INTEGRATING KEY ECOLOGICAL HEALTH AND SOCIAL DIMENSIONS IN
SUSTAINABLE WATER RESOURCES MANAGEMENT
By
Fariborz Daneshvar

A DISSERTATION
Submitted to
Michigan State University
in partial fulfilment of the requirements
for the degree of
Biosystems Engineering – Doctor of Philosophy
Mechanical Engineering – Dual Major
2017

ABSTRACT
INTEGRATING KEY ECOLOGICAL HEALTH AND SOCIAL DIMENSIONS IN
SUSTAINABLE WATER RESOURCES MANAGEMENT
By
Fariborz Daneshvar
The dynamics of coupled natural and human systems are complex and vary across time,
location, and organizational unit. So different social groups may be unequally affected by degraded
environments, which in many cases do not randomly occur over space. Therefore, the concept of
environmental justice was introduced to address this issue. One environmental resource that has
been a focus point for environmental justice is freshwater, and stream health based environmental
justice studies are the most recent approach used by researchers to describe these phenomena.
However, many of the previous studies were only performed at the census tract level and no proper
spatial level was defined for environmental justice studies with respect to stream health. On the
other hand, due to computational limitations for stream health indices estimation, only a few water
quantity and quality parameters were used to develop stream health predictive models. Therefore,
the purpose of this study is to address the following knowledge gaps in the area of stream health
based environmental justice by: 1) determining the role of spatial level of socioeconomic factors
on stream health based environmental justice studies and 2) assessing the relative importance of
parameter estimation in stream health based environmental justice modeling.
To address the first knowledge gap, three Bayesian Conditional Autoregressive (CAR)
models (ordinary regression, weighted regression and spatial) were developed for four common
stream health measures based on 17 socioeconomic and physiographical variables at three census
levels of county, census tract, and block group in the Saginaw River Basin in Michigan. This
watershed was an ideal place to perform this study since it was identified as an area of concern in

the Great Lakes region while having one of the most diverse populations in the state. For all stream
health measures, spatial models had better performance compared to the two non-spatial models
at the census tract and block group levels. In addition, multilevel Bayesian CAR models were also
developed to understand the spatial dependency across three levels. Results showed that
considering level interactions improved the predictive power of the environmental justice models.
Residual plots also showed that models developed at the block group and census tract (in contrary
to county level models) were able to capture spatial variations, which is an important aspect of
environmental justice studies.
To address the second knowledge gap, first ecologically relevant streamflow and water
quality indices were used to improve the performance of the stream health predictive models. The
outputs (fish and macroinvertebrate indices) from newly developed stream predictive models were
then used to develop similar CAR models. Results showed that incorporating the more accurate
stream health indices improved the spatial dependencies at the census tract and block group levels
compared to county level. In addition, the multilevel models had better performance than single
level models. Finally, the modified stream health indices improved stream health based
environmental justice models’ performance by reducing redundancies in independent variables.
This research finding provides a valuable tool to target vulnerable communities with respect to
access to clean water, which enables water resources policymakers to allocate resources in a way
that reduces environmental inequality.

Dedicated to my loving wife and son, Behin and Aydin,
and my amazing parents, Abdolreza and Fatemeh, for their endless support.

iv

ACKNOWLEDGEMENTS
I would like to thank all of the people who helped me through this journey. First of all, my
advisor, Dr. Amirpouyan Nejadhashemi for his mentorship, patience, guidance and support. You
made me the researcher I am today and I really appreciate it. I am also thankful to my former
advisor, Dr. Manoochehr Koochesfahani for his support and paving my way to join Michigan State
University. I would also like to thank my committee members: Dr. Ashton Shortridge, Dr. Sandra
Marquart-Pyatt, Dr. Farhad Jaberi, and Dr. Timothy Harrigan for their guidance and support to
complete this research.
My gratitude is also extended to Dr. Zhen Zhang, Dr. Ahmed Naguib, Dr. Shahram Pouya,
and all lab mates who helped me a lot and made great memories. Thanks Sean Woznicki, Matthew
Herman, Yaseem Hamaamin, Umesh Adhikari, Melissa Rojas-Downing, Elaheh Esfahanian,
Mohammad Abouali, Subhasis Giri, Georgina Sanchez, Patrick Hammer, Rohit Nehe, David
Olson, Ian Kropp, and Juan Sebastian Hernandez-Suarez. I enjoyed working with you.
Many thanks to my dear friends, especially Arash Sattari, Nariman Jahani, Nazanin Jahani,
Saman Jahani, Erfan Tavakoli, Shahrad Shahvand, Iman Barjasteh, Ehsan Kharazmi, and Raeuf
Roshangar, who have always been supportive and a source of encouragement.
Saving the most important for the last, I would like to thank my family who have always
been my endless source of energy and inspiration. My profound gratitude to my parents: Abdolreza
and Fatemeh, and my siblings: Farshid, Atefeh, and Reza, for their love and unconditional
supports. My greatest appreciation is for my wife, Behin Elahi, who has always believed in me.
Thanks for your immeasurable love, patience, and support that pushed me across the finish line!

v

TABLE OF CONTENTS
LIST OF TABLES ..................................................................................................................................... viii
LIST OF FIGURES ..................................................................................................................................... xi
KEY TO ABBREVIATIONS .................................................................................................................... xiii
1.

INTRODUCTION ................................................................................................................................ 1

2.

LITERATURE REVIEW ..................................................................................................................... 3
2.1. Coupled Natural and Human Systems .......................................................................................... 3
2.1.1.
Impact of Anthropogenic Activities on Natural Systems ..................................................... 3
2.1.2.
Impact of Natural Systems Degradation on Human Systems ............................................... 4
2.1.3.
The Concept of Environmental Justice ................................................................................. 6
2.2. Water Resources Assessment........................................................................................................ 6
2.2.1.
Water Quality Assessment .................................................................................................... 7
2.2.2.
Modeling Approaches Used for Water Resources Assessment .......................................... 11
2.3. Stream Health and Biological Integrity Assessment ................................................................... 16
2.3.1.
Stream Health Indices and Metrics ..................................................................................... 17
2.3.2.
Modeling Used for Biological Integrity Assessment .......................................................... 23
2.4. Socioeconomic Assessment ........................................................................................................ 26
2.4.1.
Socioeconomic Aspects of Environmental Justice Assessment .......................................... 28
2.4.2.
Statistical Models for Socioeconomic Assessment ............................................................. 28

3.

INTRODUCTION TO METHODOLOGY AND RESULTS ............................................................ 32

4. EVALUATING STREAM HEALTH BASED ENVIRONMENTAL JUSTICE MODEL
PERFORMANCE AT DIFFERENT SPATIAL SCALES ......................................................................... 34
4.1. Introduction ................................................................................................................................. 34
4.2. Methodology ............................................................................................................................... 37
4.2.1.
Study Area .......................................................................................................................... 37
4.2.2.
Stream Health Indicators ..................................................................................................... 38
4.2.3.
Socioeconomic and Physiographic Indicators .................................................................... 40
4.2.4.
Data Analysis and Modeling ............................................................................................... 42
4.2.5.
Markov Chain Monte Carlo Implementation Details.......................................................... 46
4.3. Results and Discussions .............................................................................................................. 48
4.3.1. Variables Distribution and Pairwise Correlations ....................................................................... 48
4.3.2. Understand the Spatial Dependency Between Stream Health Indicators and Control Parameters
Using Regression Analysis ..................................................................................................................... 53
4.4. Conclusions ................................................................................................................................. 64
5. ASSESSING THE RELATIVE IMPORTANCE OF PARAMETER ESTIMATION IN STREAM
HEALTH BASED ENVIRONMENTAL JUSTICE MODELING ............................................................ 66
5.1. Introduction ................................................................................................................................. 66
5.2. Materials and Methods ................................................................................................................ 69
5.2.1.
Study Area .......................................................................................................................... 69
5.2.2.
Stream Health Indices ......................................................................................................... 70
5.2.3.
Socioeconomic/Physiographic Indices................................................................................ 71
5.2.4.
Modeling Process ................................................................................................................ 73
vi

5.2.5.
Data Analysis ...................................................................................................................... 77
5.3. Results and Discussion ............................................................................................................... 81
5.3.1.
Stream Health Indices ......................................................................................................... 81
5.3.2.
Variables Distribution and Pairwise Correlations ............................................................... 83
5.3.3.
Identifying High Priority Area ............................................................................................ 86
5.3.4.
Single Level (with No Random Effect) Stream Health Based Environmental Justice
Regression Models .............................................................................................................................. 87
5.3.5.
Multilevel (with Random Effect) Stream Health Based Environmental Justice Regression
Models ……………………………………………………………………………………………..90
5.4. Conclusion .................................................................................................................................. 93
6.

CONCLUSIONS................................................................................................................................. 95

7.

FUTURE RESEARCH RECOMMENDATIONS .............................................................................. 98

APPENDICES .......................................................................................................................................... 100
APPENDIX A: Study One .................................................................................................................... 101
APPENDIX B: Study Two ................................................................................................................... 115
REFERENCES ......................................................................................................................................... 135

vii

LIST OF TABLES
Table 1. Summary of common modeling tools used for water resources assessment .................. 16
Table 2. Comparison of stream health indices (Fierro et al., 2017).............................................. 19
Table 3. Commonly used macroinvertebrate indices (Herman and Nejadhashemi, 2015) .......... 21
Table 4. Summary of common statistical models used for socioeconomic assessment ............... 31
Table 5. Summary of stream health measures in Saginaw River Basin ....................................... 39
Table 6. List of the socioeconomic/physiographic indicators (Census bureau, 2010) ................. 41
Table 7. Regression models for FIBI at county level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................... 54
Table 8. Regression models for EPT at county level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................... 55
Table 9. Regression models for HBI at county level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................... 56
Table 10. Regression models for IBI at county level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................... 57
Table 11. DICs for multilevel models with random effects (boldfaced values represent best models
at each census level)*........................................................................................................ 59
Table 12. Significant parameters among all selected best models................................................ 62
Table 13. Socioeconomic/Physiographic indices ......................................................................... 72
Table 14. Comparison of coefficient of determination of developed stream health predictive
models ............................................................................................................................... 82
Table 15. Absolute percent of change in the stream health measures prediction between one- and
two-phase approaches ....................................................................................................... 83
Table 16. Comparison of pairwise correlations among stream health indices at the county level.
(Blue upper right values represent correlations among the new developed stream health
indices using a two-phase approach, while red lower left values are correlations reported
by Daneshvar et al. (2016) using a one-phase approach) ................................................. 85
Table 17. Comparison of pairwise correlations among stream health indices at the census tract
level. (Blue upper right values represent correlations among the new developed stream
health indices using a two-phase approach, while red lower left values are correlations
reported by Daneshvar et al. (2016) using a one-phase approach) ................................... 85
viii

Table 18. Comparison of pairwise correlations among stream health indices at the block group
level. (Blue upper right values represent correlations among the new developed stream
health indices using a two-phase approach, while red lower left values are correlations
reported by Daneshvar et al. (2016) using a one-phase approach) ................................... 86
Table 19. DICs of single level (with no random effect) regression models (Boldfaced values
indicate best selected models with lower DICs) ............................................................... 88
Table 20. Significant parameters of new developed single level (with no random effect) regression
models ............................................................................................................................... 89
Table 21. DICs of the best selected regression models for the census tract and block group levels
........................................................................................................................................... 91
Table 22. Significant parameters (in black) for the best-selected stream health based environmental
justice models (Boldfaced values indicate repeated indices from Daneshvar et al. (2016),
while red indices are those from Daneshvar et al. (2016) that are eliminated with the new
approach)........................................................................................................................... 92
Table A1. Regression models for FIBI at census tract level (boldfaced values indicates a
significant parameter at the 0.05 level)………………………………………………….107
Table A2. Regression models for EPT at census tract level (boldfaced values indicates a
significant parameter at the 0.05 level) ........................................................................... 108
Table A3. Regression models for HBI at census tract level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................. 109
Table A4. Regression models for IBI at census tract level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................. 110
Table A5. Regression models for FIBI at block group level (boldfaced values indicates a
significant parameter at the 0.05 level) ........................................................................... 111
Table A6. Regression models for EPT at block group level (boldfaced values indicates a
significant parameter at the 0.05 level) ........................................................................... 112
Table A7. Regression models for HBI at block group level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................. 113
Table A8. Regression models for IBI at block group level (boldfaced values indicates a significant
parameter at the 0.05 level) ............................................................................................. 114
Table B1. Input parameters used for stream health predictive models ....................................... 115
Table B2. Comparison of root-mean-square error of developed stream health predictive models
......................................................................................................................................... 116

ix

Table B3. Regression models for IBI at county level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 117
Table B4. Regression models for HBI at county level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 118
Table B5. Regression models for FIBI at county level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 119
Table B6. Regression models for EPT at county level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 120
Table B7. Regression models for IBI at census tract level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 121
Table B8. Regression models for HBI at census tract level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 122
Table B9. Regression models for FIBI at census tract level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 123
Table B10. Regression models for EPT at census tract level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 124
Table B11. Regression models for IBI at block group level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 125
Table B12. Regression models for HBI at block group level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 126
Table B13. Regression models for FIBI at block group level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 127
Table B14. Regression models for EPT at block group level (Boldfaced values indicate significant
parameters at the 0.05 level) ........................................................................................... 128
Table B15. Significant parameters of former developed single level (with no random effect)
regression models (adapted from Daneshvar et al. (2016)) ............................................ 129
Table B16. DICs of multilevel models with random effect (boldfaced values represent best models
at each census level)........................................................................................................ 130

x

LIST OF FIGURES
Figure 1. TMDL implication in the CWA (U.S. EPA, 2017d) ..................................................... 10
Figure 2. Geographic hierarchy of census data collection (U.S. Census Bureau, 2015) .............. 27
Figure 3. Saginaw River Basin ..................................................................................................... 37
Figure 4. Stream health condition across Saginaw River Basin: (a) IBI, (b) HBI, (c) FIBI, and (d)
EPT (adapted from Einheuser et al., 2012; 2013a). .......................................................... 40
Figure 5. Boundary maps: (a) counties, (b) census tracts, and (c) block groups across Saginaw
River Basin........................................................................................................................ 42
Figure 6. Spearman rank correlation matrix between dependent and independent variables at the
county level. Boldfaced value indicates significance at the 0.05 level and correlation less
than 0.7, Boldfaced value in red indicates significance at the 0.05 level and strongly
positive correlation equal or above 0.7, and value in blue indicates significance at the 0.05
level and strongly negative correlation equal or below -0.7 ............................................. 49
Figure 7. model prediction residuals at county level for a) EPT, b) FIBI, c) HBI, d) IBI ............ 63
Figure 8. The locations of biological monitoring sites at the Saginaw River Basin ..................... 70
Figure 9. Census units of (a) counties, (b) census tracts, and (c) block groups overlapping with the
Saginaw River Basin ......................................................................................................... 73
Figure 10. The overall modeling processes .................................................................................. 74
Figure 11. Correlation matrix of indices at the county level. The diagonal represents the
scatterplots, while lower level and upper levels represent pairwise distributions and
correlation coefficients, respectively. Boldfaced numbers represent significant correlation
coefficients at the 0.05 level. Red and blue values represent positive and negative
significant correlation coefficients with absolute value above 0.7 at 0.05 level .............. 84
Figure 12. Bivariate map of overall stream measures and their predictors across Saginaw River
Basin at (a) county, (b) census tract, and (c) block group levels ...................................... 87
Figure A1. Spearman ranks correlation matrix between dependent and independent variables at the
census tract level. Boldfaced value indicates significance at the 0.05 level and correlation
less than 0.7, Boldfaced value in red indicates significance at the 0.05 level and strongly
positive correlation equal or above 0.7, value in blue indicates significance at the 0.05 level
and strongly negative correlation equal or below -0.7 .................................................... 101
Figure A2. Spearman rank correlation matrix between dependent and independent variables at the
block group level. Boldfaced value indicates significance at the 0.05 level and correlation
less than 0.7, Boldfaced value in red indicates significance at the 0.05 level and strongly
xi

positive correlation equal or above 0.7, value in blue indicates significance at the 0.05 level
and strongly negative correlation equal or below -0.7 .................................................... 102
Figure A3. EPT model residuals at: a) census tract single level (no random effect), b) census tract
level with multilevel (random) effect, c) block group single level (no random effect), d)
block group level with multilevel (nested random) effect .............................................. 103
Figure A4. HBI model residuals at: a) census tract single level (no random effect), b) census tract
level with multilevel (random) effect, c) block group single level (no random effect), d)
block group level with multilevel (nested random) effect .............................................. 104
Figure A5. FIBI model residuals at: a) census tract single level (no random effect), b) census tract
level with multilevel (random) effect, c) block group single level (no random effect), d)
block group level with multilevel (nested random) effect .............................................. 105
Figure A6. IBI model residuals at: a) census tract single level (no random effect), b) census tract
level with multilevel (random) effect, c) block group single level (no random effect), d)
block group level with multilevel (nested random) effect .............................................. 106
Figure B1. Predicted stream health indices for Saginaw River Basin: (a) IBI, (b) HBI, (c) FIBI, (d)
EPT using the two-phased approach (data for sections b, c, and d are adapted from
Daneshvar et al. (2017)) .................................................................................................. 132
Figure B2. Correlation matrix of indices at the census tract level. The diagonal represents the
scatterplots, while lower level and upper levels represent pairwise distributions and
correlation coefficients, respectively. Boldfaced numbers represent significant correlation
coefficients at the 0.05 level. Red and blue values represent positive and negative
significant correlation coefficients with absolute value above 0.7 at 0.05 level ............ 133
Figure B3. Correlation matrix of indices at the block group level. The diagonal represents the
scatterplots, while lower level and upper levels represent pairwise distributions and
correlation coefficients, respectively. Boldfaced numbers represent significant correlation
coefficients at the 0.05 level. Red and blue values represent positive and negative
significant correlation coefficients with absolute value above 0.7 at 0.05 level ............ 134

xii

KEY TO ABBREVIATIONS
ANFIS: Adaptive Neuro-Fuzzy Inference System
ANN: Artificial Neural Network
AQUATOX: Aquatic Ecosystem Simulation Model
ARM: Agricultural Runoff Management
ARS: Agricultural Research Service
AusRivAS: Australian River Assessment Scheme
BASINS: Better Assessment Science Integrating point and Nonpoint Source
B-IBI: Benthic Index of Biotic Integrity
BMPs: Best Management Practices
CAR: Conditional Autoregressive
CWA: Clean Water Act
DIC4: Deviance Information Criterion
ELOHA: Ecological Limits of Hydrologic Alteration
EPA: Environmental Protection Agency
EPT: Ephemeroptera, Plecoptera, and Trichoptera
GHGs: Greenhouse Gases
HBI: Hilsenhoff Biotic Index
HEC-DSS: Hydrologic Engineering Center-Data Storage System
HEC-HMS: Hydrologic Engineering Center-Hydrologic Modeling System
HIT: Hydrological Index Tool
HLM: Hierarchical Linear Modeling
HRU: Hydrological Response Units
xiii

