example of the scarce population size is a census tract in
downtown Portland, Oregon, which only had a population of 0–6 throughout the
study period. Another example is a census tract in the Fort McDermitt Paiute
and Shoshone Tribes Reservation in southeastern Oregon, where the estimated
population remained at zero for the entire study period. Additionally, four island
tracts were excluded to satisfy an assumption of spatial modeling of each tract
having at least one neighbor (Table B.5). Consequently, the final data comprised
845 and 1,439 census tracts in Oregon and Washington for thirteen years, totaling
10,985 and 18,707 census tracts in Oregon and Washington, respectively.
3.2.4 Model formation.
3.2.4.1 Spatiotemporal interaction model. The analysis carried out
was a Bayesian hierarchical spatiotemporal regression, which was structured to
accommodate spatiotemporal dependencies present in the mortality data through
the inclusion of purely spatial, purely temporal, and spatiotemporal interaction
components. The hierarchical models offered the advantage of accounting for
the spatial and temporal autocorrelation in the spatiotemporal data. I could
either uncover spatial disparities of greenspace effects or propose a new set of
hypotheses to explain such disparities by using a spatially varying model approach
37
(Janko et al., 2019). It is important to note that the models were fitted separately
for Oregon and Washington to avoid potential systematic differences in factors
influencing both outcomes and covariates between the two states, such as variations
in the diagnosis, treatment, and recording of mental illnesses and practices in
patient support (Ganguli & Rodriguez, 1999; Gao et al., 2018).
I employed a zero-inflated Poisson likelihood, which divides zeros into
structural zeros (pzero) and sampling zeros ((1 − pzero)Poisson) within a Poisson
distribution. This necessitated introducing the probability of excess zeros, resulting
in Formula 3.1.
p(yit = 0) = pzero + (1− pzero)Poisson(λit = 0) (3.1)p(yit > 0) = (1− pzero)Poisson(λit > 0)
In this formula, yit represents mental illness mortality in census tract i at
year t. The terms bi·, γ·t, and δit, as given in the full model specification (Formula
B.6), correspond to purely spatial, purely temporal, and spatiotemporal interaction
components respectively. log (Pit) is the population offset, and x denotes the kthitk
covariate value in census tract i at year t. More specifically, xit1 denotes greenspace
exposure in census tract i at year t. The total effect of greenspace exposure at each
census tract βi1+ is made up of the fixed main effect β1 and the spatially structured
effect βi1. The spatial random slope βi1, which adjusts the fixed effect β1, is the
primary interest of the analysis.
βi1+ = β1 + βi1 (3.2)
38
In Formulae 3.1 and 3.2, the spatial components b1· in the main effect
and βi1 in the random slope follow the modified Besag-York-Molli’e (BYM)
formulation (Besag et al., 1991; Riebler et al., 2016). This approach was developed
to distinguish between spatially structured and unstructured components and to
scale the spatially structured component (M. Quick & Luan, 2021; Riebler et al.,
2016). The main temporal component was structured as a first-order autoregressive
model, accommodating the overall trend in the crude mental illness mortality rate
with the autocorrelation parameter ρ.
The spatiotemporal interaction (STINT) term δit conveys the convolution of
spatial and temporal processes. This term can be formulated in one of four distinct
types (denoted as Roman numerals I–IV), depending on whether the spatial and
temporal processes are independent or structured (Knorr-Held, 2000). These four
(2 × 2) interactions arise from all possible combinations of these processes in each
of the spatial and temporal parts (Blangiardo & Cameletti, 2015; Haining & Li,
2020). Models both without (Model 1) and with the interaction term in four types
(Models 2–5) were fitted and compared. A comprehensive model specification,
including details of the modified BYM for spatial random effect, the temporal
effect, the spatial random slope, and the spatiotemporal interaction terms, is
provided in the Appendix B.
3.2.5 Model fitting and sensitivity analysis. The models were
implemented with the Integrated Nested Laplace approximation (INLA) method,
a form of Bayesian computing that approximates posterior marginals with Gaussian
marginal distributions (Rue et al., 2009). The INLA method, in contrast to
sampling-based Monte Carlo approaches like Markov Chain or Hamiltonian, is
known for its computational efficiency, particularly in fitting complex spatial and
39
spatiotemporal models (Blangiardo & Cameletti, 2015; Lindgren & Rue, 2013;
Rue et al., 2017). The statistical analysis was performed using R-INLA package
version 2023.03.17 in R version 4.2.2 (Niekerk et al., 2021; R Core Team, 2022).
Five primary models and three sensitivity analysis models were compared using
deviance information criterion (DIC) (Spiegelhalter et al., 2002) and Watanabe-
Akaike information criterion (WAIC) (Watanabe, 2013), both of which account for
model complexity and accuracy with the effective number of parameters and the log
likelihood, respectively.
The default priors for hyperparameters in the modified BYM formulation
within the R-INLA package are the penalized complexity (PC) priors. These priors
account for model complexity by introducing the Kullback-Leibler divergence
between model specifications with and without additional parameters (Simpson
et al., 2017). The probability density function of a PC prior is defined as P (σθ >
θ1) = θ2, or more succinctly PC(θ1, θ2), where σθ denotes the standard deviation
of a hyperparameter θ. A larger θ2 results in a flatter prior, similar to a non-
informative uniform prior. In this study, I used a weakly informative prior PC(1,
0.01) for precision hyperparameters and PC(0.5, 0.5) for mixing hyperparameters.
By comparing three priors with DIC and WAIC, I assessed the sensitivity of the
prior configuration.
3.3 Results
3.3.1 Descriptive results. Census tract-level mental illness mortality rates
in Oregon and Washington showed an increasing trend throughout the study
period, with Oregon consistently reporting higher rates than Washington. The
range of mortality counts by census tracts was 0 to 13 (mean=0.40, standard
40
deviation [sd]=0.76), and 20,864 tracts reported zero counts. The annual mortality
rate per 10,000 population during the study period ranged from 0.89 to 1.75 in
Oregon and from 0.59 to 0.82 in Washington. Oregon’s rates were 1.44 (2009) to
2.13 (2018) times higher than those of Washington (Table 5).
Covariates showed different variations. Environmental factors, particularly
greenspace and bluespace exposure, had higher coefficients of variation (CV;
[standard deviation]/[mean]) (2.323–3.009) compared to other covariates, with
the exception of the number of care facilities per 10,000 population (1.280–1.515).
PM2.5 had relatively lower CVs (0.272–0.342) than the other two environmental
covariates. Among demographic covariates, the percentage of the non-white
population and the number of care facilities per 10,000 population showed more
dispersion than the percentage of the senior population and negative marital status.
Socioeconomic covariates exhibited moderate relative dispersion (Table B.6).
Table 5. Annual rate of mental illness mortality per 10,000 population in Oregon
and Washington in 2006–2018
Unit: per 10,000 population
State 2006 2007 2008 2009 2010 2011 2012
Oregon 0.87 0.92 1.02 0.95 0.99 1.03 1.16
Washington 0.59 0.58 0.60 0.66 0.61 0.63 0.63
State 2013 2014 2015 2016 2017 2018 Average
Oregon 1.12 1.23 1.41 1.48 1.57 1.75 1.17
Washington 0.60 0.64 0.67 0.71 0.84 0.82 0.66
3.3.2 Model results. Comparisons of Models 1–5 indicate that Model 5,
featuring a type IV STINT component, provided the best fit for the data. The DIC
41
and WAIC values of Model 5 decreased in both states (Oregon: ∆DIC=-207.87,
∆WAIC=-208.98; Washington: ∆DIC=-180.85, ∆WAIC=-200.63) compared
to those of Model 1 (Table 6). The area of parks per 10,000 population, the
primary variable of interest, had a fixed effect of 0.908 (95 % CrI = [0.843, 0.978])
in Oregon and 0.949 ([0.903, 0.999]) in Washington, indicating that greenspace
exposure had an overall protective effect on mental illness mortality in both states.
However, the RRs of the spatial random slope ranged from 0.935 ([0.803, 1.090])
to 1.120 ([0.950, 1.321]) in Oregon and from 0.976 ([0.885, 1.076]) to 1.033 ([0.954,
1.119]) in Washington, adjusting the fixed effect RR of the greenspace exposure
(Table 7 and Figure B.2). The posterior probability of the random slope RR being
smaller than zero (p(RRi1 < 1)) was between 0.5 and 0.8 near Portland in Oregon
and southwestern Washington (Figure 3). The census tracts intersecting national
and state forests were negatively associated with mental illness mortality, although
the associations were marginal (0.996 [0.893, 1.111] in Oregon and 0.960 [0.831,
1.108] in Washington).
42
Table 6. Deviance and Watanabe-Akaike information criteria of five model
settings with and without spatiotemporal interaction
Oregon Washington
DIC1 WAIC2 DIC WAIC
Model 1: 19528.87 19537.96 24737.75 24746.40
base model without spatiotemporal interaction
Model 2: 19543.06 19542.67 24796.34 24787.55
spatiotemporal interaction type I
Model 3: 19507.28 19493.98 24759.35 24708.86
spatiotemporal interaction type II
Model 4: 19426.61 19413.61 24797.70 24763.45
spatiotemporal interaction type III
Model 5: 19321.00 19328.98 24556.90 24545.77
spatiotemporal interaction type IV
1 Deviance information criterion, 2 Watanabe-Akaike information criterion.
43
44
Figure 3. Tract-level random slope relative risk (RRi1 = exp (βi1)) of one standard deviation increase of the park areas
per 10,000 population to mental illness mortality and its posterior probability of being smaller than one in Oregon and
Washington
Note: black lines are county borders.
The results from the analysis of environmental covariates suggest
statistically significant effects of waterbodies on mental illness mortality. For
example, in both Oregon and Washington, one standard deviation (SD) increase
in the proportion of waterbodies (5.9 % in Oregon and 8.77 % in Washington)
was associated with a marginal 2.1 % ([-6.0 %, 2.0 %]) and 3.4 % ([-7.6 %, 1.1 %])
lowering of risk in Oregon and Washington, respectively. However, one SD increase
of average PM2.5 (1.94 micrograms per cubic meter [µg/m3] in Oregon and 1.60
µg/m3 in Washington) was associated with a 6.1 % ([0.7 %, 11.8 %]) and 2.6 %
([-2.4 %, 7.8 %]) increase of mental illness mortality risk, indicating that PM2.5
significantly raises the risk only in Oregon.
For demographic covariates, the proportion of the non-white population
was marginally negatively associated in both states (RR=0.973 [0.924, 1.026] in
Oregon and 0.975 [0.920, 1.034] in Washington) while the number of care facilities
per 10,000 population in Oregon showed a marginal positive association (1.049
[0.974, 1.129]). SES was found to have a significantly protective effect on mental
illness mortality, with its relative risk (RR) being 0.931 ([0.901, 0.962]) in Oregon
and 0.926 ([0.891, 0.962]) in Washington (Table 7). Sensitivity analysis confirmed
that model results with three alternative prior specifications were similar to those
from Model 5 with the base prior PC(1, 0.01) (Table B.7).
45
46
Table 7. Estimated relative risks of explanatory factors from Model 5
Oregon Washington
Relative risk 95 % Credible Interval Relative risk 95 % Credible Interval
Area of parks per 10,000 population
Fixed effect coefficient 0.908 0.843, 0.978 0.949 0.903, 0.999
Random effect coefficients
Minimum 0.935 0.803, 1.090 0.976 0.885, 1.076
Maximum 1.120 0.950, 1.321 1.033 0.954, 1.119
Combined effect coefficients
Minimum 0.849 0.725, 0.994 0.927 0.832, 1.032
Maximum 1.017 0.856, 1.208 0.981 0.901, 1.068
National/State parks & forests
No intersection Reference Reference
Intersection 0.996 0.893, 1.111 0.960 0.831, 1.108
PM 32.5 (µg/m ) 1.061 1.007, 1.118 1.026 0.976, 1.078
Waterbodies (%) 0.979 0.940, 1.020 0.966 0.924, 1.011
Number of care facilities per 1.049 0.974, 1.129 1.067 1.017, 1.120
10,000 population
65 years old or older (%) 1.233 1.178, 1.292 1.311 1.250, 1.375
Negative marital status (%) 1.125 1.081, 1.172 1.167 1.112, 1.225
Non-white population (%) 0.973 0.924, 1.026 0.975 0.920, 1.034
Socioeconomic deprivation 0.931 0.901, 0.962 0.926 0.891, 0.962
3.4 Discussion
The results revealed spatial variation in the effects of greenspace exposure
on mental illness mortality across census tracts in Oregon and Washington. This