HSP: Hydrocomp Simulation Program
HSPF: Hydrologic Simulation Program-Fortran
HUC: Hydrologic Unit Code
IBI: Index of Biotic Integrity
IHD: International Hydrological Decade
IHP: International Hydrological Program
LA: Load Allocation
LID: Low Impact Development
MCMC: Markov chain Monte Carlo
MDEQ: Michigan Department of Environmental Quality
MHIT: MATLAB Hydrological Index Tool
MOS: Margin of Safety
NATHAT: National Hydrologic Assessment Tool
NAWQA: National Water Quality Assessment
NPDES: National Pollutant Discharge Elimination System
NPS: Non-Point Source
NSE: Nash-Sutcliffe efficiency
NWIS: National Water Information System
PBIAS: Percent bias
PHABSIM: Physical Habitat Simulation Model
PLSR: Partial Least Square Regression
R2: Coefficient of determination
RIVPACS: River Invertebrate Prediction and Classification System

xiv

RMSE: Root Mean Square Error
RSR: root mean square error-observations standard deviation ratio
SAR: Simultaneous Autoregressive
SEM: Structural Equation Modeling
SUSTAIN: System for Urban Stormwater Treatment and Analysis Integration
SWAT: Soil and Water Assessment Tool
SWMM: Storm Water Management Model
SWMM-CAT: Storm Water Management Model-Climate Adjustment Tool
TMDL: Total Maximum Daily Load
UNESCO: United Nations Educational, Scientific and Cultural Organization
UNICEF: United Nations Children’s Fund
USCB: U.S. Census Bureau
USDA: U.S. Department of Agriculture
USDA-ARS: U.S. Department of Agriculture-Agricultural Research Service
USGS: U.S. Geological Survey
WHO: World Health Organization
WIN: Watershed Initiative Network
WLA: Waste Load Allocation
WMO: World Meteorological Organization
WUA: Weighted Usable Area

xv

1. INTRODUCTION
Anthropogenic activities in many areas resulted in the degradation of natural ecosystems.
Almost half of land surfaces are transformed and many natural resources are altered by human
activities that turned the earth to a human-dominated planet (Vitousek et al., 1997). Meanwhile,
natural and human ecosystems are interconnected and impaired natural ecosystems have negative
impacts on human ecosystems. In order to address this complex system, the concept of coupled
natural and human systems was developed to evaluate the mutual impacts of these systems.
However, these mutual impacts are dynamic and vary across time, location, and administrative
units. As a result, different communities are impacted in different ways. Therefore, the concept of
environmental justice was introduced to provide equal access to healthy environment, and equal
right of being involved in environmental policy making as a right for all human beings.
Due to the fact that freshwater is a limited natural resource that is vital for both natural and
human ecosystems, environmental justice studies with respect to clean water have been an area of
research for years. For this purpose, both socioeconomic and water resources assessments must be
conducted. In terms of social dimensions, socioeconomic indicators representing sociological and
economical aspects of the society are used for environmental justice studies. These indicators are
developed on top of census data collected by the U.S. Census Bureau at different spatial levels.
While most environmental justice studies used data collected at the census tract level, studies show
that socioeconomic data collected at different levels may result in dissimilar conclusions. To the
best of my knowledge, no proper spatial level has been defined for environmental justice studies
with respect to stream health. Therefore, one of the goals of this study is to address this knowledge
gap by assessing the role of spatial levels in environmental justice studies with respect to stream
health.
1

In terms of evaluating the health of water resources, several techniques have been used that
mainly rely on water quality to evaluate the health of waterbodies. However, the newly introduced
method known as bioassessment is considered as a more comprehensive approach since it
measures the final impact of physical, chemical, and biological activities on aquatic species.
However, it is almost impossible to sample all waterbodies to perform comprehensive stream
health assessments. Therefore, many studies used water quantity and water quality parameters to
evaluate the biological integrity of streams beyond the monitoring points. However, due to the
complexity of the natural systems, the predictability of stream health models is low in general.
Therefore, the goal of the second study is to evaluate whether the incorporation of more reliable
stream health measures (fish and macroinvertebrate indices) can improve the overall performance
of stream health based environmental justice modeling.
In the next six chapters (2 to 7), we address the aforementioned goals and provide a
roadmap for future studies. Chapter 2 synthesizes key aspects of water resources and
socioeconomic assessment, followed by modeling techniques used for these assessments. In
chapter 3, we provide a summary of the knowledge gaps that will be addressed in chapters 4 and
5. In chapter 4, spatial dependencies among socioeconomic indices and water quality measures are
evaluated at three levels of county, census tract, and block group. Then the role of level change
and nested effects on their spatial dependencies are evaluated. In chapter 5, the role of water quality
measures prediction on spatial dependencies are assessed. For this purpose, more recent
developments in ecosystem modeling are used to develop accurate biological measures and then
these predictions are used to re-evaluate the objectives defined in study one. The overall
conclusions of both studies are summarized in chapter 6, followed by recommendations for future
research in chapter 7.

2

2. LITERATURE REVIEW
2.1. Coupled Natural and Human Systems
The dynamic of both natural and human systems are complex and interrelated. For this
purpose, multidisciplinary researches that integrate biological, physiological and socioeconomic
sciences are needed (Carpenter et al., 2009; Alberti et al., 2011). The concept of coupled natural
and human systems was introduced to address these complex and reciprocal effects at the same
time (Liu et al., 2007a, b). Assessing impacts of natural systems on human systems and vice versa
are two key aspects of this concept and have been extensively studied (Ostrom and Nagendra,
2006; Liu et al., 2007a; Alberti et al., 2011; NSF, 2014; Chen, 2015).
2.1.1. Impact of Anthropogenic Activities on Natural Systems
Anthropogenic activities influenced natural ecosystem in many aspects. Population
increase and high demand for using resources such as land and freshwater have drastically affected
terrestrial and aquatic ecosystems and made the earth a human dominated planet (Vitousek et al.,
1997; Tilman et al., 2001; Tilman and Lehman, 2001; Halpern et al., 2008). Meanwhile,
agricultural practices and urbanization have transformed the land as humans continue to modify
natural system (Sanderson et al., 2002; Foley et al., 2005). As a result, more than half of the Earth’s
landscapes have been changed (Vitousek et al., 1997). Land transformation for agricultural
practices are predicted to increase by up to ten million square kilometers by 2050 (Tilman et al.,
2001). All of these changes result in broader impacts beyond transformed lands (Dupouey et al.,
2002; Lambin and Geist, 2008). These alterations include but are not limited to increase in
greenhouse gasses (GHGs) emission and climate change (Smith and Conen, 2004; Falloon and
Betts, 2010), urban heat island development (Peng et al., 2011), and deforestation (HendersonSellers and Gornits, 1984). These changes will negatively affect the integrity of natural ecosystems
3

in many ways such as change in abundance and diversity of birds (Jets et al., 2007) mammals
(Murray and Dickman, 2000; Thuiller et al., 2006), and plants (Thuiller et al., 2008).
At the same time, increase in freshwater demand for drinking and agricultural uses have
put water resources at risk (Peters and Meybeck, 2000; Viessman et al., 2009). Although more
than 70% of Earth’s surface is covered by water, only 2.5% of that is freshwater that can be used
for drinking, agricultural, industrial and recreational purposes (USGS, 2016). However, up to 90%
of freshwater are either in the forms of groundwater, ice, or glaciers; and only about 0.007% of
global water is available in rivers and lakes in form of surface water (Gleick, 1993). Due to the
high demand for water usage, most rivers and lakes have been regulated while only one-third of
Earth’s rivers were undisturbed by the end of the twentieth century (Abramovitz, 1996; Vitousek
et al., 1997). These changes to riverine ecosystems not only affect water quantity and quality, but
also alter aquatic ecosystems (Kingsford, 2000; Halpern et al., 2008; Wei et al., 2009). Halpern et
al. (2008) reported that more than 40% of aquatic ecosystems are highly impacted by human
activities. As an example, excess agricultural nutrients (such as nitrogen and phosphorus) released
into waterbodies enhanced eutrophication and diminished dissolved oxygen (U.S. EPA, 2017a).
These degradations resulted in severe environments for aquatic species. Studies showed that by
2050, most of the existing species might become extinct (Schaaf et al., 2006; Halpern et al., 2008).
On the other hand, fisheries that mainly target specific types of aquatic species, have modified
natural predator–prey cycles, ending up with change in abundance and distribution of aquatic
species (Vitousek et al., 1997; Pauly et al., 2005).
2.1.2. Impact of Natural Systems Degradation on Human Systems
Excess use of natural resources and ecosystem degradation caused by anthropogenic
activities have impacted human systems as well. Water shortages, air pollution, and excess of water

4

borne and respiratory diseases are just some examples of the impacts of natural systems
degradation on human health (Stikker, 1998; Kampa and Castanas, 2008; U.S. EPA, 2017a).
Climate change impacts on water resources and high demand for limited freshwater have
made water shortages and water crises some of the main concerns of the 21st century (Saeijs and
Berkel, 1995; Stikker, 1998). Almost a billion people around the word do not have access to clean
drinking water, and more than two billion do not have proper sanitation facilities (WHO/UNICEF,
2008). Besides that, surges in use of fertilizers and pesticides threaten human health by polluting
freshwater resources (Novotny, 1999). Stomach cancer in adults and methemoglobinemia in
infants are just two examples of health problems associated with polluted water from agricultural
practices (Almasri and Kaluarachchi, 2004). Water contamination also leads to widespread waterborne diseases caused by pathogenic microorganisms that exist in polluted water (Grabow, 1996).
Cholera, Diarrhea, Hepatitis, Malaria, and SARS are just some out of many water-borne diseases
that can be spread by polluted water (Lenntech, 2017). According to the World Health
Organization (WHO), water-borne diseases kill more than three million (mostly children) every
year (WHO, 2017).
Human activities have polluted air as well as water. Excess use of fossil fuels increase
GHGs that not only cause global warming but also are harmful for human health (Ramanathan and
Feng, 2009). Carbon monoxide, sulfur dioxide, nitrogen oxides and ozone are just some of the air
pollutants generated as byproducts of fossil fuels combustion that cause health issues such as
respiratory irritation, respiratory infection, bronchitis, heart disease and lung cancer (Kampa and
Castanas, 2008). According to the WHO report, air pollution is the cause of almost 7 million annual
premature deaths in the world (WHO, 2017).

5

2.1.3. The Concept of Environmental Justice
The mutual interactions of human and natural systems are dynamic and vary spatially
among different organizational units (Liu et al., 2007a). In other words, impacts of degraded
environments are not proportionally distributed among different groups, while some communities
such as low-income people, minorities and people of color are usually more affected than others,
which is called environmental inequality (Downey and Liam, 2008). According to the U.S.
Environmental Protection Agency (U.S. EPA) report, hazardous facilities and industrial wastes are
mostly located near poor and minority neighborhoods (Massey, 2004). The concern of
environmental inequality raised movements in 1980s that resulted in the Environmental Justice
executive order signed by President Clinton in 1994. The U.S. EPA interpreted the Civil Rights
Act of 1964 to extent to cover the concept of Environmental Justice, which means that fair
treatment and significant participation of all people regardless of their race, ethnicity, income, or
national origin with respect to the environmental law, regulations and policies (U.S. EPA, 2017b).
In other words, it means all people must have equal access to healthy environment (e.g. clean air
and clean water) and the right of being actively involved in environmental policy making.
2.2. Water Resources Assessment
The concept of water resources assessment that includes both water quantity and quality
evaluates the impact of human activities and excess in freshwater consumption on waterbodies
integrity (GWP, 2013). Population growth and excess demand for limited available water
resources raised concerns about water resources management in the late twentieth century. Back
in 1965, the United Nations Educational, Scientific and Cultural Organization (UNESCO) started
a worldwide program called the International Hydrological Decade (IHD) in order to raise
awareness on the importance of the hydrological cycle’s study that enhanced the field of hydrology

6

as a professional research area (Miloradov and Marjanovic, 1998). By the end of IHD in 1975,
UNESCO started a global educational program called the International Hydrological Program
(IHP) to address problems associated with excess water resources consumption (Miloradov and
Marjanovic, 1998). In 1977, the IHP objectives were targeted to address conservation of water
resources, in which water resources assessment was defined in order to pursue water resources
management (Miloradov and Marjanovic, 1998). Water resources must be assessed for many
reasons including water demand analysis, environmental and social impacts, and risk analysis of
sustainable water resources (SSWM, 2016).

According to the International Glossary of

Hydrology, water resources assessment is defined as the “determination of the sources, extent,
dependability and quality of water resources for their utilization and control” (UNESCO/WMO,
2012). For this purpose, hydrological data including water quantity and water quality and
physiographical data including topography, river network, land use and soil must be collected.
Statistical analysis is required to cover missing or out dated data. These data must be transferred
into information and assessed by decision makers for both short term and long-term water
resources management and policy making (SSWM, 2016).
2.2.1. Water Quality Assessment
Three classes of physical, chemical, and biological characteristics are being used to assess
waterbodies including rivers, lakes and groundwater (Chapman, 1996). Physical characteristics
such as stream meandering, depth, and slope affect water movement, while chemical
characteristics such as acidity, dissolved solids, oxygen and nutrient contents represent water
pollution status. Finally, biological characteristics such as abundance and integrity of instream
organisms are being used to evaluate the responses of aquatic ecosystems to water quality. Based
on these three criteria, water quality assessment is defined as “the overall process of evaluation of

7

the physical, chemical and biological nature of water in relation to natural quality, human effects
and intended uses, particularly uses which may affect human health and the health of the aquatic
system itself” (Chapman, 1996). However, more attention was placed on chemical evaluation
compared to the two other aspects of water quality assessment and early studies have mainly
focused on chemical evaluation (U.S. EPA, 2006; Abbasi and Abbasi, 2012).
2.2.1.1. Clean Water Act
Due to public awareness and concerns raised for waterbodies pollution, the first water
regulatory amendment called Clean Water Act (CWA) was established in 1972 in order to regulate
pollution discharge to waterbodies (U.S. EPA, 2016). It is the first environmental law enforcement
that authorized by the U.S. EPA to implement pollution control programs.
The National Pollutant Discharge Elimination System (NPDES) is part of the CWA that
limits point source pollution discharge (such as pollution discharge from pipes or ditches) to the
nation’s water (U.S. EPA, 2017c). There are ten regional offices established by U.S. EPA around
the nation that work with local governments to enforce the NPDES program. Under the NPDES
program, any point source pollutant discharge requires a NPDES permit that limits the amount and
type of pollutant released and enforces follow up monitoring and reporting to make sure that
discharged pollutants are not affecting water quality (U.S. EPA, 2017c).
Under the CWA, the U.S. EPA has also developed water quality standards for states,
territories and tribes in order to define desired waterbody condition, required protection, and
planning to reach desired conditions for each water body (U.S. EPA, 2014a). These standards
empower the U.S. EPA to eliminate pollutant discharge from sources such as industrial sites, sewer
systems, and water treatment plants to waterbodies, unless four major issues of 1) designated use,

8

2) criteria, 3) antidegradation requirements, and 4) general policies have been addressed (U.S.
EPA, 2014a).
1) Designated use: Federal and state agencies should define the purpose and amount of water
that must be allocated for designated uses such as drinking water supply, recreation, and
fisheries and wildlife protection.
2) Criteria: Water quality criteria defined by states, territories, and tribes limit the amount of
pollutant release to designated waterbodies and must be followed by agencies.
3) Antidegradation requirements: The framework provided by agencies to protect and
maintain waterbodies by designated use and defined criteria.
4) General policies: States, territories and tribes can adopt policies in term of local water
quality standards. These policies must be approved by the U.S. EPA before
implementation.
2.2.1.2. Total Maximum Daily Load
Under the section 303(d) of the CWA, all states, tribes and territories must monitor
waterbody status and provide a list of waterbodies that do not meet water quality standards (called
impaired), or are at risk of being impaired in future (called threatened) (U.S. EPA, 2017d).
Impaired and threatened waterbodies must be prioritized and the threshold for pollutant discharge
to them should be defined by agencies. Therefore, the Total Maximum Daily Load (TMDL) is
defined as the maximum allowed discharge amount of each pollutant to a waterbody on a daily
basis, while meeting water quality standards with respect to that pollutant (U.S. EPA, 2015a).
Figure 1 shows how TMDL will be incorporated to reach water quality standards.

9

Figure 1. TMDL implication in the CWA (U.S. EPA, 2017d)
TMDLs are defined for each waterbody/pollutant combination as sums of waste load
allocation from point sources (WLA), load allocation from natural background and other non-point
sources (LA), and margin of safety (MOS) that considers uncertainty of prediction and will be
calculated as follows (U.S. EPA, 2015a):
TMDL = ∑ WLA + ∑ LA + MOS

(1)

Defined TMDL by agencies must be approved by U.S. EPA before implementation.
NPDES permits are required to address WLA, while voluntary or statewide projects funded by
U.S. EPA aim to reduce LA from non-point sources (U.S. EPA, 2015a). The EPA also enforces
states to monitor TMDL implementation and monitoring of impaired and threatened waterbodies
status every two years until they reach desired water quality standards.
2.2.1.3. National Water Quality Assessment Program
In order to provide a reliable nationwide baseline for water quality assessment, in 1991 the
U.S. Geological Survey (USGS) developed the National Water Quality Assessment (NAWQA)
program. The four major objectives of this program were: 1) evaluating the current health status
of waterbodies including streams, lakes, and groundwater around the U.S., 2) monitoring long10

term water quality variation 3) assessing the role of natural stressors and anthropogenic activities
on waterbodies, and 4) finding the most vulnerable areas in terms of water quality (USGS, 2014).
The NAWQA program requires durable and comprehensive data collection that can be used for
initial assessments and further analysis. These data must represent the hydrology and chemistry of
surface water and groundwater, stream ecology and land use changes over time (USGS, 2014).
The first decade of the NAWQA program implementation (from 1991 to 2001) was focused on
the first objective. For this purpose, water quality assessment was performed for 51 major river
basins within the U.S. that resulted in baseline development for assessment of drinking water and
aquatic ecosystem health, and resource management (Hamilton et al., 2008). The second decade
of the NAWQA program implementation (from 2001 to 2012) was mostly focused on the second
and third objectives that aimed to monitor the trend of water quality change over time and evaluate
the response of waterbodies to natural and human stressors. Assessing responses of aquatic
ecosystems to agrichemicals, nutrient enrichment and urbanization were some of the major
concerns that were considered in this period (USGS, 2014). The NAWQA program is currently in
the process for the third decade (from 2013 to 2023) that aims to maintain the program’s integrity
and meet stakeholders’ demands while resources are facing degradation (National Research
Council, 2012).
2.2.2. Modeling Approaches Used for Water Resources Assessment
Water resources assessment requires continuous data collection and data validation. For
this purpose, widespread monitoring sites must be implemented and maintained for the long-term
that is a costly and challenging endeavor. For instance, study units for NAWQA were reduced
from 51 to 42 in the program’s second decade (from 2001 to 2012) and one of the main concerns
of the current program running for the third decade (from 2013 to 2023) is to maintain the program

11

while reducing associated costs (USGS, 2014). It is also impossible to perform monitoring for all
waterbodies within the current and predict possible future scenarios, which is why modeling has
been widely used to perform long term and wide-spread assessment of water resources, and to
predict their response to possible upcoming conditions.
2.2.2.1. Soil and Water Assessment Tool
The Soil and Water Assessment Tool (SWAT) is a physically based and semi-distributed
watershed model developed by U.S. Department of Agriculture (USDA) – Agricultural Research
Service (ARS) (Gassman et al., 2007). SWAT uses topographic and river network data to divide
the watershed into smaller sections called subwatersheds. Each subwatershed is then divided into
unique Hydrological Response Units (HRUs) based on land use, soil, and slope variation within
the subwatershed; each HRU will be considered as a homogenous cell for further analysis (Neitsch
et al., 2011). Each subwatershed contains a single reach/stream segment that is connected to the
tributary channel passing through the watershed and draining into the outlet (Arnold et al., 2012).
SWAT models are able to: 1) simulate water quantity and water quality parameters for each
stream segment on a daily or sub-daily basis, 2) route it to the stream network, and 3) deliver it to
the watershed outlet. SWAT is also able to assess long-term impacts of agricultural management
practices on surface runoff, sediment, nutrients (nitrogen and phosphorus), pesticides, and bacteria
yields at the watershed scale (Neitsch et al., 2011). The ArcGIS version of SWAT, called
ArcSWAT, provides a graphical user interface for SWAT that made it user friendly. SWAT is one
of the most widely used water resources assessment models and so far has been used in more than
2000 peer-reviewed articles (SWAT Literature Database, 2017).

12

2.2.2.2. System for Urban Stormwater Treatment and Analysis Integration
System for Urban Stormwater Treatment and Analysis Integration (SUSTAIN) is a
decision support system developed by U.S. EPA to assess performance of Best Management
Practices (BMPs) implementation on runoff and pollution regulation (Lee et al., 2012). SUSTAIN
is able to assess 1) effectiveness of different BMPs for surface runoff and associated pollutants
mitigation, 2) cost-effectiveness of proposed approaches to achieve desired water quantity and
water quality standards, and 3) proper size and location of BMPs to meet these goals (U.S. EPA,
2014b).
SUSTAIN can simulate various types of BMPs implementation to control either point
source or non-point source pollutants release that make it suitable for hydrology and water quality
assessment of both urban and non-urban systems (U.S. EPA, 2014b). Considering both
environmental and economic aspects of BMPs implementation scenarios, SUSTAIN provides a
unique tool for water resources policy makers to meet water quality standards and maintain
sustainable water resources (U.S. EPA, 2014b).
2.2.2.3. Hydrologic Simulation Program-Fortran
The Hydrologic Simulation Program-Fortran (HSPF) is an integrated hydrologic model
developed by U.S. EPA for watershed scale water quantity and water quality assessment (U.S.
EPA, 2015b). It has been developed on top of three former U.S. EPA models including Hydrocomp
Simulation Program (HSP), Agricultural Runoff Management (ARM), and the Non-Point Source
(NPS) pollutant loading that can simulate one-dimensional runoff as well as fate and transport of
pollutants released from various land uses into streams, lakes, and well-mixed reservoirs (Duda et
al., 2012). HSPF is able to provide continuous time series of simulated hydrologic cycle

13

components, temperature, sediment yield and removal, dissolved oxygen, nutrients cycle, and
pesticide processes (Duda et al., 2012).
HSPF is a stand-alone program that can be integrated into the BASINS (Better Assessment
Science Integrating point and Nonpoint Source) platform through a Windows interface called
WinHSPF (Duda et al., 2001). Integrated HPSF and BASINS provides a unique tool for TMDL
assessment and water quality criteria development at the watershed level (U.S. EPA, 2015b).
2.2.2.4. Storm Water Management Model
The Storm Water Management Model (SWMM) is a coupled hydrology-hydraulic water
quality model developed by U.S. EPA to simulate stormwater runoff and its routing through urban
drainage systems (U.S. EPA, 2014c). SWMM is able to simulate long-term continuous storm
events and the quantity and quality of associated runoff. For this purpose, SWMM divides the
region or catchment to smaller homogeneous regions called sub-catchments that produce surface
runoff from precipitation falling within the sub-catchment. Surface runoff and associated pollutant
loads will be routed through the urban sewage system that includes series of pipes, channels,
storage and regulatory facilities (Rossman, 2015). SWMM generates time series of runoff quantity
and quality passing through the drainage system that provides a useful tool for stormwater
management design and planning (U.S. EPA, 2014c).
SWMM is able to assess the performance of some Low Impact Development (LID)
controls such as rain gardens, vegetative swales, and green roofs on urban sewage system
(Rossman, 2015). It enables water resources decision makers to design drainage systems that are
suitable for flood control (U.S. EPA, 2014c). SWMM has also been equipped with Climate
Adjustment Tool (SWMM-CAT) that enables it to simulate storm events under future climate
scenarios (Rossman, 2014).

14

2.2.2.5. Hydrologic Engineering Center - Hydrologic Modeling System
The Hydrologic Modeling System developed by Hydrologic Engineering Center of the
U.S. Army Corp of Engineers (HEC-HMS) is a hydrologic model that simulates precipitationrunoff process in dendritic watersheds (Scharffenberg, 2016). It is capable of using several
alternative mathematical models for each part of hydrologic cycle that make it suitable for
simulation in different topographic conditions ranging from large river basins to small urban
watersheds (Scharffenberg, 2016). HEC-HMS is a comprehensive hydrologic model that can be
used for optimization, forecasting, sediment transport and water quality studies (Hydrologic
Engineering Center, 2016).
HEC-HMS uses an integrated system that includes database, computations, and reporting
frameworks. Model outputs will be stored in Data Storage System (HEC-DSS) that make them
accessible for being used with other software for further studies and comparisons (Hydrologic
Engineering Center, 2016).
Table 1 summarizes the five models discussed for water resources management, and
compares their applicability for different case studies as follows:

15

Table 1. Summary of common modeling tools used for water resources assessment
Modeling tool
SWAT

Modeling type
Physically based,
and semidistributed
watershed model

Application
Assessing long-term impacts of
agricultural management practices on
surface runoff, sediment, nutrients,
pesticides, and bacteria yields at the
watershed scale

Major Outputs
Daily and sub-daily
water quantity and
water quality
parameters

SUSTAIN

Coupled
hydrologyhydraulic water
quality model

Decision support system to assess
performance of BMPs implementation
on runoff and pollution regulation

Suitable places for
BMPs
implementation

HSPF

Integrated
hydrological
model

Assessing the impact of land-use change,
point and nonpoint source treatments,
and flow alteration on the water quantity
and water quality at the watershed scale

Daily and sub-daily
streamflow
hydrographs and
pollutographs

SWMM

Coupled
hydrologyhydraulic water
quality model

Evaluating performance of LID controls
on urban sewage systems

Continuous water
quantity and water
quality of storm
events runoff

HEC-HMS

Hydrologic
model

Optimization, forecasting, sediment
transport, and water quality simulation of
dendritic watersheds

Precipitation-runoff
process

2.3. Stream Health and Biological Integrity Assessment
A healthy stream is defined based on a combination of physical, chemical, and biological
conditions, while chemical criteria is the most common approach for stream health assessment
(Karr, 1981; Karr et al., 1986; Herman and Nejadhashemi, 2015). In order to assess the
effectiveness of chemical criteria for stream health assessment, the U.S. EPA performed a
nationwide evaluation of biological and recreational status of riverine ecosystems in summer 2008
to 2009. They performed assessments for almost two thousands streams with accumulative of more
than a million miles to ensure covering all forms of riverine ecosystems (U.S. EPA, 2015c). They
found that despite all regulations (such as CWA and TMDL) implemented, almost half of
monitored streams are still in poor biological condition, while only twenty eight percent of streams

16

were in good condition and the rest were in fair condition (U.S. EPA, 2015c). In other words,
implemented regulations have not addressed water quality concerns while all physical, chemical,
and biological conditions must be evaluated in order to perform overall stream health assessment.
So, the concept of biological integrity assessment was introduced in order to evaluate the final
impact of the combination of physical, chemical, and biological activities on aquatic ecosystems
(NSCEP, 2011; U.S. EPA, 2015c). It is also called the gold standard in water quality assessment
since it measures the response of aquatic species as endpoints in riverine ecosystems to pollutants
(Karr and Yoder, 2004; Woznicki, 2015).
2.3.1. Stream Health Indices and Metrics
Biological metrics are defined to quantify aquatic ecosystem conditions. These metrics
enable stream ecologists to develop stream health indices that can be used for biological integrity
assessment (Herman and Nejadhashemi, 2015). Biological metrics quantify 1) species abundance
and condition, 2) species richness and composition, and 3) species trophic composition (Van Hoey
et al., 2007; Herman and Nejadhashemi, 2015).
Species abundance and condition metrics are developed to quantify the number of collected
species and their status, representing what percentage of collected species are healthy, damaged or
have diseases (Karr et al., 1986). While species richness and composition metrics are qualitative
measures of species diversity and distribution in a region (Karr et al., 1986). In general, streams
with more diverse species have better stream health conditions than streams with limited species
due to harsh environments that exist in those streams (Wan et al., 2010). The third group of metrics
called species trophic composition, use the nutrients transfer among different functional feeding
groups of riverine ecosystems for stream health assessment (Herman and Nejadhashemi, 2015).
Nutrients level variation directly impacts the food chain of instream species; therefore, assessing

17

distribution of functional feeding groups represents the chemical status of aquatic ecosystem
(Smith et al., 2007).
Stream health indices developed based on biological metrics are divided into two major
groups of 1) biotic, and 2) multi-metric indices (Herman and Nejadhashemi, 2015). Biotic indices
also called uni-metric indices, only measure one metric for stream health assessment. The major
application of biotic indices is to evaluate the impact of organic pollutants on instream organisms
(Hilsenhoff, 1987; Ollis et al., 2006). The calculation of these indices is simple which makes them
suitable for local stream health assessment. The Hilsenhoff Biotic Index (HBI) is one of the popular
biotic indices used to evaluate response of macroinvertebrate indices to organic pollutants
(Hilsenhoff, 1987). However, biotic indices do not consider other forms of instream pollutants
(such as sediment, nitrogen, and phosphorus). Therefore, multi-metric indices have been
developed in order to provide more comprehensive assessment of complex riverine ecosystems
(Herman and Nejadhashemi, 2015).
Compared to biotic indices, multi-metric indices are able to assess the response of aquatic
ecosystems to several stressors at the same time; however, their calculation is more complex than
biotic indices (Fierro et al., 2017). The Index of Biotic Integrity (IBI) and Benthic Index of Biotic
Integrity (B-IBI) are two major multi-metric indices that are developed from several metrics to
provide comprehensive assessment of fish and macroinvertebrates communities, respectively
(Karr, 1981; Kerans and Karr, 1994). The Ephemeroptera, Plecoptera, and Trichoptera (EPT)
index is another common multi-metric index that evaluates comprehensive responses of three
macroinvertebrates including Ephemeroptera (mayflies), Plecoptera (stoneflies), and Trichoptera
(caddisflies) to organic pollutants (Lenat, 1988).