finding expands the studies on the relationship between greenspace and mental
health outcomes since most previous studies assumed the effect to be spatially
stationary across the entire sample (Banay et al., 2019; Dadvand et al., 2015;
Engemann et al., 2019; Nutsford et al., 2013; Nutsford et al., 2016; Tomita et al.,
2017; Tost et al., 2019). The overall protective effect of greenspace exposure on
mental illness mortality, which was found to be significant, adjusted to different
directions when accounting for the random slopes. This variability in spatial
random RRs of greenspace exposure implies that the impact of greenspace exposure
on mental illness mortality is not spatially constant over the entire study region.
Rather, local effects exist, and this supports the variability in local greenspace
effects on mortality (Jiang et al., 2021; Richardson et al., 2010). Recognizing these
local impacts of greenspace exposure has important implications for establishing
geographically-tailored interventions, thus is equally important to assessing fine-
grained greenspace exposure (Yoo & Roberts, 2022; R. Zhang et al., 2021).
The findings presented in this study provide evidence of different
associations between mental health outcomes and covariates across the two
states. This implies that conceptual models may operate differently by regions.
For instance, PM2.5 in Oregon and care facility rates in Washington exhibited
significant positive associations. Other covariates showed consistent patterns of
significance in both states. The ratio of individuals aged 65 years or older and
negative marital status were significantly positively associated with mental health
mortality, while socioeconomic deprivation was significantly negatively associated.
47
Bluespace exposure and the proportion of non-white population exhibited
marginally negative associations. These findings offer limited evidence that
racial and ethnic diversity may have a beneficial impact on mental health status
(Henderson et al., 2005). However, these results do not reject the possibility that
tracts with higher mental illness mortality may feature greater racial and ethnic
diversity, considering that racial and ethnic diversity in Oregon and Washington
marked below the national average based on the U.S. Census Bureau’s diversity
index (U.S. Census Bureau, 2021a).
The protective effect of greenspace is pronounced in contiguous census
tracts lying between Seattle and Portland, aligning with previous research that
reported beneficial effects of greenspace exposure in urban populations (Akpinar
et al., 2016; Astell-Burt & Feng, 2019; Astell-Burt et al., 2022; Bijnens et al., 2020;
M. P. White et al., 2013). The finding adds to the literature with evidence of the
urban greenspace benefits in the combined urban-rural setting. Furthermore, areas
with protective greenspace exposure effect on mental illness mortality are typically
featured with flatter topography and milder climates than others in the study
region. This suggests that the significance of the greenspace effect may be affected
by the physical characteristics of an area. The presence of dense vegetation in these
areas also implies a potential interaction between the quality, types, and physical
features of greenspace and its effects on mental illness mortality. Future analyses
should consider environmental barriers such as slopes and curvature to incorporate
greenspace accessibility into the assessment of the health effects of environmental
exposures on mental health outcomes (Liang et al., 2022).
Spatial random RRs exceeding 1.0, which offset the protective fixed effect,
necessitate a careful interpretation. There are three possible explanations. First,
48
areas with a high spatial RR could be preferred by high-risk populations, implying
that patients with critical mental illness might not have been hospitalized or
moved into residential care facilities, leading to unprotective effect estimates. This
hypothesis can be further examined through qualitative surveys on the residential
preference of high-risk population and patients with mental illness, along with the
analysis of spatial accessibility and economic affordability of mental healthcare
systems, which often exhibit disparities along socioeconomic gradients (McConnell
et al., 2020; Zhu et al., 2022). Second, parks in these areas might not be accessible
to high-risk populations, limiting their effect on mental health outcomes. This lack
of accessibility could be due to parks being located away from residential areas or
parks having few entrances to the residential area. Accurate spatial information on
park entrances and exits is needed to evaluate actual accessibility. Third, there
might be no easily accessible greenspace for residents in certain areas. In such
cases, tracts with higher mental illness mortality might also be more racially and
ethnically diverse, suggesting a need for further investigation into the role of racial
and ethnic diversity in mental illness. Third, there is no available greenspace
that can be easily accessed by the residents in such area. The census tracts with
elevated spatial risk exceeding 1.05 partly overlap or are surrounded by large
National or State forests, which severely delimits usable land for both residence and
parks. It may lead to biased effect estimates in tracts with some mortality counts
surrounded by tracts with zero or very low mortality counts and less greenspace
exposure.
There are four limitations that should be acknowledged in this study.
First, the accuracy of information in death certificates relies on the expertise and
experience of certifiers, such as physicians or nurse practitioners. The recording
49
of mental illness as a cause of death may differ between the two states. Although
death certificates and preparation protocols of these are standardized across the
United States, there may be systematic differences in diagnosing mental illness
among patients in different geographic areas, such as counties or states. The data
is not completely immune to such issues. Second, there may be unaccounted factors
that could have influenced the severity or duration of mental illness and the actual
utilization of greenspace. For example, incidental (e.g., trauma) and collective
effects such as social networks (the impact of relationships with others), social
grouping effects (the impact of group identification in individuals), and social
cohesion can mediate both the progression of mental illness and the utilization of
greenspace (Jennings & Bamkole, 2019). This limitation is primarily due to the
nature of death register data, which do not provide actual residential circumstances
beyond residence of decedents. Third, census tracts may not fully capture the
actual characteristics of residential neighborhoods. Census tracts are delineated
for administrative purposes (i.e., enumeration); thus, the actual activity space may
not align with census tract boundaries. The relevant geographic context may differ
across census tracts (Kwan, 2012; L. Zhang et al., 2021). Lastly, the uncertainty in
covariates, such as margin of errors in ACS data, needs to be properly incorporated
into models using measurement error models.
I suggest four directions for future research. The first direction is to
examine spatially varying associations in other environmental and socioeconomic
factors. This approach presents challenges in justifying mechanisms, which identify
different spatial spheres of influence of such explanatory factors, and dealing with
computational complexity. The second direction is to develop a suitable method
for assessing greenspace exposure across regions with heterogeneous environments.
50
Similar to integrating ecological region information in a nationwide study (Coleman
et al., 2022), future studies should develop a comprehensive measure of greenspace
exposure that considers the fundamental environmental differences across regions.
This aligns with the development of integrated environmental assessment measures
(Marek et al., 2021). The third is to analyze the association between mental illness
mortality and greenspace exposure separately or concurrently by gender and
racial/ethnic subgroups. Such analyses will be feasible and warrant their results
if mortality data in ethnic subgroups have sufficient sample sizes. Finally, the
approach employed in this study can be expanded to other states in the United
States, as well as subnational geographic areas in other countries, particularly
in low- and middle-income countries (Nawrath et al., 2021). Such expansion is
expected to provide additional evidence on the spatially varying relationship
between mental illness mortality and greenspace exposure.
3.5 Conclusions
This chapter challenged the conventional assumption of spatially stationary
effects of greenspace exposure on mental illness mortality. The relative risk of
greenspace exposure on mental illness mortality varied from 0.935 to 1.120 across
census tracts in the Pacific Northwest region. The protective effects of greenspace
were higher in areas between Seattle and Portland. This suggests that interventions
to improve greenspace exposure should be tailored to specific locations to reduce
mental illness mortality in the region.
51
CHAPTER IV
LOCALIZED CAUSAL EFFECTS OF GREENSPACE EXPOSURE TO MENTAL
ILLNESS MORTALITY: A PIONEERING STUDY IN THE STATE OF
WASHINGTON, 2018
4.1 Introduction
In recent years, researchers have increasingly paid attention to the potential
benefits of greenspace on human mental health (Gascon et al., 2016; Roberts et al.,
2019; World Health Organization, 2021). Observational studies have concentrated
on the association between greenspace and mental health outcomes, however, a
growing body of literature explores causal relationship through experimental study
designs (Collins et al., 2020). Numerous pathways and mechanisms have been
developed to explain and conceptualize the impact of greenspace on mental health,
many of which can be examined using causal frameworks (Dzhambov, Markevych,
Hartig, et al., 2018; Markevych et al., 2017; Mueller et al., 2020; R. Zhang et al.,
2021).
From a spatial standpoint, studies have found protective effects of
greenspace across various study regions (M. P. White et al., 2021). Urban areas
and a few national registries were the major spatial sample frame (Engemann et al.,
2019, 2020; Luque-García et al., 2022). Although these studies have considerably
broadened our understanding of the protective influence of greenspace exposure
on mental health outcomes, there is limited exploration of the spatial distribution
of greenspace exposure across various regions. The consideration of the spatial
difference in greenspace exposure can help to comprehend the spatial disparity in
greenspace exposure effects. The two research agendas of causal effect estimation
52
and spatial differences in the effect of greenspace exposure’s effect on mental illness
mortality lead to the following research questions of our study.
First, is the causal effect of greenspace exposure on mental illness mortality
different across subpopulation groups?
Second, does the effect of greenspace exposure on mental illness mortality
depend on the absolute quantity of greenspace across the entire study area or
is it contingent on local area contexts?
To answer these questions, I employ matching methods on retrospective,
state-wide death register data from the State of Washington in 2018. This approach
allows me to examine the causal effect of greenspace exposure on mental illness
mortality, under the socio-environmental pathways and mechanisms currently
suggested in the literature (Aerts et al., 2022; Dzhambov, Markevych, Hartig, et al.,
2018; Dzhambov, Markevych, Tilov, & Dimitrova, 2018; Helbich et al., 2018; Labib
et al., 2020; Markevych et al., 2017). Furthermore, it facilitates the exploration
of spatial differences in the causal effect of greenspace on mental illness mortality
across regions. Through this study, I aim to build upon existing findings that
highlight the association of greenspace with reduced cognitive decline in mid-age
adults (de Keijzer et al., 2018) and lowered mortality in national cohorts (Wan
et al., 2022) by investigating the causal effect of residential greenspace exposure on
mental illness mortality.
The structure of this chapter is as follows. It begins with an introduction
to the concepts of causal inference, their spatial expansion, and applications in
assessing the association between mental illness mortality and greenspace exposure.
Subsequently, the chapter delves into the methodology and data description,
53