18

There is another group of stream health measures called multivariate indices that unlike
biotic and multi-metric indices, uses modeling approaches instead of metrics for stream health
assessment. Multivariate indices use physical and chemical characteristic of waterbodies to
develop predictive models for aquatic ecosystem status (Reynoldson et al., 1995). The Australian
River Assessment Scheme (AusRivAS), and River Invertebrate Prediction and Classification
System (RIVPACS) are two common multivariate models developed for stream health assessment
(Reynoldson et al., 1997; Fierro et al., 2017). Multivariate indices development requires modeling
processes and model calibration that make them more complicated than metric based indices;
however, multivariate indices can be easily applied for large scale assessments since they are not
limited to sampling stations (Herman and Nejadhashemi, 2015). Table 2 summarizes different
types of stream health indices and their specifications.
Table 2. Comparison of stream health indices (Fierro et al., 2017)
Advantages

Biotic indices
easy calculation, good
for local assessment

Stream health assessment indices
Multi-metric indices
Multivariate indices
providing
good for large-scale
comprehensive
assessment beyond
assessment
monitoring sites

Disadvantages

limited to organic
pollutants and cannot
evaluate response to
sediment and nutrients
pollutants

requires several metrics
for index development,
limited by requirements
of all used metrics

Commonly used

Hilsenhoff Biotic
Index (HBI),
Biological Monitoring
Working Party Index
(BMWP)

Index of Biotic
Integrity (IBI),
Benthic Index of
Biotic Integrity (BIBI)

complicated model
development and
calibration processes,
sensitive to model inputs

Australian River Assessment
Scheme (AusRivAS), River
Invertebrate Prediction and
Classification System
(RIVPACS)

2.3.1.1.Fish Indices
Fish characteristics are representative of water quality status and are widely used for stream
health assessment (Karr, 1981; Carlisle et al., 2013). Unlike many other instream species, fish
19

exists in many trophic levels (e.g. omnivores, and herbivores) and can be found in the most
waterbodies (Karr, 1981). Besides that, fish are representative of a wide range of instream stressors
since their wellbeing is connected to various aquatic species (Karr, 1981; Barbour et al., 1999).
All these characteristics make fish a suitable representative of stream health status and fish indices
development (Herman and Nejadhashemi, 2015).
Fish indices are commonly used for large scale and long-term assessments since fish can
move through the entire waterbody and will be affected by both spatial and temporal aquatic
stressors (Barbour et al., 1999; Herman and Nejadhashemi, 2015). Fish indices also represent the
response of aquatic ecosystems to flow altering structures (e.g. dams) since fish are highly
sensitive to flow variation (Navarro-LlĂĄcer et al., 2010). Several fish indices including biotic
indices (e.g., fish species biotic index, and fish response curves), multi-metric indices (e.g. index
of biotic integrity, fish community index, and similarity index), and multivariate indices (e.g.
stressor gradients) are being used for stream health assessment (Karr, 1981; Paller et al., 1996;
Jordan et al., 2010; Angradi et al., 2009; Navarro-LlĂĄcer et al., 2010; Zorn et al., 2012; Herman
and Nejadhashemi, 2015). Among those, the IBI (Index of Biotic Integrity) that has been
developed based on 12 metrics, is the most commonly used fish index for overall stream health
assessment (Karr, 1981; Herman and Nejadhashemi, 2015). The IBI provides comprehensive fish
assessment based on species richness, abundance, and trophic composition and reports overall
stream health scores ranging from zero to 60 (Karr et al., 1981; Hu et al., 2007; Herman and
Nejadhashemi, 2015). One of the most recent forms of IBI index implementation is the Fish-Based
Index (FBI) that uses 15 metrics instead of 12 and is suitable for detecting degraded waterbodies
(Launois et al., 2011). This new index ranges from zero to 100, where 100 represents excellent
status (Herman and Nejadhashemi, 2015).

20

2.3.1.2. Macroinvertebrate Indices
Macroinvertebrates are another group of instream species that are used for stream health
assessment and several indices have been developed that utilize their communities. Unlike fish,
macroinvertebrates have limited mobility that make them suitable for local assessment (Kerans
and Karr, 1994). Besides that, macroinvertebrates are highly sensitive to slight instream alterations
that make them valuable indicators of early stage degradation of water quality (Compin and
CĂŠrĂŠghino, 2003). These unique characteristics require different indices to be developed for
various stream types. So far, more than 40 macroinvertebrate indices have been developed. Among
those, three indices including one biotic index (Hilsenhoff Biotic Index (HBI)), and two multimetric indices (Benthic Index of Biotic Integrity (B-IBI), and Ephemeroptera, Plecoptera,
Trichoptera (EPT) Index) are the most commonly used (Herman and Nejadhashemi, 2015). Table
3 summarizes these indices specifications and measurement criteria.
Table 3. Commonly used macroinvertebrate indices (Herman and Nejadhashemi, 2015)

*

Index
name
HBI

Score range
(min – max)
10 – 0

Measurement

Application

quantifies dissolved
oxygen level

evaluates chemical degradation
of stream with focus on organic
pollutants

B-IBI

0 – 65

uses 13 metrics to
quantify organism
communities based on
taxa richness,
composition, and aquatic
ecosystem

assesses industrial degradation to
riverine ecosystem, measures
response of aquatic ecosystem to
watershed management scenarios

EPT

0–
maximum*

quantifies richness and
abundance of mayflies,
stoneflies, and caddisflies

early detection of locally
impacted regions with organic
pollutants. Applicable for wide
range of streams

Maximum EPT score is defined based on the study area

21

2.3.1.3. Sampling Survey
In-stream sampling of fish and macroinvertebrate species is required to develop metrics
and indices. Depending on the stream size and type (e.g. headwater, or large rivers), different
species exist and require different techniques and equipment for sampling (Vannote et al., 1980;
Butcher et al., 2003). The U.S. EPA proposed a classification for aquatic species sampling, which
divides waterbodies to two major groups: wadeable and non-wadeable (U.S. EPA, 2006).
Wadeable waterbodies are those that are shallow enough to be sampled by samplers
walking through them (U.S. EPA, 2006). Almost 90% of nation’s streams fall in this category; that
makes them the main focus of the U.S. EPA oversight (U.S. EPA, 2006). Regarding
macroinvertebrate sampling in wadeable waterbodies, methods such as: surbers, hesses, D-frame
dip nets, rectangular dip nets, and kick nets are proposed that can collect instream species in depths
less than one meter (Plakfin et al., 1989). Among those, kick nets are the most commonly used
method. The standard recommended mesh size by the U.S. EPA for macroinvertebrates sampling
is 500 Âľ; however, it can vary depending on the sampling site location (U.S. EPA, 2012). The
major drawback of this method is that it is only able to collect samples from the streambed at
transects (Blocksom and Flotemersch, 2005). To overcome this issue, several samplings along the
transects are recommended. Regarding fish, electrofishing is the most common approach in
wadeable waterbodies (Terra et al., 2013). In this method, an electric current is used to stun fish
that must be collected (Plakfin et al., 1989). A major limitation of this method is that it does not
consider seasonal variations in fish populations (Roset et al., 2007). To address this issue, several
samplings in different times of the year is recommended (Herman and Nejadhashemi, 2015).
Unlike wadeable waterbodies, non-wadeable waterbodies cannot be accessed by walking
sampling and require the use of a boat (U.S. EPA, 2006). Large rivers, lakes, and coastal regions

22

fall in this category (Herman and Nejadhashemi, 2015). Regarding the macroinvertebrates, drift
nets and multi-plate samplers are commonly used in deep regions, while wadeable methods will
be used for the edges (Blocksom and Flotemersch, 2005). Regarding the fish, electrofishing
conducted on boat is a common approach in deep rivers, while trawling nets is recommended for
deep lakes and coastal regions (Esselman et al., 2013).
2.3.2. Modeling Used for Biological Integrity Assessment
It is impossible to exhaustively sample the biological integrity of the entire riverine
ecosystem. One approach for performing overall assessment is using probability-based (or
random) sampling in which a few streams will be surveyed in a way that represents the entire
riverine ecosystem (Larsen, 1997; U.S. EPA, 2006). Modeling is another approach and
ecohydrological models are developed in order to evaluate aquatic health beyond sampling stations
(Woznicki et al., 2016a).
2.3.2.1. Physical Habitat Simulation Model
The Physical Habitat Simulation Model (PHABSIM) was developed by the USGS in order
to assess the response of aquatic ecosystems to anthropogenic activities. For this purpose,
PHABSIM simulates physical microhabitat changes as a function of streamflow variations
(Milhous et al., 1984). It assumes that flow-dependent microhabitat structures are representative
of the stream health and any alteration of physical microhabitats directly impacts health status of
instream species such as fish and macroinvertebrates (Waddle, 2001).
PHABSIM only uses physical characteristics (e.g. velocity, depth, and bathymetry) and
does not consider water quality components (e.g. temperature) and energy input (e.g. nutrients)
(Milhous et al., 1984; Wu et al., 2006). One of the most common parameters calculated by
PHABSIM is the Weighted Usable Area (WUA) that measures the density of microhabitats in a

23

defined length of stream. WUA is known as well representative of both quantity and quality of
microhabitats and can be used for further aquatic ecosystems health assessment (Milhous et al.,
1984).
2.3.2.2. AQUATOX
AQUATOX is a biophysical model developed by the U.S. EPA to assess the impact of
nutrients and toxic organic chemicals on aquatic ecosystems and is one of the most comprehensive
risk assessment models. It can simulate fate of up to twenty organic chemicals processes and their
impacts on aquatic biota (Park et al., 2008).
AQUATOX is also able to provide uncertainty analysis and ranges of possible scenarios
that make it suitable for ecological risk assessment of aquatic ecosystems (U.S. EPA, 2014d).
Developed models are applicable for streams, lakes, ponds, and reservoirs. AQUATOX models
can also be linked to SWAT and HSPF in order to perform aquatic risk assessment at the watershed
level (Park et al., 2008).
2.3.2.3. Ecological Limits of Hydrologic Alteration
Anthropogenic activities have altered flow regimes that not only degraded aquatic
ecosystems, but also impaired human wellbeing (Dyson et al., 2003). The concept of
Environmental Flow is defined in order to describe the minimum threshold of water quantity and
timing needed to sustain aquatic ecosystems and human wellbeing at the same time (O Keeffe et
al., 2012). The traditional approach was assessment of each individual stream in order to meet the
minimum flow requirement. However, a holistic approach is needed in order to develop largescale water resources management and planning (Le Quesne et al., 2010). Ecological Limits of
Hydrologic Alteration (ELOHA) is a comprehensive framework developed for environmental flow
assessment at the watershed, and statewide scales (Le Quesne et al., 2010).

24

ELOHA uses existing hydrological and ecological data to develop empirical equations to
assess aquatic ecosystems response to flow alteration in a defined region (Poff et al., 2010). For
this purpose, hydrologic models must be developed to predict baseline and current flow patterns
in each stream segment. Streams classification based on common features is the next step. Then
flow alteration-ecological response curves will be developed for each stream class based on current
and baseline flow patterns (Poff et al., 2010). These empirical curves not only provide a guideline
for water policy makers to find ecologically vulnerable areas, but also aids to minimize the impact
of future water development projects on aquatic ecosystems (Poff et al., 2010).
2.3.2.4. Hydrological Index Tool
The ecological integrity of riverine ecosystems highly relies on physiochemical
characteristics of streams also called “master variables” (Poff et al., 1997). These characteristics
are defined based on five major components of flow regime including 1) magnitude, 2) frequency,
3) duration, 4) timing, and 5) rate of change (Poff et al., 1997). 171 ecologically relevant
hydrological indices are introduced in order to quantify these five major components for average,
low, and high flow rates (Olden and Poff, 2003). The Hydrological Index Tool (HIT) was
developed by the USGS in order to calculate these ecologically relevant hydrological indices based
on daily and peak flow records (Henriksen et al., 2006).
HIT was originally designed to calculate ecologically relevant hydrological indices from
data collected by the USGS National Water Information System (NWIS). However, this has been
expanded beyond the USGS observation points including observed and simulated daily streamflow
datasets (Henriksen et al., 2006).

25

2.3.2.5. National Hydrologic Assessment Tool
Similar to HIT, the National Hydrologic Assessment Tool (NATHAT) was also developed
to assess ecologically relevant hydrological indices, but it uses ten hydrologic classifications
defined by Poff (1996) based on data collected from 420 monitoring sites across the United States
(Cade, 2006). NATHAT can be used for hydrologic baseline (reference time period) development,
and assessing response of riverine ecosystems to current and proposed future hydrologic
modifications (Cade, 2006). Both HIT and NATHAT are commonly used by federal, states, and
nongovernmental agencies that aim to maintain ecological integrity of aquatic ecosystems
(Henriksen et al., 2006).
2.4. Socioeconomic Assessment
Biophysical assessment is the common approach of evaluating the impact of anthropogenic
activities on the environment including land, air, water, and wildlife (Slootweg et al., 2001).
However, recent studies revealed the significance of socioeconomic assessment as well as
biophysical assessment in order to maintain sustainable environment for both human and natural
ecosystems (Environmentalist, 2014). Socioeconomic assessment is defined as evaluation of
proposed developments on socioeconomic status of individuals and communities (MVEI, 2007).
Socioeconomic status is defined based on combination of sociological and economic measures
such as income, education and social reputation (APA, 2017). These measures are usually
developed from census data. The U.S. Census Bureau (USCB) is the principal agency in the U.S.
for collecting and producing sociological and economic data.
Census data are collected every ten years, while estimations and projections are used for
years in between. Census data include population, economy, business, education, employment,
health, housing, income and poverty information that can be used for decision making in resource

26

allocation to schools, hospitals, and transportation infrastructure development (U.S. Census
Bureau, 2013). These data are collected at the census block level that is the finest level in the
geographic hierarchy (Figure 2) and are tabulated and reported in coarser geographic levels
ranging from block group to the national level (U.S. Census Bureau, 2015).

Figure 2. Geographic hierarchy of census data collection (U.S. Census Bureau, 2015)
The average block group contains 39 census blocks with a population range of 600 to 3,000
people. Aggregation of block groups result in census tract development with a population range of
1,200 to 8,000 people. County is the next level in the hierarchy; counties have varying numbers of
census tracts. Based on the USCB report, 3,144 counties are defined within the 50 states and
27

territories around the nation (U.S. Census Bureau, 2017). Nine divisions are defined on top of the
states, these divisions are grouped into four main regions of the nation including West, Midwest,
South, and Northeast (U.S. Census Bureau, 2017).
2.4.1. Socioeconomic Aspects of Environmental Justice Assessment
Uneven socioeconomic status has been an area of concern as they are growing around the
world (Boyce et al., 2007). Socioeconomic status is also known as the measure of social inequality
since its variation represents unequal distribution of resources and power (Hasenfeld, 1987).
Typically, three major socioeconomic levels are defined as 1) poor or lower class, 2) middle class,
and 3) wealthy or upper class, while more detailed classifications are also provided that include up
to twelve socioeconomic levels (Eichar, 1989; Beegle et al., 2007). However, these classifications
do not provide useful information on social and environmental inequalities (Sampson et al., 2008).
Further analysis of socioeconomic data is required in order to find socioeconomic aspects of these
inequalities. In terms of Environmental Justice, socioeconomic indicators that represent
distribution of age, race, housing, welfare, employment, and educational status of a society are
commonly used as predictors (Sampson et al., 2008). These indices are obtained from census data
collected at different spatial levels such as county, census tract, and block group.
2.4.2. Statistical Models for Socioeconomic Assessment
Socioeconomic data collected by the U.S. Census Bureau contains spatial information.
Therefore, spatial statistical modeling is used to reveal spatial dependencies that may exist among
collected data.
2.4.2.1. Structural Equation Modeling
Structural Equation Modeling (SEM) is a multivariate statistical method that combines
factor analysis and multiple regression analysis to assess structural relationships (Schumacker and

28

Lomax, 2004). Factor analysis is a statistical approach to find unobserved potential variables called
factors that can describe variability and correlation among observed data (Thompson, 2004), while
regression analysis aims to find relationships among observed variables. That makes SEM a useful
tool for researchers to consider multiple and interrelated dependencies simultaneously (Statistics
Solutions, 2017).
SEM helps social science researchers to evaluate theoretical assumptions that are
developed based on observed data and to assess how they might be affected by unmeasured
variables (Schumacker and Lomax, 2004). Additionally, SEM is a useful tool for assessing the
unreliability of conducted measurements by constructing latent variables that were not seen in data
collection, and also data reduction (Chin, 1998).
2.4.2.2. Hierarchical Linear Modeling
Hierarchical Linear Modeling (HLM) is an extension of linear regression modeling that
considers the hierarchy of nested data (Woltman et al., 2012). It can reveal the complexity of nested
multilevel data with spatial, temporal, or organizational dependencies while providing a
framework for data collected at each level (Snijders and Bosker, 2012).
HLM is useful for social science studies since socioeconomic data are nested in spatial and
temporal levels (Stevens, 2012). HLM is defined by five groups of multilevel analysis including
1) one-way analysis of variance with random effects, 2) one-way analysis of covariance with
random effects, 3) random coefficient regression model, 4) intercepts and slopes as outcome, and
5) means as outcome (Snijders and Bosker, 2012, Sanchez, 2014). HLM can be also used for either
multilevel prediction or data reduction.

29

2.4.2.3. Conditional Autoregressive Models
The Conditional Autoregressive (CAR) models are regression models in which, spatial
dependencies are taken into account for model development. For this purpose, CAR models
estimate values conditioned based on neighboring values (de Smith, 2015), which requires
implementation of a diagonal weighting matrix in regression analysis (Besag, 1974). This feature
makes CAR models suitable for areal data analysis that are required in many fields such as
demography, economy, epidemiology, and geography (Arab et al., 2008; Oliveira et al., 2012).
CAR models can also reveal spatial dependencies among data, quantify spatial variation of
parameters of interest, and detect hot spots (Oliveira et al., 2012). CAR models typically use
Bayesian frameworks in which prior distributions of parameters will be used to predict posterior
distributions (Lee, 2013; Banerjee et al., 2014).
2.4.2.4. Simultaneous Autoregressive Models
The Simultaneous Autoregressive (SAR) models are another type of autoregressive models
developed for areal data analysis (Besag, 1974). While CAR models only consider neighbor’s
effects (first-order dependency), SAR models use information of neighbors of neighbors (secondorder dependency) in model prediction as well. In other words, CAR models use defined study
area for neighborhood matrix development that makes them suitable for local spatial analysis,
while SAR models are more common for global spatial analysis (Baltagi et al., 2016). Depending
on the data set and type of study, the proper model must be selected, however in some cases both
SAR and CAR models may produce similar results (Lichstein et al., 2002; Wall, 2004). Finally, a
summary of statistical models that are commonly used in socioeconomic assessment is presented
in Table 4.

30

Table 4. Summary of common statistical models used for socioeconomic assessment
Model name
SEM

Statistical analysis
Factor analysis and multiple
regression analysis

Major application
Assessing irregularity of existing
measurements by constructing variables that
are not covered in collected data

HLM

Extension of linear regression, with
hierarchy effect of nested data

Conducting multilevel analysis of nested data
with spatial, temporal, or organizational
dependencies

CAR

Spatial auto-regression, with firstorder neighbors’ dependency

Suitable for local spatial analysis, while
revealing areal dependencies among data

SAR

Spatial auto-regression, with secondorder neighbors’ dependency

Suitable for global spatial analysis, while
revealing areal dependencies among data

31

3. INTRODUCTION TO METHODOLOGY AND RESULTS
This dissertation consists of two studies that improve the performance of stream health
based environmental justice models. The first study focuses on the role of spatial levels on
environmental justice analysis concerning stream health. The second study builds upon the first
study by improving stream health prediction and evaluates the significance of the incorporation of
more accurate stream health scores in environmental justice studies.
The first study, titled “Evaluating stream health based environmental justice model
performance at different spatial scales”, focuses on the spatial dependencies among stream health,
socioeconomic, and physiographic indices used for environmental justice studies. The Saginaw
River Basin in Michigan is selected as the study area. Four biological indices that quantify the
response of fish and macroinvertebrates to instream stressors are used for stream health
assessment. However, these indices are monitored for only a few stations; therefore, stream health
predictive models are used to evaluate these indices beyond the limited monitoring stations.
Seventeen socioeconomic and physiographic indices representing concentrated disadvantages are
used for the environmental justice assessment. These indices are collected at three census levels
of county, census tract, and block group. For each level of study, the correlation of the indices are
evaluated, and spatial data analysis are conducted to evaluate spatial dependencies among the
stream health indices and independent socioeconomic and physiographic indices. Finally,
multilevel models, in which the nested effect of data collected at different levels is also
incorporated, are developed and their performances are compared with single level models.
The second study, titled “Assessing the Relative Importance of Parameter Estimation in
Stream Health Based Environmental Justice Modeling”, uses the same datasets as are used in the
first study, while focusing on improvement of stream health prediction impacts on environmental

32

justice studies. For this purpose, ecologically relevant streamflow and water quality parameters
are used for the development of stream health predictive models, while in earlier studies, the role
of these parameters was not considered. As a result, more reliable stream health indices are
estimated within the study area. This information are then used in the development and evaluation
of the new stream health based environmental justice models. Similar modeling practices as study
one are adopted in study two in order to make the results of the two studies comparable.

33

4. EVALUATING STREAM HEALTH BASED ENVIRONMENTAL JUSTICE MODEL
PERFORMANCE AT DIFFERENT SPATIAL SCALES
4.1. Introduction
Human and natural ecosystems are interconnected and affect one another. Studies show
that human activities can substantially alter ecosystems, changing biological diversity, land
surface, and other resources that often have long-term environmental effects (Skole and Tucker,
1993; Vitousek et al., 1997, Halpern et al., 2008, Einheuser et al., 2013a). Anthropogenic activities
have changed more than one-third of land surfaces (Vitousek et al., 1997; Allan 2004). Halpern et
al. (2008) reported that no marine ecosystem has been left untouched by human activities, while
more than forty percent of these ecosystems have faced notable changes. Fresh water
contamination is one of the more apparent impacts of human interventions, which also negatively
affects human health (Smith et al., 1999; Pomati et al., 2006; Vairavamoorthy et al., 2007) through
waterborne diseases such as diarrhea, cholera, SARS, and hepatitis (Levine et al., 1990; Wu et al.,
1999; Ashbolt, 2004; Mieiro et al., 2009). Therefore, sustaining healthy streams can be beneficial
to both human and natural systems.
A healthy stream is a stream that is sustainable and resilient, while maintaining both
societal and ecological necessities (Meyer, 1997). In order to evaluate stream health conditions,
biological indicators are used to quantify the ecological integrity of river systems (Cairns et al.,
1993). In other words, biological indicators represent aquatic communities’ response to human
and natural disturbances (Barbour et al., 1999; Flinders et al., 2008). Fish and macroinvertebrates
are commonly used for the development of biological indicators (Meyer, 1997; Hering et al., 2006;
Wang et al., 2007; Walters et al., 2009; Holguin-Gonzalez et al., 2013; MuĂąoz-Mas et al., 2014).
Macroinvertebrates are used for assessing local habitat conditions due to limited mobility, while
34

fish are often used for large-scale stream health assessment because of seasonal migrations within
stream systems (Karr, 1981; Lenat, 1988; Plafkin et al., 1989; Lammert and Allan, 1999; Young
et al., 2000; Herman and Nejadhashemi, 2015).
On the contrary, unhealthy streams negatively affect ecosystem services that ultimately
influence human well-being, social health, and access to resources (Corvalan et al., 2005).
However, the level of influences are different between racial or ethnic groups, in particular
minorities and low-income communities are generally more affected (Pollock and Vittas, 1995;
Helfand and Peyton, 1999). In order to address these issues, the concept of ‘Environmental Justice’
was introduced that deals with the fair distribution of resources to all people regardless of race,
color, national origin or income (U.S. EPA, 2014e). Therefore, environmental justice by nature
deals with different elements that vary across space, time and organizational units (Picket et al.,
2005; Liu et al., 2007a; An, 2012). However, using the wrong scale can lead to the wrong decision
(Wilson et al., 1999; Silver, 2008; Maantay, 2007; Maantay and Maroko, 2009). For example,
while the census tract is the most commonly used unit in environmental justice studies (Jerret et
al., 2001; Corburn et al., 2006; Gilbert et al., 2011; Sanchez et al., 2014; Sanchez et al., 2015),
socioeconomic data are also collected at county, block group, and census block scales (U.S. Census
Bureau, 2010).
Zimmerman (1993) reported that using jurisdictional boundaries, such as counties, results
in different environmental equity results compared to non-jurisdictional boundaries, such as census
tract (Zimmerman, 1993). Fisher et al. (2006) studied air toxic pollution (point source) in the
context of environmental justice and across various spatial levels (census tract, block group, and
census block). They concluded that using census tract data is not a proper scale for a point source
pollutants study, since it assumes uniform distribution of pollutant and population among census

35

tracts, regardless of their size or shape (Fisher et al., 2006). Zou et al. (2014) used socioeconomic
data at three spatial levels (zip code, census tract and block group) in an environmental justice
study in the context of sulfur dioxide exposure. Using whites as a reference for racial inequality
analysis, they showed that not only pollutant source (e.g. industrial or vehicle) but also spatial
scale (e.g. county or census tract) affect final outcomes. For example, less exposure to pollutants
was reported at the block group level compared to the zip code and census tract levels in black
populations. In general, more reliable results were obtained at the smallest spatial scale, which was
block group (Maantay, 2007). Apart from that, Arcaya et al. (2012) showed that considering
multilevel dependency between the U.S. life dataset of 1999 at different scales (county, state, and
region) improved projection of the life expectancy pattern (Arcaya et al., 2012).
The goal of this study is to evaluate the effects of spatial data resolution on environmental
justice analysis with respect to stream health integrity. We hypothesis that the environmental
justice analysis using socioeconomic data at the block group level is the most reliable and will
capture more spatial dependency between socioeconomic and environmental (stream health)
parameters compare to census tract and county levels. We also hypothesis that considering
multilevel dependency between socioeconomic data may improve the predictably of the
environmental justice models. This study is unique since to the best of knowledge no study has
considered both the effects of socioeconomic spatial resolutions and multilevel interactions in the
context of stream health. The specific objectives are to: a) measure the degree of dependency
between stream health indicators and control parameters across the three spatial scales (county,
census tract, and block group); b) understand the spatial dependency at the three levels and among
stream health indicators and control parameters using regression analysis; and c) evaluate the
importance of multilevel analysis in improving the environmental justice model predictability.

36

4.2. Methodology
4.2.1. Study Area
The study area is the Saginaw River Basin, the largest six-digit hydrologic unit located in
Michigan. Each hydrologic unit is identified by a unique hydrologic unit code (HUC). The HUC
for the Saginaw River Basin is 040802. The study area contains six hydrologic units Tittabawassee
(04080201), Pine (04080202), Shiawassee (04080203), Flint (04080204), Cass (04080205) and
Saginaw (04080206), which drains to the Lake Huron (Figure 3). The size of study area is 16,120
square kilometers. Approximately, half of the study area is agricultural land, mostly covered by
corn and soybean, 25% is forestlands, while developed areas, wetlands, rangeland, and surface
water cover the rest.

Figure 3. Saginaw River Basin
Increase in soil erosion, contaminated sediment, and nutrients, has degraded aquatic life
and recreational values in the study area to the extent that the U.S. Environmental Protection

37

Agency (EPA) has identified the Saginaw River as an area of concern in the Great Lakes basin
(U.S. EPA, 2015d).
4.2.2. Stream Health Indicators
In order to evaluate stream health, four biological indicators, which represent
macroinvertebrates and fish abundance, were used in this study (Karr, 1981; Lenat, 1988;
Hilsenhoff, 1987; Lyons 1992; Kerans and Karr, 1994; Sponseller et al., 2001; Infante et al., 2008;
Einheuser et al., 2012; Einheuser et al., 2013b). The first indicator is the Index of Biotic Integrity
(IBI); it describes a series of fish measures such as species richness and composition, trophic
composition, abundance and condition that are evaluated by a numeric score that ranges from 0 to
100 (Karr, 1981; Kerans and Karr, 1994, Herman and Nejadhashemi, 2015). The lower scores
represent high level of stream disturbance and vice versa. The Hilsenhoff Biotic Index (HBI) is a
common macroinvertebrate indicator, which represents tolerance values of organic pollution
within different species. It is varied from 0 to 10, where 10 suggests very poor water quality and
0 represents an excellent water quality in terms of organic pollution (Hilsenhoff, 1987). The next
macroinvertebrate indicator is the Family-level Index of Biological Integrity (FIBI), which relates
the composition of species in a family taxonomic resolution to pollution tolerance, ranging from 0
to 45 (Woznicki et al., 2015). For this index, higher values represent better stream health
conditions. Ephemeroptera (mayflies), Plecoptera (stoneflies), and Trichoptera (caddisflies), also
known as EPT taxa, are orders that are sensitive to degradation and commonly used in
bioassessment. EPT scores below three will be considered as very poor stream health conditions
and scores above 10 will be classified as excellent (Woznicki et al., 2015).
Fish monitoring was performed in 193 monitoring sites from 1982 to 2007, while
macroinvertebrate were monitored between 1996 to 2003 for 262 sites within the study area

38

(MDEQ 1997; Seelbach and Wiley, 1997). Electrofishing techniques such as backpack, tow-barge
and boom units were used for fish sampling in the field (Seelbach and Wiley, 1997). While
sampling methods such as hand picking and dip nets were used to obtain about 300Âą60 organism
within the minimum 20 min for each site for macroinvertebrates (Einheuser et al., 2012). The
ranges of the four indices recorded within the study area are summarized in Table 5.
Table 5. Summary of stream health measures in Saginaw River Basin
Variable
IBI
HBI
FIBI
EPT

Min
0
3.61
0
0

Max
100
7.89
36
17

Using the Soil and Water Assessment Tool (SWAT) and Adaptive Neuro Fuzzy Inference
System (ANFIS) a predictive model was developed to calculate stream health indicators
throughout the study area (Einheuser et al., 2012; Einheuser et al., 2013a). The current stream
health conditions based on the four biological indicators for the 13,831 stream segments are
presented in Figure 4.

39

Figure 4. Stream health condition across Saginaw River Basin: (a) IBI, (b) HBI, (c) FIBI, and
(d) EPT (adapted from Einheuser et al., 2012; 2013a).
4.2.3. Socioeconomic and Physiographic Indicators
From numerous reported socioeconomic measures, 16 indicators were selected in this study
(Table 6). These indicators were selected since they have been widely used in many environmental
justice researches and represent concentrated disadvantage (Bowen et al., 1995; Bowen, 2002,
Taquino et al., 2002, Brulle and Pellow, 2006, Bullard et al., 2008, Sampson et. al. 2008; Lin and
Morefield, 2011, Malley et al., 2012). Selected indicators represent population (S2 and S3),
household composition (S4, S5, S8, S9), racial composition of household (S6), female-headed
households (S7), housing (S10, S11), educational disadvantage (S12), economic disadvantage
(poverty) (S13, S14, S15), welfare receipt (S16) and unemployment (S17). These indicators were
40

obtained from the U.S. Census Bureau for three census levels of county, census tract, and block
groups (U.S. Census Bureau, 2010).
Table 6. List of the socioeconomic/physiographic indicators (Census bureau, 2010)
ID
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
S17

Socioeconomic/physiographic indicators
Drainage density
Population density (per sq. mile)
Percentage of land area
Percentage of population under 18 years
Percentage of population age 65 and over
Percentage of black or African American population:
Percentage of family households: Female householder, no husband present
Percentage of households: Nonfamily households: Householder living alone
Average household size
Housing units
Percentage of occupied housing units
Percentage of population 25 years and over: Less than high school education level
Percentage of families: Income in 2010 below poverty level
Average household income (In 2010 inflation adjusted dollars)
Aggregate household income (In 2010 inflation adjusted dollars)
Percentage of households: With public assistance income
Percentage of unemployed civilian population 16 years and over

The Saginaw River Basin was covered by 21 counties (Figure 5a), 393 census tracts (Figure
5b), and 1,076 block groups (Figure 5c). According to U.S. Census Bureau (2010), more than 1.5
million people are living in the study area. 71.6% of the population are living in urban and 28.6%
in rural area. The race distribution is: 83.1% white, 10.6% black or African American, 2.8% Asian
and 3.5% others.
In addition to socioeconomic indicators, a watershed physiographical indicator called
drainage density was used to account for the accessibility of people to water bodies. In this study,
the drainage density was defined as the ratio of the total length of all rivers divided by the
socioeconomic area of interest (counties boundary, census tract, and block group). Scale
adjustment was also performed to match socioeconomic and stream health measures, because
stream health was calculated in much finer resolution (13,831 stream segments) than the

41

socioeconomic data. This was accomplished by calculating the weighted average of stream health
scores by length for the different census levels.

Figure 5. Boundary maps: (a) counties, (b) census tracts, and (c) block groups across
Saginaw River Basin.
4.2.4. Data Analysis and Modeling
Scatterplot matrices including histograms of each individual variable distribution (the four
stream health indicators, drainage density, and sixteen socioeconomic indicators) and pairwise
correlation coefficients at three census levels were calculated based on the Spearman’s rank
correlation coefficient, a non-parametric measure of statistical dependence between two
variables (Lehmann and D'Abrera 1998). However, to better understand the spatial dependency

42

among control parameters and stream health indicators, regression analysis was performed using
spatial Conditional Autoregressive (CAR) models (Banerjee et al., 2014).
First, assume counties are represented by 𝑖 = 1,2, … , 𝐼, census tracts are represented by 𝑗 =
1,2, … , 𝐽, and block groups are represented by 𝑘 = 1,2, … , 𝐾. Since the three levels are nested,
𝐾 = ∑𝐽𝑗=1 𝐾𝑗 where 𝐾𝑗 is the number of block groups in the 𝑗th census tract, and 𝐽 = ∑𝐼𝑖=1 𝐽𝑖 where
𝐽𝑖 is the number of census tracts in the 𝑖th county. Therefore, the total observation for each block
𝐽

𝑖
group at the finest resolution is 𝐾 = ∑𝐽𝑗=1 𝐾𝑗 = ∑𝐼𝑖=1 ∑𝑗=1
𝐾𝑗 .