followed by a comparison of causal effect estimates derived from both absolute
and relative definitions of treatment conditions for continuous greenspace exposure
in the entire study population as well as subregional populations. I will estimate
the causal effect through propensity score matching to examine the variability of
effect estimates across the subregions. Lastly, I reflect upon the implications and
potential extensions of my study findings.
4.2 Spatial Causal Inference and Statement of Problems
The concept of causal inference from observational data is traditionally
explored through two frameworks: the potential outcome and the probabilistic
approach (Pearl, 2009). The potential outcome framework, in which researchers
emulate randomized controlled trials, was developed to overcome observational
study design limitations. One limitation is the inability to observe a true treatment
effect, as both treated and controlled states cannot be observed in an entity
simultaneously. This motivated the development of matching methods as a subset
of causal inference methods. These methods aim to achieve balance between
treated and control groups based on pre-treatment covariates, thereby enabling the
estimation of counterfactual outcomes (Rubin, 1974; Splawa-Neyman et al., 1990).
These methods assume three conditions: (1) random assignment of treatment,
(2) the existence of only one treatment condition per unit (e.g., person), and (3)
stability of treatment effect within the treated groups (referred to as the stable
unit treatment value assumption [SUTVA]) (Imbens & Rubin, 2015). The average
treatment effect (ATE) is the result of this counterfactual analysis, due to the
aggregated comparison between treated and controlled groups. When there are
54
multiple subgroups in the population of interest, one can estimate local average
treatment effect (LATE) within each subgroup.
Causal inference in geography has been addressed through dichotomous
treatment and partial regression analysis (Davidson, 1976; Pringle, 1981). These
methods were inspired by the Simon-Blalock method for analyzing spurious
correlation in multivariate settings (Blalock, 1961; Simon, 1954). In the past two
decades, causal inference methods such as difference-in-differences (DiD) and
propensity score matching (PSM) oftentimes have been used in the literature in
geography and cognate fields, most of which were published in economic geography
and epidemiology (Li, 2022).
The geographical perspective in recent causal inference literature can be
categorized into two major viewpoints (Akbari et al., 2023; Reich et al., 2021).
The first treats geography as a condition affecting study subjects. Researchers
focus on a set of small areas whose boundaries determine a treatment condition,
for example, a local tax code on residential properties in one of two neighboring
jurisdictions. This view has been integrated into natural experiment and regression
discontinuity designs for causal inference in the literature (Keele & Titiunik, 2015,
2016; Keele et al., 2015). The second is geography as a source of spatial dependence
in measured or unmeasured variables for inferential models. This branch inherited
tradition in spatial statistics where scholars aimed to attain random errors by
adding spatial components into models. Thus, handling spatial dependence with
a set of spatial regression models (e.g., spatial error, spatial Durbin, and spatial
autoregressive models) is often found in the literature. Examples include adding
spatial autoregressive term into the DiD model (Dubé et al., 2014), combining
spatial distance and propensity score matching (Papadogeorgou et al., 2019),
55
multiscale geographically weighted regression for instrumental variables (Bilgel,
2020), and removing spatial autocorrelation in covariates before performing
regression analysis (Dupont et al., 2022).
Meanwhile, the concept of LATE derived from geographic subregions raises
questions about spatial differences in LATE, especially in the context of greenspace-
mental health research. Despite assertions that LATE generally differs from
ATE due to the heterogeneity of subpopulations (Xie, 2013), this claim remains
untested in cases where the subpopulation is geographically defined. Furthermore,
as greenspace exposure is conditioned by physical and social environments and is
highly spatially autocorrelated, there is potential for violation of SUTVA (Akbari
et al., 2023). If these conditions are considered and the entire population is divided
into subpopulations with similar physical environment characteristics, it becomes
feasible to draw causal interpretations from these subpopulations. This also leads
to the following question on the relativity of greenspace exposure in a subregion.
For instance, if two subregions have distinctly different distributions of greenspace
exposure, one might ask whether the absolute quantity of exposure metrics or intra-
region relative greenspace exposure is more crucial in reducing the risk of adverse
mental health outcomes.
Taking these issues into account, I aim to examine the spatial differences
in the effects of greenspace exposure on mental illness mortality, focusing on the
boundaries of combined ecological regions and urban areas. To conduct a causal
analysis, I introduce two additional assumptions: first, there are no unmeasured
confounders; second, there are no interferences between individuals or mediations
between any combination of covariates. These assumptions allow me to interpret
the estimates causally after matching individuals in treated and control groups.
56
4.3 Methods
4.3.1 Data. Individual death register data for the year 2018 were gathered
from the Washington State Department of Health. This dataset includes essential
personal details such as sex, race, age, marital status, educational attainment,
length of residence at the time of death, manner of death, and up to twenty
recorded causes of death. The residential locations of the decedents were provided
in a separate file and were integrated into the main dataset using unique death
certificate identifiers.
I selected decedents who were 18 years or older at the time of death
and had died naturally (e.g., disease or aging). The underlying and multiple
causes of death, coded in the tenth revision of International Classification of
Disease system, were screened to include subchapters of F20–29 (Schizophrenia,
schizotypal, delusional, and non-mood psychotic disorders), F30–39 (Mood or
affective disorders), F40–48 (Anxiety, dissociative, stress-related, somatoform
and nonpsychotic mental disorders), F50–59 (Behavioral symptoms associated
with physiological disturbances and physical factors), F60–69 (Disorders of adult
personality and behavior), F70–F79 (Intellectual disabilities), F80–F89 (Pervasive
and specific developmental disorders), F90–F98 (Behavioral and emotional disorders
with onset usually occurring in childhood and adolescence), and F99 (Unspecified
mental disorder). Substance use disorders were excluded as their association with
greenspace exposure is inconsistent across studies (Weeland et al., 2019; Wiley
et al., 2022). I included decedents who had resided in their reported residence for
five years or more for exposure assessment. As a result, 31, 245 decedents met my
study population criteria, with 273 of these related to mental illness (Figure 4).
57
Figure 4. Data selection flowchart
The dataset was obtained under the exemption approval of the Institutional Review
Board at the University of Oregon (protocol number: 12212020.026).
4.3.2 Exposure assessment. The Normalized Difference Vegetation Index
(NDVI) from the Landsat-8 OLI sensor (with a spatial resolution of 30 meters) was
used to assess greenspace exposure, which is widely recognized in previous research.
NDVI quantifies greenness at each pixel, with its values impacted by waterbodies
or impervious surfaces such as buildings or barren land (Cardinali et al., 2023).
Consequently, Therefore, we considered modified normalized difference water index
(MNDWI) for water features (Xu, 2006) and normalized difference built-up index
(NDBI) (Zha et al., 2003) for buildings to balance their distributions in subsequent
matching analysis. NDVI data is based on eight-day average data from level 1
images (orthorectified), while the other two indices were directly derived from near
58
and shortwave infrared bands in eight-day raw level 2 images (orthorectified and
atmospherically corrected) without cloud cover. Images collected every eight days
were used to calculate the five-year (2013–2017) average. All spectral indices from
satellite data were obtained from the United States Geological Survey via Google
Earth Engine.
Residential exposure was assessed at individual residential locations. The
exposure was defined as the area within a 15-minute walking distance along the
road network, assuming a walking pace of 5 kilometers per hour. This approach,
yielding a mean of 1.77 km2 and a standard deviation of 0.70 km2, aligns with the
standard definition of a residential neighborhood of an 800-meter radius circular
buffer from residences (0.82 × π = 2.01 km2) (Astell-Burt et al., 2022; Hartley et al.,
2021; Sturm & Cohen, 2014). Using the Open Source Routing Machine (OSRM)
and the OpenStreetMap road network data, the walking distance area was derived
from each residence (Giraud, 2022; Luxen & Vetter, 2011).
4.3.3 Covariates. Individual and neighborhood covariates were included in
the propensity score estimation model. Three groups of covariates were identified
from the mechanisms and pathways in the literature: individual characteristics,
environmental exposures, and neighborhood contexts. Individual characteristics
that were recorded in the death certificates include sex, age, marital status,
educational attainment, and smoking status. Environmental exposures were
assessed within the 15-minute walking area and consisted of NDBI, MNDWI,
traffic noise, and air pollution exposure. Traffic noise estimation data for
2018 came from the United States Department of Transportation Bureau of
Transportation Statistics, which includes road, rail, and aviation noise across the
continental United States (United States Department of Transportation Bureau of
59
Transportation Statistics, 2020). Particulate matter with aerodynamic diameter
less than 2.5 micrometers (PM2.5) air pollution prediction data was sourced from
Washington University at Saint Louis, covering the continental United States
at 1-kilometer spatial resolution from 2000 (van Donkelaar et al., 2021). Five-
year (2013–2017) PM2.5 average was calculated from these datasets, and the
individual exposure was calculated as the average of pixel values in each walking
distance area. The neighborhood-level contextual variables were extracted at the
decedents’ residential census tract from the American Community Survey five-
year (2013-2017) data tables. These variables–rate of below poverty line, rate of
non-white population, median household income, and unemployment rate–reflect
neighborhood socioeconomic characteristics.
4.3.4 Propensity score matching. I used propensity score matching (PSM)
to estimate causal effects. PSM seeks to minimize the difference in the probability
of having been treated (propensity score or distance) between treated and controlled
groups, and to balance the mean and variance of covariates. The process comprises
three steps: estimating propensity scores using observed treatment information
and covariates, matching units in the treated and controlled groups with minimal
distance, and, after obtaining the matched dataset, estimating the causal effect by
performing a simple regression of the outcome against the treatment variable. To
balance covariates, the Covariate Balancing Propensity Score (CBPS) model was
employed, which uses weights from inverse propensity score to achieve the minimum
covariate mean difference between treated and controlled groups (Imai & Ratkovic,
2014). Decedents with the exact sex and race were matched given the different
characteristics in mental health status and outcomes (Zheng & Echave, 2021). I
evaluated and compared matching results using covariate balance, as measured by
60
the standardized mean difference for each covariate. These results are reported in
Appendix C.
4.3.5 Subregion definition. The State of Washington, located in the
northwestern part of the continental United States, is divided into two distinct
ecological regions–the forested western region and the desert eastern region–by the
Cascade mountain range. Given the higher-level impacts of ecology and climate
on greenspace, ecoregions were used as a criterion to divide the entire region into