For each resolution level of data presentation, the spatial CAR model is presented as
follows:
a)

County level data: Assume 𝑌𝑖 represents the steam health indicator, 𝑋𝑖 includes the
corresponding 𝑝 socioeconomic indicators plus an intercept to account for the mean level
of the response, i.e. 𝑋𝑖 = (1, 𝑆𝑖1 , … , 𝑆𝑖𝑝 ) for the 𝑖th sample. We consider:
1) Spatial CAR model (Model [1]):
𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 (𝑀𝐼 − 𝛾𝐼 𝑊𝐼 )−1 )

(2)

where, 𝑊𝐼 denotes the spatial neighborhood matrix for the 𝐼 counties and 𝑀𝐼 represents
the diagonal matrix with the number of total neighbors as the diagonal entries. In this
model, 𝜏𝐼2 measures the variation and 𝛾𝐼 measures the spatial dependence. The vector
𝛽 = (𝛽0 , 𝛽1 , … , 𝛽𝑝 ) includes the regression coefficients, hence 𝑋𝑖 𝛽 = 𝛽0 + ∑𝑝𝑡=1 𝑆𝑖𝑡 𝛽𝑡
in (1).
To evaluate the importance of modeling spatial dependence, two partial
implementations were considered:
i) the weighted regression model (Model [2]):

43

𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 𝑀𝐼−1 ),

𝑖 = 1,2, … , 𝐼

(3)

where, 𝛾𝐼 = 0 is fixed, i.e., no spatial dependence but the residual variance is
weighted by the number of neighbors; and
ii) the ordinary regression model (Model [3]):
𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 𝐼𝐼 ),

𝑖 = 1,2, … , 𝐼

(4)

where, 𝑀𝐼 = 𝐼𝐼 the identity matrix. In this model, no spatial information is
included; therefore, it becomes the ordinary regression model.
In the following context whenever a CAR structure is incorporated, the full and the two
partial implementations (weighted least squares and ordinary least squares) were
considered.
b) Census tract level data:
2) Spatial CAR model with no random effect (single level):
𝑌𝑗 = 𝑋𝑗 𝛽 + 𝜀𝑗 ,

𝜺 ~ 𝑁(0, 𝜏𝐽2 𝐷𝐽 (𝛾𝐽 )),

𝑗 = 1,2, … , 𝐽

(5)

with a total of three submodels and double index for [county, census tract],
𝐷𝐽 (𝛾𝐽 ) = (𝑀𝐽 − 𝛾𝐽 𝑊𝐽 )−1 as full implementation (Model [0.1]) that accounts for the
spatial dependence, and two partial implementations 𝐷𝐽 (𝛾𝐽 ) = 𝑀𝐽−1 (Model [0.2]) that
considers spatial heterogeneity using the number of surrounding regions as weights,
and 𝐷𝐽 (𝛾𝐽 ) = 𝐼𝐽 (Model [0.3]) that is just simple multiple regression without
considering any spatial information.
3) Spatial CAR model with random effect on county (multilevel):
𝑌𝑖𝑗 = 𝑋𝑖𝑗 𝛽 + 𝑢𝑖 + 𝜀𝑖𝑗 ,

𝜺 ~ 𝑁(0, 𝜏𝐽2 𝐷(𝛾𝐽 )), 𝒖 ~ 𝑁(0, 𝜏𝐼2 𝐷(𝛾𝐼 ))
𝑗 = 1,2, … , 𝐽𝑖 ,

44

𝑖 = 1,2, … , 𝐼

(6)

with a total of 3 × 3 = 9 submodels while considering the full implementation and two
partial implementations on both levels, indexed from Model [1.1] to Model [3.3].
c) Block group level data:
4) Spatial CAR model with no random effect (single level)
𝑌𝑘 = 𝑋𝑘 𝛽 + 𝜀𝑘 ,

𝜺 ~ 𝑁(0, 𝜏𝐾2 𝐷𝐾 (𝛾𝐾 )),

𝑘 = 1,2, … , 𝐾

(7)

with a total of three submodels and triple index for [county, census tract, block group],
𝐷𝐾 (𝛾𝐾 ) = (𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )−1 as full implementation (Model [0.0.1]), and two partial
implementations 𝐷𝐾 (𝛾𝐾 ) = 𝑀𝐾−1 (Model [0.0.2]) and 𝐷𝐾 (𝛾𝐾 ) = 𝐼𝐾 (Model [0.0.3]).
5) Spatial CAR model with nested random effects on county and census tract
(multilevel):
𝑌𝑖𝑗𝑘 = 𝑋𝑖𝑗𝑘 𝛽 + 𝑢𝑖 + 𝑣𝑖𝑗 + 𝜀𝑖𝑗𝑘 ,
𝜺 ~ 𝑁(0, 𝜏𝐾2 𝐷(𝛾𝐾 )),

(8)
𝒖 ~ 𝑁(0, 𝜏𝐼2 𝐷(𝛾𝐼 )),

𝑘 = 1,2, … 𝐾𝑗 ,

𝑗 = 1,2, … , 𝐽𝑖 ,

𝒗 ~ 𝑁(0, 𝜏𝐽2 𝐷(𝛾𝐽 ))
𝑖 = 1,2, … , 𝐼

with the total of 3 × 4 × 4 − 3 = 45 submodels by considering the full implementation
and two partial implementations on all three levels, and with either 𝒖 or 𝒗 fixed at 0
(but not both), indexed from Model [0.1.1] to Model [3.3.3] with the triple index for
[county, census tract, block group].
In total, 63 models (3 + 12 + 48) were fitted to the data at different resolution level and
by considering the interactions between levels and spatial dependence structure. The model fit is
carried out by running six Markov chain Monte Carlo (MCMC) per model with distinct starting
values and a total of 6,000 iterations. After convergence, the last 1,000 samples for each chain is
stacked as posterior samples for inference.

45

4.2.5. Markov Chain Monte Carlo Implementation Details
Equation 7 is considered as the full spatial CAR model with nested random effects on
county and census tract for the block group data. Other models are either nested or reduced at
simpler levels but having similar format. Equation (7) can be rewritten in format of the mixedeffect model as follows:
𝒀 = 𝑿𝛽 + 𝑍𝑢 𝒖 + 𝑍𝑣 𝒗 + 𝜺
𝜺 ~ 𝑁(0, 𝜏𝐾2 𝐷(𝛾𝐾 )),

(9)
𝒖 ~ 𝑁(0, 𝜏𝐼2 𝐷(𝛾𝐼 )),

𝒗 ~ 𝑁(0, 𝜏𝐽2 𝐷(𝛾𝐽 ))

The associated model parameters were estimated through the full Bayesian framework by
eliciting prior assumptions. A flat prior on the regression coefficient 𝛽 but a conjugate prior for
the variation parameters 𝜏𝐼2 , 𝜏𝐽2 , and 𝜏𝐾2 were assumed. This is an inverse-gamma distribution with
shape 𝑎 and scale 𝑏. One option is to assume 𝑎 = 2 and 𝑏 = 0.01 that yields a rather dispersed
prior distribution when there is a lack of strong prior knowledge. In addition, uniform prior
distributions were considered on 𝛾𝐼 , 𝛾𝐽 and 𝛾𝐾 over their required ranges to guarantee the
corresponding matrices𝐷(𝛾𝐼 ), 𝐷(𝛾𝐽 ) and 𝐷(𝛾𝐾 ) would be valid covariance matrices for CAR
model. In the next step, posterior samples of the parameters were drawn by combing the selected
diffused prior distributions and data likelihood via the MCMC technique. More specifically, the
Gibbs sampler was used, which involves updating a set of parameters given the data and the
remaining parameters, from their full conditional densities at each iteration of the MCMC runs.
Due to the conjugate prior choice, the full conditional distribution of 𝛽 is 𝑁(𝜇𝛽 , 𝛴𝛽 ) was adopted
where;
{

𝛴𝛽 = 𝜏𝐾2 (𝑿′ (𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )𝑿)−1
𝜇𝛽 = 𝛴𝛽 𝑿′(𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )(𝒀 − 𝑍𝑢 𝒖 − 𝑍𝑣 𝒗)

(10)

46

and at each Gibbs circle a sample of 𝛽 from the full conditional distribution above was first
simulated. Similarly, the full conditional distribution of county random effect 𝒖 is 𝑁(𝜇𝑢 , 𝛴𝑢 )
where;
𝜏𝐾2

𝜏2

′

−1

(𝑍𝑢 (𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )𝑍𝑢 + (𝑀𝐼 − 𝛾𝐼 𝑊𝐼 ) 𝜏𝐾2 )

𝛴 =
{ 𝑢
𝐼
𝜇𝑢 = 𝛴𝑢 𝑍𝑢 ′(𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )(𝒀 − 𝑿𝛽 − 𝑍𝑣 𝒗)/𝜏𝐾2

(11)

The full conditional distribution of census tract random effect 𝒗 is 𝑁(𝜇𝑣 , 𝛴𝑣 ) where;
𝜏2

𝛴 = 𝜏𝐾2 (𝑍𝑣 ′ (𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )𝑍𝑣 + (𝑀𝐽 − 𝛾𝐽 𝑊𝐽 ) 𝜏𝐾2 )
{ 𝑣
𝐽
𝜇𝑣 = 𝛴𝑣 𝑍𝑣 ′(𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )(𝒀 − 𝑿𝛽 − 𝑍𝑢 𝒖)/𝜏𝐾2

−1

(12)

The full conditional distribution of 𝜏𝐼2 is inverse-gamma with shape 𝑎𝐼 and scale 𝑏𝐼 ,
where;
{

𝑎𝐼 = 𝑎 + 𝐼/2
𝑏𝐼 = 𝑏 + 𝒖′(𝑀𝐼 − 𝛾𝐼 𝑊𝐼 )𝒖/2

(13)

The full conditional distribution of 𝜏𝐽2 is inverse-gamma with shape 𝑎𝐽 and scale 𝑏𝐽 ,
where;
{

𝑎𝐽 = 𝑎 + 𝐽/2

(14)

𝑏𝐽 = 𝑏 + 𝒗′(𝑀𝐽 − 𝛾𝐽 𝑊𝐽 )𝒗/2

The full conditional distribution of 𝜏𝐾2 is inverse-gamma with shape 𝑎𝐾 and scale 𝑏𝐾 ,
where;
𝑎𝐾 = 𝑎 + 𝐾/2
{

𝑏𝐾 = 𝑏 +

𝒆′ (𝑀𝐾 −𝛾𝐾 𝑊𝐾 )𝒆

(15)

2

𝑤𝑖𝑡ℎ 𝒆 = 𝒀 − 𝑿𝛽 − 𝑍𝑢 𝒖 − 𝑍𝑣 𝒗
𝛾𝐼 was also sampled from its full conditional distribution with density proportional to
|𝑀𝐼 − 𝛾𝐼 𝑊𝐼 |1/2 exp{𝛾𝐼 𝒖′ 𝑊𝐼 𝒖/(2𝜏𝐼2 )}

(16)

47

Similar sampling was performed for 𝛾𝐽 and 𝛾𝐾 . Updating all parameters completes one
Gibbs circle, and this procedure is repeated over a large number of iterations in order to obtain
posterior samples for inferential stage after convergence of multiple MCMC runs. Finally,
Deviance Information Criterion (DIC4) was used for mixed-effect model evaluation (Celeux et al
2006).
4.3. Results and Discussions
4.3.1. Variables Distribution and Pairwise Correlations
Figures 6, A1, and A2 show the correlation matrixes for the three census levels of county,
census tract, and block group, respectively. Histograms of each individual variable distribution are
shown on the diagonal of each matrix. The upper and lower parts of the matrices are spearman
rank correlation coefficients and scatter plots of each pair of variables, respectively.
4.3.1.1. Variables Distribution
Understanding the variable distribution is important for selecting appropriate analysis
techniques or examining the underlying assumption about a set of variables. Among the four
stream health indicators at the three levels (county, census tract, and block group), the HBI and
IBI had the most bell-shaped histograms, especially at the census tract and block group levels,
while a little skewness to the right can be seen in both indices at the county level. This shows that
the level of study has an effect on variable distribution as the aforementioned indices have normal
distributions at the census tract and block group levels but skewed at the county level. Besides
that, these two indices are less sensitive to aggregation at the county level compared to the FIBI
and EPT. The FIBI and EPT were right-skewed at the census tract and block group level meaning
that most of the units (census tracts or block groups) have low scores, which is consistent with low
stream health scores reported at the reach level (Figure 4 (c) and (d)).

48

Figure 6. Spearman rank correlation matrix between dependent and independent variables at
the county level. Boldfaced value indicates significance at the 0.05 level and correlation less
than 0.7, Boldfaced value in red indicates significance at the 0.05 level and strongly positive
correlation equal or above 0.7, and value in blue indicates significance at the 0.05 level and
strongly negative correlation equal or below -0.7
However, their distributions were the opposite at the county level and showed left-skewness,
meaning that most of units have high FIBI and EPT scores. These results show how using coarse
census resolutions can be misleading in stream health data analysis, especially for FIBI and EPT,
which were more sensitive to the level change. Considering stream health scores at the reach level
(Figure 4) also suggests that census tract and block group levels can better represent stream health
data distribution compared to the county level.
Regarding the socioeconomic data, most of them had consistent distributions at the census
tract and block group levels, and in general, were less affected at the county level than the stream

49

health measures. This means that these indices are less sensitive to aggregation than the stream
health measures. Among the 16 socioeconomic parameters, only S17 (percentage of unemployed
population of 16 years old and above) had normal distributions at all three levels. The S3
(percentage of land area), S9 (average house size) and S11 (percentage of housing units occupied)
parameters were left-skewed. The left skewness of S3 means that the majority of census units (at
each level) have few water bodies and are mostly covered by land. While the distributions for S9
and S11 show that the majority of house units in the study area are larger than average and most
of them are occupied. The rest of the parameters were right-skewed. The right skewness of S2 and
S10 showed that many of the census units have low population densities (S2) and few housing
units (S10), which correlates with the house size (S9) distribution mentioned above. The same
pattern was seen for S6 (percentage of black or African American population), meaning that only
a few census units have the majority of the population as black or African American. The S7
(percentage of households with female householder) and S8 (percentage of householders living
alone) distributions, also showed that few units of study have a high percentage of households with
a female householder or householders living alone. Poverty and welfare receipt indicators also
showed that only a few census units are dominated by people with low incomes (S14 and S15),
incomes below poverty level (S13), or receive public assistance (S16). These distributions can help
decision makers to select areas, which have higher priorities for environmental justice practices.
4.3.1.2. Stream Health Indicators Correlations at Three Levels
Considering the census tract and block group levels, the IBI, FIBI and EPT were positively
correlated with each other and all were negatively correlated with HBI, which is consistent with
their definitions where high values for the IBI, FIBI and EPT indicate better stream health
conditions, while for the HBI lower values indicate better stream health conditions. However, this

50

consistency is lost at the county level, where the IBI had a reversed correlation with
macroinvertebrate indices. This means that streams, which had better conditions for
macroinvertebrates (having high FIB, high EPT and low HBI scores), had worse conditions for
fish (low IBI scores). Furthermore, significant correlations between the IBI and FIBI and EPT
indices at the census tract and block group levels were also lost at the county level. Overall,
correlations among stream health measures show how sensitive they are to census data resolution
and how their aggregation at the county level can be misleading conclusions compared to the
census tract and block group levels. These changes in data interpretation among different census
levels also matches with their histograms comparison.
4.3.1.3. Socioeconomic/Physiographic Indicators Correlations at Three Levels
Almost all of the socioeconomic/physiographic indicators had significant correlations with
each other at the county level with thirty-one absolute correlation coefficients above 0.7 (shown
in red) and three correlation coefficients above 0.9 among S2 (population density) and S10
(housing units), S2 and S15 (aggregate household income). However, moving from county to
census tract level, these correlation values drastically dropped with only three absolute values
above 0.7 among S8 (householders living alone) and S9 (average household size), S12 (population
above 25 years old and education less than high school) and S14 (average household income), and
S13 (families with income below poverty level) and S14. However, none of them were significant.
Like the census tract level, only three absolute correlation values were above 0.7, for S8 and S9,
S13 and S14, and S14 and S15 at the block group level. Overall, correlation values were even less
at block group level. For example, correlation coefficients between S13 and S14 dropped from 0.83 to -0.71 at the block group compared to the census tract level. In addition, the correlation
coefficients of S12 and S14 dropped from -0.75 at the census tract to -0.58 at the block group,