subregions with similar ecological processes. For this division, I used the level 2
ecoregions from the Commission for Environmental Cooperation (Commission
for Environmental Cooperation, 1997). Additionally, large urban areas where
greenspace is sparse were separated. On top of the highly heterogenous nature
of the spatial distribution of environmental exposure (Jarvis et al., 2020), the
choice is supported by the preliminary finding of average NDVI values within 15-
minute walking areas, which showed that urban areas such as Seattle and Spokane
had lower NDVI values than other areas (Figure C.1). This also aligns with the
literature on the protective effects of greenspace in urban areas (Astell-Burt &
Feng, 2019; Collins et al., 2020; Dzhambov, Markevych, Tilov, & Dimitrova,
2018; Nutsford et al., 2013). Thus, I obtained Seattle-Tacoma and Spokane city
boundaries from the urban growth areas in the Washington Geospatial Portal. Five
subregions–Seattle-Tacoma, Western Cascades, Spokane, Western Cordillera, and
Columbia Plateau–were established for the comparison of the effects of greenspace
exposure. The Seattle-Tacoma area overlaps the Western Cascades, while Spokane
extends across the Western Cordillera and Columbia Plateau (Figure 5). For a
sensitivity analysis of subregion definition, the census core-based statistical areas
were compared with the main results.
61
Figure 5. Five subregions in State of Washington based on level 2 ecoregions and
urban growth areas with the distribution of five-year (2013-2017) average NDVI
values (above) and the distribution of average NDVI values in 15-minute walking
areas by subregions
(Note: the base map is from Stamen design)
62
4.3.6 Treatment setting with absolute and relative greenspace
exposure. Defining binary treatment poses a challenge as greenspace exposure is
a continuous variable. Stitelman et al. (2010) suggested two necessary conditions
for dichotomization of a continuous variable in a causal inference context:
mechanism and effect equivalence. Mechanism equivalence implies that the
probability of being treated remains constant regardless of exposure values,
provided that these values surpass the predefined threshold (Stitelman et al., 2010).
Stitelman et al. (2010) distinguished the intended and observed mechanisms in
which they assumed intentionally different treatment probabilities across pre-
dichotomization exposure groups (Stitelman et al., 2010). However, in our case
of using observation data, we checked whether the treatment probability of each
subgroup estimated by the covariates was identical to the treatment probability
given various thresholds. The expectation is a negligible difference between these
two estimated treatment probability values (Table 8). Effect equivalence requires
that expected outcomes, which are estimated by covariates, remain constant across
exposure subgroups above the threshold (Stitelman et al., 2010). To satisfy this
condition, when plotting expected outcomes against exposure values, the data
points should align horizontally. I investigated the fulfillment of these equivalence
conditions in both the entire and subregional populations.
Equivalence conditions were examined as follows. I checked five threshold
values, namely 50th, 60th, 70th, 80th, and 90th percentiles of greenspace exposure,
for both the entire population and each subregional population. Using each
threshold, I grouped the exposure values into 2 percent intervals and estimated
the treatment probability for each interval group, with and without the binary
variable indicating whether the value exceeds the threshold. The difference between
63
Table 8. Equivalence conditions for dichotomizing continuous exposure variables
from Stitelman et al. (2010)
Conditions Description Mathematical expression
Mechanism Probability of treatment assignment ∗ ′ ′
equivalence is the same regardless of
p (A |V ) = p(A |A = 1, V )
dichotomization ∀A
′ ∈ {1, · · · , j}
Effect Expected potential outcomes are [ ] [ ]
equivalence the same across E Y
∆(1)|V = · · · = E Y ∆(j)|V
the pre-dichotomization strata
Notations
A′: Multi-class treatment to be dichotomized
A: Dichotomized treatment
V : Covariates
Y : Potential outcome
Y ∆(V ): Potential outcome adjusted with covariates
p, p∗: Intended and observed probability of having been treated
the two treatment probability values were then compared. For example, when
the 60th percentile was set as the threshold, I grouped the exposure values into 2
percentile intervals (e.g., [60, 62), [62, 64), · · · , [98, 100] percentiles) and calculated
the difference between the probabilities of each percentile group, with and without
the indicator for values exceeding the 60th percentile. The mean difference was
calculated at each 2 percentile interval for the five thresholds.
4.3.7 Examination of research questions. I assessed the fulfillment of
equivalence conditions in each subregion to examine the research questions. Based
on this assessment, I addressed the first research question by comparing causal
effect estimates from propensity score matching in three subregions where both
equivalence conditions were met. To answer the second question, I applied absolute
(0.28–0.31) and relative (50th–90th percentiles) greenspace exposure to the entire
population and subregional populations. The absolute values were chosen based on
64
the distribution of greenspace exposure to ensure non-empty treated groups in all
subregions.
4.4 Results
4.4.1 Descriptive analysis. The majority of decedents in the State of
Washington resided in the western part of the State, with 74.44 % living in the
Seattle-Tacoma and Western Cascades areas (23,259 out of 31,245), which is
proportional to the population distribution in the area (76.14 % or 5,867,317 out
of 7,705,281 in the 2020 Census). The rate of mental illness mortality among
the naturally deceased residents was 0.87 % (273 out of 31,245), resulting in a
rate of 3.54 per 100,000 population (based on the 2020 Census population). The
average age at death was 76.72 years, showing a mild right-skewness (mean =
76.72, median = 78.00). The racial composition was highly skewed, with 89.32
% of the decedents (27,909 out of 31,245) being non-Hispanic whites, while other
racial groups accounted for 1.19 % (all others) to 3.85 % (Asian) (Table C.1). The
decedents commonly had education beyond high school (86.65 %) and were married
or widowed at the time of death (75.39 %). In terms of environmental exposures,
NDVI exposure followed a normal distribution (mean = 0.27, standard deviation
[sd] = 0.05). Similar normality was observed for MNDWI and NDBI. However,
traffic noise exposure exhibited a highly right-skewed distribution (mean = 14.34,
median = 8.90, sd = 15.58). Likewise, neighborhood socioeconomic covariates were
predominantly right-skewed. To meet the linearity assumption in the matching
analysis, these skewed variables were transformed using the square root (Table
C.1).
65
4.4.2 Dichotomization conditions. The analysis demonstrated that the
mechanism equivalence condition for dichotomization was satisfied across all
thresholds. The mean difference between probability values in subgroups at 2
percentile intervals was consistently close to zero, with a small range in the entire
study population. Similar results were observed in the subregional populations,
except for Spokane and Western Cordillera, which exhibited higher variability
in the differences compared to the other three subregions (Figure 6). Regarding
effect equivalence, the probability of mental illness mortality remained stable
across the entire population, ranging from 0.007 to 0.010 for every 2 percentile
greenspace exposure interval. However, subregional results varied significantly. The
probability of mental illness mortality remained stable in the Western Cascades and
Columbia Plateau for every 2 percentile greenspace exposure interval. In Spokane,
the probability showed random fluctuations along the greenspace exposure, while
decreasing patterns were observed in the Seattle-Tacoma and Western Cordillera
regions. Specifically, the probability mildly decreased at high exposure values in
Seattle-Tacoma and sharply decreased up to NDVI = 0.3 in Western Cordillera.
Consequently, I estimated the causal effects for the entire study population, Seattle-
Tacoma, Western Cascades, and Columbia Plateau by ensuring the fulfillment of
the equivalence conditions (Figure 7).
4.4.3 Matching analysis results. The results from the matching analysis
performed on the entire study population revealed a mildly decreasing trend as the
treatment was defined by higher percentiles. For instance, treatment defined by
the 50th percentile or higher yielded an estimate of 0.30, while defining treatment
by the 90th percentile or higher resulted in an estimate of −0.11. The subregional
results helped to address the two primary research questions posed in this study.
66
Figure 6. Difference between treatment probability by dichotomization (a) in
the entire study population and (b) among the five subregional populations at 2
percentile intervals across 50-90 percentile thresholds
67
Notably, these results showed that subregional causal effect estimates diverged
from the global causal effect obtained from the entire study population (Figure 8).
This observation provides evidence for spatial differences in causal effect estimates.
More specifically, the effect estimates derived from relative treatment definitions
using percentiles demonstrated a downward trend in the Seattle-Tacoma region
(from 0.00 at the 50th percentile and higher to −0.41 at the 90th percentile and
higher). Conversely, the Western Cascades and Columbia Plateau subregions
showed an increasing trend in effect estimates, with a sudden drop observed at the
80th percentile (from −0.32 to 0.12 in Western Cascades and from 0.00 to 0.41 in
Columbia Plateau) (Figure 8, panel (a)). On the other hand, defining the treatment
in absolute terms by applying fixed NDVI values yielded highly volatile effect
estimates. The range of estimates from the entire population fluctuated between
−0.17 at a 0.29 threshold NDVI to 0.11 at a 0.28 threshold. Except for the Western
Figure 7. Average probability of mental illness mortality at 2 percentile intervals
across 50-90 percentile greenspace exposure thresholds from local (red) and global
(orange) data in the State of Washington
68
Cascades subregion, where estimates were consistently protective (ranging from
−0.23 to −0.03) at thresholds above 0.29, subregional results showed variability.
For instance, estimates for the Seattle-Tacoma region became zero at a threshold
above 0.30 due to the absence of mental illness mortality cases in the treated group.
Additionally, a sharp increase in effect estimates was observed in the Columbia
Plateau subregion at thresholds above 0.29 (from −1.11 at a threshold of 0.29
to 0.00 at a threshold of 0.31) (Figure 8). In conclusion, the comparison between
absolute and relative treatment definitions provided answers to the second research
question.
Individual-level covariates were well-balanced, whereas environmental
exposures and neighborhood-level covariates exhibited varying magnitudes of
difference. Most of the standardized mean differences between the treated and
controlled groups ranged from -1 to 1, with NDBI being an exception (Figures
C.1–C.2). Sensitivity analysis reveals that five metropolitan areas out of nineteen
CBSAs met the conditions for reliable estimates. Among these, two metropolitan
areas, Seattle-Tacoma-Bellevue and Spokane, showed consistent effect estimates.
However, the remaining three areas displayed fluctuations in effect estimates
and failed to produce reliable estimates at the 80th and 90th percentiles of the
treatment definition (Figure C.2).
4.5 Discussion
This study examined spatial differences in causal effects of greenspace
exposure on mental illness mortality. Additionally, the reliability of causal effect
estimates using relative treatment definitions was assessed in subregions. By
examining the equivalence conditions for the binary treatment definition, the
69
Figure 8. Causal effect estimates from the State of Washington and three
subregions by percentiles (a) and values (b) of greenspace exposure thresholds
(Note: grey bars are 95 percent confidence interval from the simple regression of
the NDVI treatment against mental illness mortality)
70
entire study population was divided into five subregions to estimate the causal
effect of greenspace exposure on mental illness mortality. The results revealed
that considering spatial subpopulations was crucial for identifying the causal
effects of greenspace exposure on mental health outcomes. In other words, it is