51

while correlation coefficients for S14 and S15 increased from 0.65 to 0.73 when the block group
level is compared to the census tract level. These examples show how correlations found between
different indicators can vary among census levels and can lead to different interpretations. In
general, socioeconomic/physiographic data showed high correlations among each other at course
resolutions (e.g. county level) while these correlations were lost at finer census levels (e.g. census
tract and block groups), which are more detailed and can better represent spatial distribution.
4.3.1.4. Interaction of Stream Health Measures and Socioeconomic/Physiographic Indicators
at Three Levels
Like the interactions of the socioeconomic/physiographic indicators with each other, the
highest correlation coefficients with the four stream health measures were also found at the county
level, followed by the census tract and block group levels. In addition, more variables are
significantly correlated at the county level. However, the values reported for these correlations
were much lower than the numbers found among the socioeconomic/physiographic indicators. For
example, the highest correlation of EPT with a socioeconomic/physiographic indicator at the
county level was 0.43 with S13 (families with income below poverty level), which is much smaller
than the correlations reported in the previous section (e.g. three correlation coefficients were above
0.9). Furthermore, significantly correlated socioeconomic/physiographic indicators for each
stream health measure vary across the census levels. For example, at the county level the HBI had
significant correlations with three household composition indicators (S5, S8, and S9). However,
of these three only S8 continued to be significant at the census tract level. S9 was replaced with
another household indicator (S7: Female-headed households). Besides that, a racial composition
indicator (S6) and one population indicator (S3: percentage of land area) became significant at this

52

level. While at the block group level, one more population indicator (S2: population density) was
also added to this list.
In general, all stream health measures had higher correlation coefficients at the county
level, compared to the census tract and block group levels. Furthermore, the significant
socioeconomic/physiographic indicators were not the same at all three levels, which again shows
the role of census level resolution in data interpretation for each stream health measure.
4.3.2. Understand the Spatial Dependency Between Stream Health Indicators and
Control Parameters Using Regression Analysis
In this stage, regression analysis was developed using spatial CAR models to discover
spatial dependency among control parameters and stream health indicators with and without
random effect as follows:
4.3.2.1. Spatial CAR Models with No Random Effect (Single Level)
Considering each stream health indicator, three models (spatial, weighted regression, and
ordinary regression) were developed. These models were applied for each census level, so 36
models (4 response variables, 3 levels, and 3 models) were developed at this stage (Tables 7-10
and A1 to A8). In these tables, DIC, which is a measure of relative quality of a statistical model,
was used to identify the best model at each level. However, this value should not be used to
compare the models’ performances from multiple levels (e.g. county versus census tract) due to
differences in sample sizes. In addition to DIC, 𝛾 was reported to present spatial dependence in
which 0 means no spatial effect while 1 mean full spatially dependency. Finally, each dependent
parameter that its regression coefficient (β1- β17) that does not contain zero in the range of their
upper and lower bands can be considered as a significant parameter and are bolded for each model.

53

Table 7. Regression models for FIBI at county level (boldfaced values indicates a significant
parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
14.68
0.09
-18.32
2.18
-0.79
1.81
-3.25
0.98
-0.38
-0.51
47.36
-0.38
-0.98
-1.33
-1.41
-28.88
0.06
-3.91
3.2
-0.12

Spatial
lower
14.15
-0.63
-26.10
0.87
-2.38
-0.36
-5.45
-1.10
-4.88
-6.18
29.04
-2.07
-3.47
-3.20
-4.44
-41.66
-1.36
-6.15
1.0
-0.97
71.55

upper
15.22
0.78
-10.70
3.54
0.77
4.03
-1.03
3.11
4.17
5.13
66.21
1.36
1.62
0.57
1.61
-16.28
1.39
-1.54
8.5
0.93

Ordinary regression
mean
lower upper
14.69
14.29 15.09
0.08
-0.63
0.84
-18.39
-26.17 -10.72
2.21
0.78
3.54
-0.82
-2.35
0.75
1.83
-0.45
4.06
-3.22
-5.39
-1.00
0.96
-1.23
3.09
-0.36
-5.04
4.27
-0.47
-6.40
5.23
47.39
28.51 66.04
-0.37
-2.16
1.42
-0.94
-3.67
1.58
-1.35
-3.25
0.58
-1.40
-4.51
1.50
-28.89
-41.93 -15.89
0.07
-1.33
1.52
-3.94
-6.33
-1.58
3.5
1.1
10.34
0
0
0
71.47

Weighted regression
mean
lower
upper
14.64
14.18
15.09
0.05
-0.82
0.90
-18.26 -27.05
-9.66
2.26
0.77
3.72
-0.78
-2.63
1.018
1.79
-1.11
4.65
-3.10
-5.54
-0.72
0.82
-1.53
3.26
-0.57
-5.73
4.68
-0.77
-7.21
5.84
47.69
27.80
67.81
-0.20
-2.25
1.81
-0.88
-3.77
1.98
-1.26
-3.12
0.66
-1.52
-4.86
1.72
-29.28 -43.40 -15.06
-0.02
-1.74
1.69
-4.03
-6.70
-1.28
1.1
0.3
3.4
0
0
0
75.60

At the county level (Tables 7 to 10) none of the models (spatial, weighted regression, and
ordinary regression) had significant spatial dependency (all four 𝛾 ranges had zero). For each
stream health measure, the exact same significant parameters were highlighted among the three
developed models. Besides that, the comparison of the three DICs showed only slight differences
meaning that there is no major difference between spatial, weighted regression, and ordinary
regression models at the county level and all of them have the same patterns. Regarding the lowest
DIC, a weighted regression model for EPT, and ordinary regression models for FIBI, HBI and IBI
were identified to be the best predictive models.

54

Table 8. Regression models for EPT at county level (boldfaced values indicates a significant
parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
5.16
-0.42
-3.03
1.56
-0.79
1.63
-0.56
-0.56
3.19
3.37
8.96
0.86
0.28
-0.30
0.69
-6.94
0.30
-0.82
1.0
-0.04

Spatial
lower
4.86
-0.81
-7.20
0.81
-1.62
0.42
-1.69
-1.69
0.74
0.28
-1.01
-0.08
-1.13
-1.31
-0.96
-13.89
-0.44
-2.06
0.3
-0.96
44.79

upper
5.46
-0.02
1.05
2.28
0.01
2.81
0.61
0.61
5.63
6.37
18.87
1.79
1.63
0.71
2.25
-0.06
1.06
0.41
2.8
0.93

Ordinary regression
mean
lower
upper
5.16
4.94
5.37
-0.42
-0.81
-0.03
-3.03
-7.01
0.96
1.56
0.83
2.29
-0.79
-1.61
0.02
1.61
0.41
2.79
-0.54
-1.69
0.64
-0.59
-1.69
0.49
3.23
0.77
5.84
3.40
0.39
6.54
8.94
-0.75
18.89
0.87
-0.04
1.81
0.29
-1.02
1.68
-0.30
-1.36
0.70
0.70
-0.92
2.35
-6.94
-13.95
-0.21
0.31
-0.46
1.04
-0.80
-2.05
0.46
1.0
0.3
3.1
0
0
0
43.89

Weighted regression
mean lower
upper
5.15
4.95
5.35
-0.44 -0.83
-0.07
-3.03 -7.26
0.86
1.50
0.85
2.13
-0.76 -1.57
0.04
1.56
0.28
2.82
-0.51 -1.58
0.58
-0.63 -1.76
0.51
3.28
0.72
5.55
3.47
0.42
6.26
8.73
-0.30
18.09
0.85
-0.07
1.75
0.19
-1.07
1.38
-0.25 -1.13
0.61
0.75
-0.78
2.29
-6.75 -13.35
-0.38
0.33
-0.41
1.11
-0.71 -1.89
0.51
0.2
0.1
0.6
0
0
0
42.80

However, within in census tract level (Tables A1 to A4), more variations were seen among
spatial, weighted regression and ordinary regression models. In contrast to the county level,
significant parameters for all three models and for all four stream health measures were not the
same. In general, spatial models gave better prediction (lower DICs), meaning that the use of the
census tract level can capture more spatial patterns, while these variations were lost at the low
detailed county level. Besides that, fewer dependent parameters showed significant correlations
with each of the stream health measures at the census tract compared to the county level. For
example, the IBI at the county level had significant correlations with nine out of seventeen
indicators including one physiographic (S1), one population (S3), one household (S7), one housing
(S11), one educational disadvantages (S12), three poverty/welfare receipt (S13, S14, S16), and
one unemployment (S17). However, at the census tract level, only one welfare receipt

55

Table 9. Regression models for HBI at county level (boldfaced values indicates a significant
parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
4.85
0.14
3.44
-0.67
0.35
-1.00
0.43
-0.46
-0.62
-0.66
-6.15
0.13
0.31
0.56
0.36
3.12
-0.30
1.38
0.19
0.06

Spatial
lower
4.70
-0.04
1.60
-1.01
-0.01
-1.54
-0.09
-0.97
-1.75
-2.01
-10.67
-0.30
-0.31
0.10
-0.37
-0.06
-0.64
0.82
0.06
-0.94
12.82

upper
5.01
0.32
5.32
-0.35
0.72
-0.46
0.96
0.06
0.52
0.72
-1.60
0.54
0.93
1.0
1.11
6.24
0.04
1.93
0.54
0.96

Ordinary regression
mean
lower
upper
4.85
4.75
4.95
0.14
-0.05
0.32
3.47
1.62
5.28
-0.67
-1.01
-0.33
0.35
-0.03
0.73
-1.00
-1.53
-0.46
0.43
-0.11
0.96
-0.45
-0.95
0.06
-0.61
-1.78
0.53
-0.65
-2.10
0.76
-6.21
-10.72
-1.67
0.13
-0.31
0.55
0.32
-0.30
0.93
0.57
0.11
1.04
0.37
-0.40
1.13
3.14
-0.03
6.28
-0.31
-0.65
0.03
1.38
0.83
1.94
0.21
0.07
0.62
0
0
0
11.68

Weighted regression
mean lower
upper
4.85
4.76
4.95
0.13
-0.06
0.31
3.27
1.39
5.16
-0.66
-0.98
-0.32
0.32
-0.07
0.72
-1.01
-1.62
-0.39
0.38
-0.14
0.89
-0.38
-0.92
0.15
-0.66
-1.83
0.53
-0.70
-2.19
0.76
-5.88 -10.45
-1.43
0.13
-0.33
0.58
0.35
-0.26
0.96
0.56
0.11
0.99
0.41
-0.32
1.14
3.01
-0.18
6.28
-0.29
-0.66
0.07
1.32
0.73
1.92
0.05
0.02
0.15
0
0
0
12.50

indicator (S16) showed significant correlation with the IBI index. Other stream health measures
also had fewer significant correlations with socioeconomic/physiographic indicators at the census
tract level, compared to the county level. This indicates that using more detailed census data
reveals more distinctions among dependent variables and as a result reduces the number of
parameters required to predict stream health measures; while, some of these variables became
correlated at the county level due to the aggregation at this course level. Similar reductions in the
number of significant parameters were seen in the comparison of pairwise correlations at the two
levels (Figures 6 and A1) for all other stream health measures.
At the block group level, spatial models showed even better performance (lower DICs)
compared to weighted regressions and ordinary regression models (Tables A5 to A8). However,
comparison of 𝛾 values between spatial census tract (Tables A1 to A4) and block group models
56

Table 10. Regression models for IBI at county level (boldfaced values indicates a significant
parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
50.02
0.61
4.16
-2.34
-0.21
-0.44
-1.61
2.20
-1.97
-2.88
-9.62
3.27
2.42
2.88
3.98
4.95
-1.43
2.23
2.03
-0.03

Spatial
lower
49.56
0.01
-1.78
-3.41
-1.43
-2.17
-3.34
0.57
-5.72
-7.36
-24.83
1.91
0.37
1.35
1.56
-5.75
-2.52
0.34
0.62
-0.96
61.34

upper
50.47
1.17
10.19
-1.23
1.02
1.30
0.13
3.85
1.71
1.45
5.43
4.63
4.42
4.34
6.31
15.45
-0.28
4.06
6.09
0.95

Ordinary regression
mean
lower upper
50.02
49.70 50.34
0.61
0.01
1.22
4.11
-1.78
10.12
-2.36
-3.52
-1.28
-0.21
-1.37
1.01
-0.45
-2.25
1.33
-1.63
-3.31
0.12
2.21
0.48
3.95
-2.01
-5.52
1.63
-2.93
-7.44
1.47
-9.45
-24.09
4.84
3.29
1.89
4.70
2.40
0.33
4.51
2.87
1.40
4.41
3.99
1.66
6.42
4.85
-5.05
15.04
-1.42
-2.50
-0.28
2.25
0.43
4.22
2.24
0.68
6.95
0
0
0
61.13

Weighted regression
mean
lower
upper
50.04
49.73
50.35
0.69
0.07
1.30
4.50
-1.56
10.67
-2.34
-3.39
-1.29
-0.20
-1.49
1.11
-0.29
-2.30
1.67
-1.65
-3.36
0.05
2.24
0.59
3.95
-1.89
-5.68
1.87
-2.74
-7.55
2.12
-10.20
-24.81
4.04
3.19
1.72
4.59
2.38
0.34
4.42
2.79
1.40
4.12
3.87
1.41
6.32
5.28
-4.96
15.74
-1.45
-2.68
-0.26
2.25
0.37
4.15
0.53
0.17
1.55
0
0
0
62.56

(Tables A5 to A8) showed that higher spatial dependency exists for the three macroinvertebrates
models at the block group level than at the census tract (higher 𝛾 values and/or narrower range of
𝛾 variations). While for the IBI, higher spatial dependency was seen at the census tract level than
at the block group level. This can be explained, since macroinvertebrates are better representatives
of local habitat conditions, while fish are representative of large-level stream health due to their
mobility. Therefore, at the block group level, which is the finest level, macroinvertebrate indices
have more spatial dependency on socioeconomic/physiographic parameters, while the IBI has
higher spatial dependency at the census tract, which is a larger scale than the block group.
Like the census tract level models, significant parameters were not the same for the spatial,
weighted regression, and ordinary regression models, which again shows that, unlike the county
level, these models differ from each other at the block group level. In addition, the significant
57

parameters were also different for each stream health measure at different census levels. For IBI
spatial models for example, only S16 (percentage of households receiving public assistance) was
highlighted as significant parameter at the census tract level, while at the block group level, S2
(population density) and S7 (percentage of households with female householder) were also found
to be significant.
4.3.2.2. Spatial CAR Models with Random Effects (Multilevel)
Using three (spatial, weighted regression and ordinary regression) models for each census
level interacting with its courser resolutions (random effects) resulted in 63 models for each stream
health measure. Table 11 presents the DICs for all of these models. The best models at each census
level (lowest DIC) are bolded for each stream health measure. It is important to note that the
single-level models in subsection 4.3.2.1 can be viewed as special cases of the multi-level
modeling where we fix some of the random effects on other levels to be exactly 0.
The county level is the coarsest resolution with no higher-level interactions (no random
effect), so the first three rows in Table 11, represent the spatial, weighted regression, and ordinary
regression models the exist at this level. Like the single level (no random effect) results (Tables 7
to 10), all three models have very close DICs meaning that their performances are likely to be the
same. Here also the weighted regression and ordinary regression models had slightly lower DICs
compared to spatial models.