essential to compare greenspace exposure in a subregional context that is relevant
to the greenspace itself, rather than using a globally fixed exposure value. This is
particularly important in health effect studies of greenspace because its distribution
is highly dependent on the physical environment. The use of relative treatment
definitions in subregions allowed me to assess whether the effect of greenspace
exposure on mental illness mortality varies depending on unique spatial contexts,
supporting recent efforts to assess integrated environmental exposure assessment in
a local context (J. Ha et al., 2022; Jarvis et al., 2020). The findings of this study
suggest that locally defined greenspace treatment can effectively identify the causal
effects, emphasizing the need to consider local environmental characteristics in
exposure assessments for causal analysis.
The results of this chapter demonstrated that the causal effect of greenspace
on mental illness mortality exhibits spatial variation. The causal effect estimates in
subregions differ from those obtained for the entire study population. This finding
contributes to the existing literature by identifying a spatially varying causal
relationship between mental health outcomes and greenspace exposure, extending
beyond previous findings on spatially varying associations (Labib et al., 2020).
Furthermore, the results clearly demonstrate that the feasibility of the treatment
definition is contingent upon the characteristics of the subregional population.
It suggests that causal inference based on a binary treatment variable can be
influenced by the spatial configuration of the subregional population. Further
71
research is warranted to examine more common mental health outcomes beyond
mortality.
The balance diagnosis results of covariates provide additional insights into
the intersection of greenspace exposure and socio-environmental composition. In
Seattle-Tacoma and Western Cascades, the treated group exhibited much lower
NDBI (approximately -2 standard deviations) compared to the control group.
This can be partially attributed to the marked negative correlation between NDBI
and NDVI. It implies that residential greenspace exposure is spatially segregated,
similar to median household income and poverty rates. Environmental exposures,
including PM2.5 and traffic noise, are concentrated in urban centers or near
roads, resulting in a slight imbalance in the matching results. This suggests that
considering the spatial segregation of socio-environmental constructs is important in
health effect studies of greenspace (Łaszkiewicz et al., 2021).
Despite the novel approach used to examine spatial differences in the effect
of greenspace exposure on mental illness mortality, several limitations of this study
should be acknowledged. First, the data limitations imposed strong assumptions
for causal inference, which may not hold in reality. I was only able to identify
a subset of decedents who were reported to have died from mental illness and
directly affected or contributed to their death. As the onset of mental illness may
precede the 5-year greenspace exposure, the results are susceptible to attribution
errors. Second, I assumed no interference and mediation between covariates, which
should be evaluated using suitable methods that explicitly handle these factors
(Hernán & Robins, 2006). Third, processes operating at a finer spatial scale should
be considered. This issue relates to controlling unmeasured spatial confounding
by incorporating spatial distance between subjects in the study population
72
(Papadogeorgou et al., 2019). Lastly, the exposure assessment remained static, and
therefore, the effect estimates obtained using dynamic exposure assessment should
be compared with the results of this study (Helbich, 2018a; Henson et al., 2020;
Yoo & Roberts, 2022). Unfortunately, in this case study, static exposure assessment
was the only feasible option given the nature of the single-year cross-sectional data.
I suggest three directions for future research. First, more analysis cases with
quality data are needed to reexamine the questions investigated in this study.
Second, the treatment definition should incorporate the complex relationship
between environmental exposure measured by satellite images and visible
greenspace assessed by street images (Giannico et al., 2022; Villeneuve et al., 2018;
R. Wang et al., 2021). Third, unconsidered conditions such as interference and
mediation should be taken into account using flexible causal inference methods.
4.6 Conclusion
In conclusion, this chapter examined the causal effect of greenspace exposure
on mental illness mortality and investigated the spatial differences in this effect
across regions. The findings indicated that the causal effect of greenspace exposure
on mental health outcomes varies across subregional populations, highlighting
the importance of assessing the impact of greenspace exposure in spatial contexts
that uniquely characterize the study population. For future research, it would
be beneficial to expand the causal approach to a spatiotemporal setting, analyze
longitudinal cohort data, and investigate potential spatiotemporal differences in the
causal effect of greenspace exposure on mental illness mortality.
73
CHAPTER V
CONCLUSION
Mental illness has become a major health issue in recent years, which
demands a comprehensive understanding of the factors that affect mental illness,
both negatively and positively. This dissertation investigated the impacts of
two important risk/protective factors of mental illness mortality, unemployment
and greenspace, through three case studies with the special focus on their
spatial and temporal variations. The primary objective of this research was to
emphasize the importance of recognizing the spatial and/or temporal disparity
in the effects of socio-environmental factors, which takes a step further from the
conventional approach of describing outcome patterns and assuming constant
effects across space and time in mental health studies in health geography and
cognate fields. I addressed two research gaps that were found in the literature by
explicitly examining the spatially and temporally varying, and causal effects of
unemployment and greenspace exposure on mental illness mortality in subregions.
Each case study demonstrated that the effects of unemployment or
greenspace exhibited clear spatial disparity (Chapters 2 and 3), and the contrast
between low and high effects varied over time in response to significant events that
impact the factors of interest (Chapter 2). The feasibility of estimating causal
effects is influenced by the spatial partition of the study population, and spatial
disparity was found in regions where causal estimation is feasible (Chapter 4).
These findings highlight the significance of considering spatially and temporally
varying effects and providing researchers and public health practitioners with
74
locally-focused measures. They can use this finding as evidence to discover unique
but unknown factors and develop effective regional mental health promotion
policies. The effectiveness of policies could be guaranteed if the spatial patterns
of the spatiotemporal effects intersect the boundaries for policy implementation,
such as jurisdictions and special geographic divisions for public health purposes
(e.g., public health districts in the State of Georgia).
The most significant contribution of this dissertation to the mental health
research community is to emphasize the importance and value of directing
research focus from the universality to the uniqueness of local contexts in the
associative and causal effects of contributing factors on mental illness. The results
collectively filled research gaps in the literature by demonstrating the spatial and
spatiotemporal variation in effects and the conditioning role of regions in the causal
effect estimation. The findings indicate a way to expand the theory on the influence
of socio-environmental constructs on mental illness mortality and the application
of spatiotemporal and causal modeling methods to geospatial analysis of mental
illness. The other contribution to the field is the introduction of spatiotemporal
interaction models to account for spatial and temporal dimensions and dependency
in the data. Through Chapters 2 and 3, I extended the spatially varying coefficient
models to spatiotemporally varying coefficient models, on top of explicitly including
the interaction between spatial and temporal dependency in the outcomes, thereby
demonstrated the usefulness of Bayesian spatiotemporal models for effect mapping
beyond the traditional disease mapping in spatial mental health research contexts.
Spatiotemporal models could prove its usefulness in more applications by the
increasing availability of sizable spatiotemporal datasets in many countries. The
75
effect mapping approach is expected to reexamine the spatial disparity in socio-
environmental effects on mental illness.
Future research, which takes into account an extensive set of contributing
factors of mental illness such as individual-level medical history and genetic
information, has the potential to corroborate the spatial disparities shown in
this dissertation. Data with fine-grained spatiotemporal information, along with
detailed individual attributes, will provide more opportunities to examine the
spatially and temporally varying effects of socio-environmental factors on mental
illness. Methodologically, it is feasible to expand the spatiotemporally varying
coefficient models to multiple explanatory variables. However, this will require
scalable computational infrastructure and efficient numerical methods, which are
currently under development (Gaedke-Merzhäuser et al., 2022; Niekerk et al.,
2021), to reveal simultaneous transitions in the effects of such variables. For
spatial causal inference, I am working on developing a novel similarity matrix that
combines a spatial weight matrix and Jensen-Shannon divergence for matching
analysis to efficiently handle spatial confounding. A successful development will
lead to the reliable estimation of the causal effect of explanatory factors on mental
health outcomes. For exposure assessment, it is of utmost priority for researchers
to develop a metric for the holistic assessment of exposure to physical and
socioeconomic environments by accounting for their interaction. Such development
needs to be in line with the critical re-engagement in the exposure’s role along with
considering physical activity, modalities of activities (e.g., leisure and commuting),
and the effective exposures that actually affect mental health outcomes.
On the theoretical side, my focus is on spatial generalizability (or external
validity) of associative or causal effects of contributing factors on mental illness.
76
In this context, spatial generalizability refers to the feasibility of extrapolating
associative or causal findings from a local or higher-level spatial entity to other
locals. This issue addresses two long-standing quests of academic geography:
setting the relationship between nomothetic (seeking laws) and idiographic
(describing characteristics) approaches and closely examining the meaning of
geographic scales. There are virtually infinite possibilities that a local effect
estimate may have no relationship with the global effect, or it may align perfectly
with the global effect. All possibilities call for the reconciliation and positive
feedback of nomothetic and idiographic approaches to understand the possible
processes, if not the very reasons, of spatial disparities in the effects of socio-
environmental constructs on mental illness and its mortality. Cross-scalar validity
of an effect estimate will help us understand the tangible role of spatial scales
in mental illness and to other mental health outcomes. Such investigations can
encourage further efforts to gain deeper insights into tackling ecological and
atomistic fallacies (Robertson & Feick, 2018). Based on this dissertation work, I
will continue to reflect on the fundamental issues with empirical studies on mental
illness and general mental health outcomes.
77
APPENDIX A
CHAPTER 2 APPENDIX
A.1 Modeling spatiotemporal interaction
Let there be spatial entities comprise nine square areas as below, with the
temporal dependence of the first-order random walk and let the total length of the
time series be three.
1 2 3
4 5 6
7 8 9
In this case, area 1 is assumed to be adjacent to areas 2, 4 and 5, area 2 is
adjacent to areas 1, 3, 4, 5 and 6, and so on. Each structure can be expressed in
matrices, say, WS and WT :
 
 0 1 0 1 1 0 0 0 0 

 1 0 1 1 1 1 0 0 0    0 1 0 0 1 1 0 0 0 

1 1 0 0 1 0 1 1 0 WS =  1 1 1 1 0 1 1 1 1  (A.1) 0 1 1 0 1 0 0 1 1    0 0 0 1 1 0 0 1 0 

0 0 0 1 1 1 1 0 1 
0 0 0 0 1 1 0 1 0
D = diag ({3, 5, 3, 5, 8, 5, 3, 5, 3}) (A.2)
78
 
 3 −1 0 −1 −1 0 0 0 0 

  −1 5 −1 −1 −1 −1 0 0 0   0 −1 3 0 −1 −1 0 0 0   −1 −1 0 5 −1 0 −1 −1 0 

D−W  S =  −1 −1 −1 −1 8 −1 −1 −1 −1  (A.3) 0 −1 −1 0 −1 5 0 −1 −1  

 0 0 0 −1 −

1 0 3 −1 0 
  0 0 0 −1 −1 −1 −1 5 −1 
0 0 0 0 −1 −1 0 −1 3 1 −1 0WT =  

−1 2 −1  (A.4)
0 −1 1
Matrices WS and WT are sparse as seen above. By the definition of
Kronecker product, their interaction term is
79
  3 −3 0 1 −1 0 · · · 0 0 0 0 0 0   −3 6 −3 −1 2 −1 · · · 0 0 0 0 0 0  

 0 −3 2 0 −1 1 · · · 0 0 0 0 0 0  −1 1 0 5 −5 0 · · · 0 0 0 0 0 0 



1 −2 1 −5 10 −5 · · · 0 0 0 0 0 0 
   0 1 −1 0 −5 5 · · · 0 0 0 0 0 0 
(D−W )⊗W =  ... ... .

S T .. ... ... ... . . . ... ... ... ... ... ...
 

  0 0 0 0 0 0 · · · 5 −5 0 −1 1 0   0 0 0 0 0 0 · · · −5 10 −5 −1 2 −1  

 0 0 0 0 0 0 · · · 0 −5 5 0 −1 1    0 0 0 0 0 0 · · · 1 −1 0 3 −3 0   0 0 0 0 0 0 · · · −1 2 −1 −3 6 −3 
0 0 0 0 0 0 · · · 0 −1 1 0 −3 3
(A.5)
The result should have (9 × 3) × (9 × 3) = 27 × 27 elements. To note,
when the spatial or temporal structure was imposed as identically independently
distributed (i.i.d.), WT equals to an identity matrix. In this study, the dimensions
of the precision matrix will be (3, 108× 14)× (3, 108× 14) = 43, 512× 43, 512.
80
Table A.1. Pearson correlation matrix of dependent and independent variables
One-year lagged 
-0.266 0.425 0.043 -0.221 0.282 -0.002 -0.001 -0.018
unemployment rate
Median household income 
(inflation-adjusted dollars as -0.266 -0.727 -0.002 0.670 -0.159 -0.396 -0.331 -0.358
of 2000)
Ratio of population below 
0.425 -0.727 0.237 -0.353 0.518 0.160 0.109 -0.025
poverty level
Ratio of rented housing 0.043 -0.002 0.237 0.403 0.398 -0.507 0.265 -0.336
Ratio of population higher 
-0.221 0.670 -0.353 0.403 -0.002 -0.435 0.106 -0.255
than bachelor's degree
Ratio of non-white 
0.282 -0.159 0.518 0.398 -0.002 -0.185 -0.049 -0.339
population
Ratio of rural population -0.002 -0.396 0.160 -0.507 -0.435 -0.185 0.085 0.411
Ratio of single-person 
-0.001 -0.331 0.109 0.265 0.106 -0.049 0.085 0.576
households
Ratio of elderly population -0.018 -0.358 -0.025 -0.336 -0.255 -0.339 0.411 0.576
Note: Absolute values higher than 0.5 were highlighted.
Table A.2. Variance inflation factor (VIF) of each variable
Variable VIF
The one-year lagged unemployment rate (%) 1.293
Median household income (Inflation-adjusted as of 2000) 6.816
The ratio of non-white population (%) 1.814
The ratio of the population with or higher than bachelor’s degree (%) 3.444
The ratio of the population below the poverty level (%) 4.365
The ratio of the rural population (%) 1.781
The ratio of renter-occupied housing (%) 2.596
The ratio of single-person households (%) 2.788
The ratio of the elderly population (65 years old or older, %) 2.729
81
One-year lagged unemployment rate
Median household income (inflation-
adjusted dollars as of 2000)
Ratio of population below poverty level
Ratio of rented housing
Ratio of population higher than 
bachelor's degree
Ratio of non-white population
Ratio of rural population
Ratio of single-person households
Ratio of elderly population
Table A.3. Summary of model hyperparameters of from Model 5-IV: summary
statistics of posterior marginals and 95 % credible intervals of precisions for each
model component
Precision Posterior mean Standarddeviation 2.5 % Median 97.5 %
τu0 5.01 0.14 5.22 5.49 5.78
τv0 5005.34 50.52 4064.76 4989.64 6043.56
τγ0 40.84 24.37 9.22 35.95 101.53
ρ0 0.94 0.04 0.84 0.95 0.99
τu1 2006.20 202.50 1638.24 1995.97 2433.87
τγ1 33191.22 13185.79 14750.80 30751.57 65774.97
τδ 384.28 12.38 360.70 384.02 409.32
Figure A.1. Temporal trends of unemployment rates (grey lines) and mental
illness and substance use mortality rates (red lines) in 3,108 contiguous US counties
and the overall trends (dashed bold lines)
82
Figure A.2. Spatiotemporal distribution of one-year lagged unemployment rates
in 3,108 contiguous US counties in 2001-2014
83
Figure A.3. Spatiotemporal distribution of mental illness and substance-use
mortality rates (per 100,000 people) in 3,108 contiguous US counties in 2001-2014
84
Figure A.4. Probability map of the random slope of unemployment rates in
Model 5-IV
(Note: the map displays the probability of β1it > 0)
85
Figure A.5. Residual maps of Model 5-IV.
86
87
Figure A.6. Mental health and substance use treatment facility per 100,000 people in counties in the contiguous
United States (2018)
Data source: Substance Abuse and Mental Health Services Administration
APPENDIX B
CHAPTER 3 APPENDIX
B.1 Detailed descriptions on spatiotemporal models
B.1.1 Spatiotemporal areal model formulation. Let b a vector of a
spatial random main effect bi· given a binary spatial weight matrix (also called
graph) W. W is usually defined by distance or sharing vertex between input
spatial entities and has zeros in its diagonal, which means there is the self is not
considered as a neighbor, and strictly being symmetric. The modified Besag-York-
Mollié formulation (Besag et al., 1991; Riebler et al., 2016) is expressed as:
1 (√ √ )b|W = √ 1− ϕv+ ϕu∗ (B.1)
τb
where v and u are vectors of spatially unstructured and structured
components, respectively. The asterisk in the subscript of u∗ means that the
structured component is scaled. The mixing hyperparameter ϕ, which is bounded
between 0 and 1, controls the contribution of each component to the variance of the
random vector b. The covariance matrix of b when the τb and ϕ are given turns
out to be:
( )
Var(b|τb, ϕ,W) = τ−1b (1− ϕ)I+ ϕQ
−
∗ (B.2)
where Q−∗ is a scaled precision (inverse covariance) matrix and I is an
identity matrix. The unscaled covariance matrix Q is modeled as a Besag model,
which is also known as an intrinsic conditional autoregressive model given W.
88
[∑ Q =] D−W (B.3)
where D = diag(vec Nj=1wij ) in which diag(.) is a diagonal matrix
with a vector of length N and wij is (i, j) element of W. Formulae B.1–B.3 are
also applied to[∑the spati]al modeling for the random slope component βi1. Here a
condition vec Nj=1wij > 0 ∀ i should be fulfilled, which means all areas have
i
at least one neighbor.
The main temporal component was structured in a first-order autoregressive
model.
γ·t = ρ0γ·(t−1) + εγt (B.4)
The autoregressive parameter ρ0 models the dependence of the value at
the present time point (t) on the value of the previous time point (t − 1). εγt is
a white noise process that models remaining variations in the temporal trend. In
our analysis, Formula B.4 represents the overall trend in the crude mental illness
mortality rate.
The spatiotemporal interaction (STINT) term δit represents the convolution
between spatial and temporal processes in its precision. Four STINT types are
identified by independent or structured spatial and temporal model precisions
(formula B.5) (Knorr-Held, 2000).
89

I⊗ I · · · STINT type II⊗Rγ · · · STINT type IIPrecision(δit) = Rδ =  (B.5)Ru ⊗ I · · · STINT type IIIRu ⊗Rγ · · · STINT type IV
⊗ denotes Kronecker product, Rγ is a temporally structured precision
matrix such as pth-order autoregressive or random walk, and Ru is a spatially
structured precision matrix when W is given. Model 5 with STINT type IV is
formulated as Formula B.6:
p(yit = 0) = pzero + (1− pzeroPoisson(λit = 0))p(yit > 0) = (1− pzero)Poisson(λit > 0)
ψit = logλit ∑
ψit = logPit(+ bi· + β0 + β pi1+xi)t1 + k=2 βkxitk + εit√
b|W (1 − v √= √ 1 ϕ + ϕ)u∗ , ϕb ∼ PC(0.5, 0.5), τb ∼ P(C(1, 0).01)τb −1 ( )
γ·t ∼ N 0, (τγ(1− ρ0)2) , γ·t = ρ0γ·(t−1) + εγt, ρ −1 −10 ∼ N 0, τγ , εγt ∼ N 0, τεt
βi1+ = β0 + βi1
Precision(δit) = Rδ(= Rb ⊗Rγ√ )
{βi1} = b
√
1 = √
1 1− ϕb1v1 + ϕb1u1∗ , ϕb1 ∼ PC(0.5, 0.5), τb1 ∼ PC(1, 0.01)τb1
εit ∼ N (0, τ−1ε )
(B.6)
The model is applied to the data of each state.
90
B.1.2 Description of hyperparameter estimates. The estimated
precision of main random effects was the lowest in the STINT component
(mean=5.149–5.232), followed by that of the spatial component (9.28), and the
temporal component (41.003–148.712). The estimated probability of structural
zeros was 0.7–0.9 % (95 % credible interval [CrI] = [0.1 %, 2.2 %] in Oregon,
[0.1 %, 3.4 %] in Washington) (Table B.7), which indicates that tracts had low
probability of having no mental illness mortality. The precision of state-level
random slope was around ten times higher (mean = 450.739–1338.804) than that
of the temporal random effect (Table B.8).
91
B.2 Supplementary tables and figures
Table B.1. List of North American Industry Classification System (NAICS) codes
for identifying care facilities
Code Description
53111008 Retirement Apartments & Hotels
62311001 Adult Care Facilities
62311002 Convalescent Homes
62311008 Homes & Institutions
62311010 Homes-Personal Care Facility
62311011 Hospices
62311012 Independent Living Services for Disabled
62311013 Intermediate Care Facilities
62311014 Life Care Communities
62311015 Long Term Care Facility
62311016 Nursing Care Facilities
62311017 Nursing & Personal Care NEC
62311018 Nursing Home Services
62331101 Retirement Communities & Homes
62331103 Skilled Nursing Care Facilities
62331201 Adult Congregate Living Facilities
62331204 Senior Citizens Housing
62331205 Senior Citizens Service Organizations
62331206 Residential Care Homes
62399002 Other Residential Care Facilities
62399017 Sheltered Care Homes
92
Table B.2. Principal component analysis results for deriving socioeconomic
deprivation index
Correlation with
the principal component
Oregon Washington
Median household income
(inflation-adjusted 2010 dollars) 0.892 0.893
Poverty rate(%) -0.798 0.819
Unemployment rate (%) -0.708 -0.734
Higher than bachelor’s degree (%) 0.700 0.760
Table B.3. Correlation matrix of explanatory variables
Oregon Washington
Notes
- All correlation coefficients are statistically significant at (α=0.01).
- Variables except for mental illness mortality were standardized.
Abbreviations
MIM: mental illness mortality
PARKS_SQKM10K: the total park area (km2) per 10,000 population
PM2.5: average PM2.5 (μg/m3)
PCTWATER: the proportion of waterbodies (%)
CARE10K: residential care facilities per 10,000 population
PCTELDERLY: 65 years old or older (%)
PCTNMARITAL: negative marital status (%)
PCTNWHITE: the non-white population (%)
PCTUNEMP: unemployment rate (%)
PCTPOVERTY: poverty rate (%)
PCTEDUC: higher than bachelor’s degree (%)
MEDINC10K: median household income (inflation-adjusted 2010 dollars)
93
Table B.4. Variance inflation factors of explanatory variables
Oregon Washington
Parks (km2 /10,000 population) 1.110 1.069
PM2.5 (µg/m3) 1.441 1.226
Area of waterbodies (%) 1.040 1.078
Residential care facilities (per 10,000 population) 1.099 1.059
65 years old or older (%) 1.950 1.824
Negative marital status (%) 1.745 2.012
Non-white population (%) 1.575 1.387
Unemployment rate (%) 1.343 1.445
Poverty rate (%) 2.935 2.837
Higher than bachelor’s degree (%) 1.642 1.881
Median household income (inflation-adjusted 2010 3.572 3.713
dollars)
94
Table B.5. List of twenty-eight excluded census tracts and the reasons of
exclusion
State GEOID1 Full tract name Reason Key
geographic
feature
OR 41007990000 Clatsop County, Tract 9900 Water area
OR 41011990101 Coos County, Tract 9901.01 Water area
OR 41015990101 Curry County, Tract 9901.01 Water area
OR 41019990000 Douglas County, Tract 9900 Water area
OR 41039990000 Lane County, Tract 9900 Water area
OR 41041990100 Lincoln County, Tract 9901 Water area
OR 41045940000 Malheur County, Tract 9400 Missing or no Paiute and
population Shoshone
Tribe
Reserve
OR 41051980000 Multnomah County, Tract 9800 Missing or no Swan
population Island
Industrial
Park
OR 41057990100 Tillamook County, Tract 9901 Water area
WA 53005012000 Benton County, Tract 120 Missing or no Hanford
population nuclear
facility
cleaning
site
WA 53009990100 Clallam County, Tract 9901 Water area
WA 53021980100 Franklin County, Tract 9801 Missing or no Tri-Cities
population Airport
WA 53027990000 Grays Harbor County, Tract 9900 Water area
WA 53029992201 Island County, Tract 9922.01 Missing or no Smith
population Island
WA 53031990000 Jefferson County, Tract 9900 Water area
WA 53033990100 King County, Tract 9901 Water area
WA 53035990100 Kitsap County, Tract 9901 Water area
WA 53049990100 Pacific County, Tract 9901 Water area
WA 53055960100 San Juan County, Tract 9601 No neighbors
WA 53055960500 San Juan County, Tract 9605 No neighbors
WA 53055990100 San Juan County, Tract 9901 Water area
WA 53057990100 Skagit County, Tract 9901 Water area
WA 53061990002 Snohomish County, Tract 9900.02 Water area
WA 53061990100 Snohomish County, Tract 9901 Water area
WA 53067990100 Thurston County, Tract 9901 Water area
WA 53071920400 Walla Walla County, Tract 9204 Missing or no Washington
population State
Penitentiary
WA 53073010900 Whatcom County, Tract 109 No neighbors
WA 53073011000 Whatcom County, Tract 110 No neighbors
* Unique identifiers of census tracts are in Federal Information Processing Standards code as of
2010.
95
96
Table B.6. Descriptive statistics of the data
Oregon Washington
Mean Standard Standarddeviation Minimum Maximum Mean deviation Minimum Maximum
Mental illness mortality 0.56 0.89 0.00 10.00 0.31 0.65 0.00 13.00
Population 4681.02 1921.48 75.00 14619.00 4733.19 1756.68 48.00 14540.00
Mental illness mortality
(per 10,000 population) 1.21 2.02 0.00 26.14 0.69 1.62 0.00 71.26
Area of parks
(km2 per 10,000 population) 4.17 12.55 0.00 356.07 2.65 6.16 0.00 82.97
PM2.5 (µg/m3) 5.66 1.94 0.63 13.50 5.88 1.60 0.55 12.84
Proportion of waterbodies (%) 2.48 5.90 0.00 56.78 3.64 8.77 0.00 75.36
Number of residential care facilities
(per 10,000 population) 6.93 8.87 0.75 400.00 6.59 9.99 0.88 625.00
65 years old or older rate (%) 14.87 6.90 0.00 53.05 13.16 6.19 0.00 54.75
Negative marital status rate (%) 21.47 5.93 1.47 70.66 20.48 6.43 0.34 51.06
Non-white population rate (%) 20.58 13.10 0.65 97.13 26.39 17.91 0.00 96.44
Unemployment rate (%) 8.72 4.13 0.00 38.79 7.62 4.06 0.00 36.57
Poverty rate (%) 15.20 9.32 0.00 81.10 12.88 9.70 0.00 84.53
Higher than bachelor’s degree (%) 30.00 17.36 0.00 85.64 30.87 17.77 0.00 87.44
Median household income
(inflation-adjusted 2010 dollars) 51799.25 18832.92 7226.32 160170.05 60938.85 24030.67 4346.09 197166.29
97
Table B.7. Sensitivity analysis results
Hyperpriors
τb, τγ, τδ, τb DIC1 WAIC21 ϕb, ϕδ, ϕb1
Oregon
PC(1, 0.01) 3 PC(0.5, 0.5) 19321.20 19329.04
PC(0.1, 0.01) PC(0.5, 0.05) 19323.77 19333.37
logGamma(1, 0.0005) logGamma(0.5, 0.0005) 19321.72 19331.36
Washington
PC(1, 0.01) PC(0.5, 0.5) 24555.82 24546.06
PC(0.1, 0.01) PC(0.5, 0.05) 24552.89 24554.84
logGamma(1, 0.0005) logGamma(0.5, 0.0005) 24553.51 24545.40
1 Deviance information criterion; 2 Watanabe-Akaike information criterion; 3 Penalized complexity prior.
Table B.8. Summary of hyperparameter estimates
Mean Standard deviation 95% credible interval
Oregon
pzero 0.007 0.006 0.001, 0.022
τb 389.218 933.260 29.401, 2228.986
ϕb 0.313 0.193 0.033, 0.737
τγ 41.003 22.341 11.394, 96.719
ρ0 0.836 0.105 0.570, 0.970
τδ* 5.232 0.567 4.117, 6.345
ϕδ* 0.877 0.072 0.684, 0.964
ρ1* 0.895 0.020 0.853, 0.933
τb 450.739 1266.168 24.091, 2658.593
ϕb1 0.314 0.263 0.009, 0.894
Washington
pzero 0.009 0.009 0.001, 0.034
τb 4.764 0.881 3.296, 6.754
ϕb 0.390 0.106 0.194, 0.605
τγ 148.712 89.331 41.570, 380.354
ρ0 0.622 0.217 0.084, 0.915
τδ* 5.149 0.878 3.631, 7.083
ϕδ* 0.439 0.097 0.257, 0.637
ρ1* 0.763 0.074 0.592, 0.881
τb 1338.804 2689.515 85.762, 7165.500
ϕb1 0.295 0.173 0.052, 0.698
98
Figure B.1. Map of state, county, and census tract boundary and elevation in
Oregon and Washington
99
Figure B.2. One-year lagged annual mean normalized difference vegetation index
(NDVI) at each census tract by year during the study period (2006–2018) from the
moderate resolution imaging spectrometer (MODIS) Terra sensor
100
APPENDIX C
CHAPTER 4 APPENDIX
Table C.1. Descriptive statistics of the decedents who deceased in natural
manners in the State of Washington, 2018
Characteristic N = 31,2451
Mental illness mortality 273 (0.87%)
Subregion
Columbia Plateau 4,586 (14.68%)
Seattle-Tacoma 11,569 (37.03%)
Spokane 1,706 (5.46%)
Western Cascades 11,690 (37.41%)
Western Cordillera 1,694 (5.42%)
NDVI (5-year average in 15-minutes walking area) 0.27, 0.26 (0.05)
Age 76.72, 78.00 (13.42)
Sex
Female 15,036 (48.12%)
Male 16,209 (51.88%)
Race
White (Non-Hispanic) 27,909 (89.32%)
Black / African American 812 (2.60%)
Native American 500 (1.60%)
Hispanic 449 (1.44%)
Asian 1,203 (3.85%)
Others 372 (1.19%)
(Continued on the next page)
101
Table C.1 (Continued)
Characteristic N = 31,2451
Marital status
Married / Partnered 14,020 (44.87%)
Separated / Divorced 5,266 (16.85%)
Widowed 9,536 (30.52%)
Single / Never Married 2,378 (7.61%)
Unknown / Not Reported 45 (0.14%)
Education
No High School Diploma / GED 3,999 (12.80%)
High School Diploma to Associate Degree 20,153 (64.50%)
University Degree and Higher 6,920 (22.15%)
Unknown / Not Reported 173 (0.55%)
Smoking
Yes 4,088.00 (13.08%)
Never 16,063.00 (51.41%)
Paused / Abstained 2,595.00 (8.31%)
Unknown / Not Reported 8,499.00 (27.20%)
MNDWI -0.01, -0.01 (0.02)
NDBI -0.13, -0.13 (0.02)
PM2.5 (µg/m3) 5.86, 5.65 (1.47)
Traffic noise (decibel) 14.34, 8.90 (15.58)
67,357.96, 63,115.00
Median household income (US dollars)
(25,034.76)
Non-white rate (%) 27.64, 22.88 (17.85)
Household income less than
12.58, 11.08 (7.85)
150 % of poverty line (%)
Unemployment rate (%) 6.24, 5.56 (3.13)
Bachelor’s degree and higher (%) 31.12, 26.85 (16.95)
1n (%); Mean, Median (standard deviation)
102
Figure C.1. Standardized difference of covariates in the treated and controlled
groups by five percentile thresholds for treatment definition in the State of
Washington
103
Figure C.2. Standardized difference of covariates in the treated and controlled
groups by five percentile thresholds for treatment definition in subregions
104
Figure C.3. Effect estimates from matching analysis by five percentile thresholds
for treatment condition in five core-based statistical areas where dichotomization
conditions were fulfilled
105
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