58

Table 11. DICs for multilevel models with random effects (boldfaced values represent best
models at each census level)*
Model Level

FIBI

EPT

HBI

IBI

County

County

72.06
70.02
76.23

43.93
43.44
41.38

12.74
12.28
12.16

61.42
61.67
61.14

1943.57
2011.43
2030.39
1866.06
1938.10
1956.05
1867.88
1939.19
1957.50
1897.97
1974.39
1986.60

1606.15
1743.71
1774.0
1531.67
1717.27
1800.30
1531.13
1736.73
1765.388
1558.115
1758.908
1795.37

1062.99
1124.47
1150.45
989.11
1096.36
1123.93
985.37
1096.97
1124.67
1016.58
1093.39
1121.14

4369.31
3175.85
3166.25
3614.55
4297.06
3044.48
3072.51
3506.49
4296.65
3154.50
2988.34
3602.88
4322.78
3155.93
2981.18
3531.47
4622.22
5782.70
5172.72
5970.25
4640.88
4902.58
5043.04
5894.27
4640.55
5701.90
3350.02
5923.63
4636.55

3505.23
2292.42
2173.78
2845.55
3428.30
2224.19
2127.33
2777.09
3431.07
2145.78
2145.87
2780.58
3458.86
2374.83
2117.40
2716.33
3843.96
4656.31
4140.10
4894.86
3770.08
4579.76
4078.78
4857.45
3769.05
4582.33
4844.90
4821.54
3846.81

2305.20
968.30
1228.27
1615.11
2228.81
928.11
822.83
1413.94
2228.07
1011.15
876.93
1442.18
2258.74
959.11
980.45
1508.92
2528.03
2804.94
3002.87
2981.39
2484.65
2724.49
2914.90
2551.23
2483.71
2726.72
2915.35
2869.64
2479.80

Census
Tract

Block
Group

59

S
WR
OR

Census
Tract
-

Block
Group
-

2146.48
2216.50
2246.78
2071.61
2141.15
2174.01
2070.07
2139.39
2173.79
2100.25
2179.20
2208.49

S
S
S
WR
WR
WR
OR
OR
OR

S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR

-

5120.27
3885
3793.52
4367.52
5046.62
3730.10
3740.65
4298.93
5044.30
3757.87
3860.37
4531.91
5072.66
3915.40
3778.31
4326.08
5215.88
4928.61
4124.09
5341.34
5143.59
5771.39
3865.1
6696.03
5140.31
4867.69
3899.55
5153.44
5208.41

S
S
S
S
WR
WR
WR
WR
OR
OR
OR
OR
S
S
S
S
WR
WR
WR
WR
OR

S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
-

S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
WR
WR
WR
WR
WR
WR
WR
WR
WR
WR
WR
WR
WR

Table 11. (cont’d)
5736.15
4609.32
2752.76
4850.89
OR
S
4229.44
2653.88
2910.95
3888.06
OR
WR
5969.41
4896.13
2843.53
4471.86
OR
OR
4744.05
3956.18
2651.11
5275.56
5114.78
4770.84
2966.77
4863.84
S
4364.45
4264.09
3157.07
5061.88
WR
6137.42
5076.35
3178.44
6144.27
OR
4756.91
3967.19
2608.60
5276.87
S
5046.17
4696.45
2889.99
3924.74
S
S
5194.36
4199.25
3097.25
4035.92
S
WR
6075.38
5069.57
3119.79
6843.7
S
OR
4756.48
3966.91
2608.91
5197.52
WR
5083.31
4692.98
2888.83
3978.51
WR
S
5254.76
4966.44
3098.74
3879.62
WR
WR
6124.29
5070.39
3119.43
6065.81
WR
OR
4751.88
3963.71
2605.37
5298.28
OR
5075.60
4719.87
2917.87
4002.86
OR
S
5221.79
5039.66
3094.77
5040.38
OR
WR
6135.05
5063.93
3113.07
6086.95
OR
OR
* S: spatial, WR: weighted regression, OR: ordinary regression, -: no random effect

WR
WR
WR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR

Regarding the census tract level, interactions with the county level (random effects) were
also considered, so twelve models (rows 4 to 15) were developed at this level. Like tables A1 to
A4, the spatial models had lower DICs compared to the weighted regression and ordinary
regression models. Adding county level data improved model predictions; however, it is important
to note that adding county level random effect had a lower impact on the overall DIC than the
models used at the census level. This is also in agreement with Tables 7 to 10, which showed that
the three models had very close values at the county level. Considering the interactions of the two
levels (random effects), the FIBI combined spatial models at both the census tract and county
levels resulting in a lower DIC; while for EPT, HBI and IBI, coupled spatial models at the census
tract and weighted regression models at the county level had lower DICs, indicating better
predictions.
The next 48 rows in Table 11 belong to models developed for the block group level
interacting with the census tract and county levels (nested random effects). In general, models that
60

considered the spatial effect for the block groups had lower DICs compared to non-spatial ones.
Compared to single level (no random effect) models, inputting census tract and county levels also
had a positive impact on the models’ predictions. The lowest DIC for the IBI was achieved through
the combination of spatial models at all three (county, census tract and block group) levels. While
for the three macroinvertebrate stream health indicators, the combination of spatial models at the
block group level, weighted regression models at the census tract level, and spatial (for HBI) and
ordinary regression (for FIBI and EPT) models at county levels produced the lowest DICs. Since
the IBI is based on fish, the selection of all spatial models resulting in the lowest DIC makes sense
due to the large mobility of fish throughout a river network (Allan et al. 1997; Flinders et al. 2008).
Spatial models selected for macroinvertebrates at the block group level is also in agreement with
tables A5 to A8. However, considering the interactions of data at the census tract and block group
levels (nested random effects) suggests that weighted regression models work better with census
tract data. That can be due to the macroinvertebrate behavior of limited movement within the river
systems. Meanwhile, for county level data used in the block group level study (nested random
effect) ordinary regression models worked better for the FIBI and EPT, while weighted regression
models worked better for HBI. These variations among models is also in agreement with previous
results that all three (spatial, weighted regression and ordinary regression) models performances
were very close at county level and each of them can be selected as the best.
Overall, spatial models at the finest levels (in this case, block group) have better
performance than the two non-spatial forms. Meanwhile combining the nested effect of data
collected in upper levels improves their predictive power.
Table 12 presents the dependent parameters that were significant in the best models at each
level. Except for ETP taxa at the block group level, all stream health indicators at each level (both

61

for single level or no random effect models and models across different levels having random
effects) have the same significant parameters. In other words, while DIC values can differ and the
model performances can be improved with the addition of interactions among the different levels
(random effects), the significant parameters are not affected. However, these significant
parameters may be lost by changing the resolution level and some new parameters may show
significant effects, revealing potentially misleading results that arise from selecting an inaccurate
level or scale.
Table 12. Significant parameters among all selected best models
Levels
Block group multilevel
model (with nested
random effects)
Block group single level
model (no nested random
effects)

FIBI
S2, S5, S6, S7

EPT
S17

HBI
S1, S16

IBI
S2, S7, S16

S2, S5, S6, S7

-

S1, S16

S2, S7, S16

Census tract multilevel
model (with random
effects)
Census tract single level
model(no random effects)

S2, S10

S4, S5, S7, S9

S3

S16

S2, S10

S4, S5, S7, S9

S3

S16

S2, S3, S6, S10,
S15, S17

S1, S3, S5,
S8, S9, S15

S2, S3, S5,
S10, S13,
S17

S1, S3, S7,
S11, S12, S13,
S14, S16, S17

County level

4.3.2.3.Residual Plots
Figures 5 and A3 through A6 show the residual plots for the selected models at both
multilevel (with random effects) and single level (no random effect) cases (Tables 7 to 11 and A1
to A8). As mentioned before, county level data is not likely to be a good predictor and may cause
misinterpretations. This is further reinforced by Figure 5, which shows that the models developed
at this level have little to no variation across the study area. This lack in variation shows that these
models are unable to uncover the complexities of relations among the variables. As an important

62

contrast, for the more detailed levels (census tract and block group), shown in Figures A3 through
A6, more variations are captured.

Figure 7. model prediction residuals at county level for a) EPT, b) FIBI, c) HBI, d) IBI
EPT and HBI show very low residuals in the study area and values ranging from -5 to +5
are reported for the majority of the study area in both census tract and block group models
developed for these indices (Figures A3 and A4). It means that developed models for these two
stream health measures have acceptable performances in this region. In contrast, the FIBI and IBI
have some significant residuals in the study area (Figures A5 and A6). Most of the high residual
areas are located in highly populated areas and close to the watershed outlet, which means model
63

predictions for the FIBI and IBI at the given areas have less accuracy, compared to the rest of the
study area.

4.4. Conclusions
The goal of this study was to evaluate the effects of spatial data resolution on environmental
justice analysis with respect to stream health integrity. Seventeen socioeconomic/physiographic
indicators representing population, household composition, racial composition of household,
female headed households, housing, educational disadvantage, economic disadvantage, welfare
receipt, and unemployment in addition to four stream health measures (including one fish and three
macroinvertebrate indices) were used.
Data distributions and pairwise correlations at all three levels showed that stream health
data is highly sensitive to census level resolution. In addition, some variables had opposite
skewness and/or even correlation sign at the county level compared to two finer resolutions (census
tract and block group levels). Meanwhile, socioeconomic/physiographic data distributions were
less sensitive to census level change and most of them had similar distributions among all three
levels. Many significant correlation coefficients were found at the county level, while moving to
the census tract and block group levels, the number of significant correlations and correlation
coefficients drastically dropped. This showed that the use of the county level data can be
misleading due to aggregation.
For each stream health measure, three regression models including spatial, weighted
regression and ordinary regression were developed at each level. County level models for each
stream health measure had similar significant parameters. Besides that, each set of three models
had similar predictions with no spatial dependency. However, at the census tract and block group

64

levels, spatial models had better predictions with fewer number of significant parameters, meaning
that the census tract and block group levels were able to capture spatial variations, which were
aggregated in county level. Furthermore, using multilevel models (with random effects) also
improved model prediction compared to single level models (with no random effects); however,
did not affect significant parameters. The difference between spatial models and weighted
regression and ordinary regression models was even more pronounced at the block group level,
compared to the census tract level. The IBI had higher spatial dependency at the census tract level,
while the three macroinvertebrate indices had higher spatial dependency on dependent variables
at the block group level. This matched the movement patterns of fish and macroinvertebrates
within river systems.
Residual plots also proved that the county level models are not able to capture spatial
patterns while the census tract and block group levels do. This confirmed that the block group level
models performed better than both the county and census level models. Residual plots also showed
that for the best developed IBI and FIBI models prediction in densely populated areas and close to
the watershed outlet was less accurate compared to other places, while the best models for EPT
and HBI worked well for the whole region.
To better understand the interactions between socioeconomic variable and stream health,
it is recommended that additional studies will be performed in larger regions and different
timeframes. This provides additional information to examine the importance of spatial and
temporal variations in the context of environmental justices.

65

5. ASSESSING THE RELATIVE IMPORTANCE OF PARAMETER ESTIMATION IN
STREAM HEALTH BASED ENVIRONMENTAL JUSTICE MODELING
5.1. Introduction
Anthropogenic activities have degraded natural resources which in turn also threatens
human ecosystems due to the interwoven nature of natural and human system interactions (Liu et
al., 2007a; Carpenter et al., 2009; Alberti et al., 2011). However, degraded environments do not
equally affect various groups in society and some communities such as low income and people of
color are more vulnerable to environmental hazards than other groups (Massey, 2004; Downey
and Liam, 2008). Therefore, the concept of Environmental Justice was introduced to provide fair
treatment and involvement of all social groups in implementation and enforcement of
environmental laws and regulations (U.S. EPA, 2014e). In other words, the aim of environmental
justice is providing equal access to healthy environments as right for all people.
Water is one of the environmental resources that is considered in the environmental justice
studies. In the U.S., the traditional approach for water resources assessment was mainly focused
on water quality and physical characteristics of the water bodies. However, a nationwide
assessment of riverine ecosystems that was performed by the U.S. Environmental Protection
Agency found that despite all implemented water quality regulations, still more than 40% of
nation’s streams were in poor biological condition (U.S. EPA, 2015c). Therefore, a new criterion
called Biological Integrity Assessment was introduced in which the physical, chemical, and
biological characteristics of streams should be simultaneously considered to improve the overall
assessment of water resources (NSCEP, 2011; U.S. EPA, 2015c; Woznicki, 2015). In order to
consider biological characteristic in to overall water resources assessment, stream health indices

66

were introduced, which quantify the response of aquatic species to instream stressors (Herman and
Nejadhashemi, 2015; Van Metre et al., 2017).
Regarding the stream health indices, predictive models have been developed to evaluate
these indices beyond limited monitoring sites (Woznicki et al., 2016a). The general inputs to these
models are landscape features and in instream water quantity and water quality parameters
(Miserendino et al., 2011; Einheuser et al., 2012). Traditionally, linear regression (Frimpong et al.,
2005; Pont et al., 2009; Moya et al., 2011), and multivariate techniques (Simpson and Norris, 2009;
Aguiar, 2011) were used for stream health model development. While recent studies showed that
nonlinear techniques such as Fuzzy Logic (Adriaenssens et al., 2006; Marchini et al., 2009),
Artificial Neural Network (ANN) (Lencioni et al., 2007; Mathon et al., 2013), and Adaptive
Neuro-Fuzzy Inference Systems (ANFIS) (Einheuser et al., 2012; 2013a) provide more reliable
prediction of complex ecological systems than linear techniques. Poff and Zimmerman (2010)
reported that ecological response is very dependent to flow alteration. In particular, the magnitude,
frequency, duration, timing, and rate of change of flow are master variables that affect aquatic
species (Poff et al., 1997; Olden and Poff, 2003; Poff and Zimmerman, 2010). Therefore, several
tools such as Hydrological Index Tool (HIT) (USGS, 2017), EflowStats (EflowStats, 2015),
MATLAB Hydrological Index Tool (MHIT) (Abouali et al., 2016a) were developed to assess
ecologically relevant hydrological parameters. Studies showed that incorporating these parameters
significantly improved the accuracy of stream health predictive models (Herman et al., 2015;
Herman et al., 2016; Wozniski et al., 2016b). However, due to the complexity of naturals systems,
the predictive power of stream health models are moderate. For example, a recent study by
Wozniski et al. (2015) using both HIT tool and the ANFIS technique resulted in development of
twenty stream health models in which the range of models’ performance (R2) varies between 0.41

67

to 0.74 for macroinvertebrate indices while for a fish index, the R2 can be as low as 0.37 to as high
as 0.99 for different stream size and temperature (Woznicki et al, 2015).
These new stream health models have recently been introduced in environmental justice
studies in which fish and macroinvertebrate indices were used. Sanchez et al. (2014) used spatial
regression models and bivariate mapping to find vulnerable social communities. They used four
common stream health indices (for fish and macroinvertebrates), and nine socioeconomic indices
(representing education, housing, income, population, and race) collected at the census tract level.
The results were promising and showed high correlations between regions with the lowest stream
health status and vulnerable social communities (Sanchez et al., 2014). Sanchez et al. (2015) also
found that spatial clustering improved spatial regression models prediction. Daneshvar et al.
(2016) evaluated the role of spatial level in stream health based environmental justice models’
performance. They used sixteen commonly used socioeconomic parameters for environmental
justice studies, collected at three census levels of county, census tract, and block group, and the
same four stream health indices used by Sanchez et al. (2014; 2015) to identify significant
parameters for stream health based environmental justice models at each level (Daneshvar et al.,
2016). They also reported that more spatial dependencies were found at the block group level
compared to other levels, and that the nested effect of data collected in upper levels improved
model’s prediction (Daneshvar et al., 2016).
As described earlier, the variability in the stream health model performance can introduce
a large level of errors on stream health based environmental justice models. However, new
developments in stream health modeling, such a two-phase approach (Abouali et al., 2016b), has
resulted in significant improvement in the overall predictability for both fish and
macroinvertebrate based stream health models. Therefore, the goal of this study is to assess the

68

relative importance of parameter estimation in stream health based environmental justice models
by comparing the results against previous studies. Our hypothesis was that more accurate stream
health predictions would result in the development of more robust environmental justice models
in which spatial dependencies among biological and socioeconomic characteristics at different
spatial levels would be revealed.
5.2. Materials and Methods
5.2.1. Study Area
The Saginaw River Basin, which is located in the state of Michigan, U.S.A. was selected as
the study area (Figure 8). With the total drainage area of more than 16,000 km 2, it is the largest
watershed in Michigan and drains to the Lake Huron. Agricultural lands are the dominant landuse
(36.2%), followed by forest (24.8%), wetland/lake (14.3%), pasture (12.4%) and urban (12.3%)
lands. The U.S. Environmental Protection Agency identified the Saginaw River and Bay as an area
of concern due to degraded fisheries, sediment pollution, and loss of recreational values (U.S.
EPA, 2015d). Agricultural and urban runoff, industrial discharges, and sewer overflows are some
major sources of pollution in this region (U.S. EPA, 2015d). With more than 7,000 miles of
streams, the Saginaw River Basin provides a wide range of habitats for fish and other species
(WIN, 2017). It also addresses the needs for drinking water, electrical power generation, and
industrial consumption in this region (WIN, 2017). According to the U.S. Census Bureau (2010),
the Saginaw River Basin is home of almost 1.5 million people, where 49% are men and 51% are
women. The majority of residents are young and more than 52% of them are in the range of 25 to
65 years old, 34% are under 25 years old, while only 14% are senior (above 65 years old). More
than 85% of population is white, followed by African American (10%), while other races are less
than 5%. The Saginaw River is also a key shipping transit in Mid-Michigan that connects two

69

cities, Saginaw and Bay City. Flint is another big city in this region that has faced water
contamination problems (U.S. EPA, 2013).

Figure 8. The locations of biological monitoring sites at the Saginaw River Basin
5.2.2. Stream Health Indices
Four common stream health indices including: (1) the Index of Biotic Integrity (IBI) for
fish, and (2) the Hilsenhoff Biotic Intex (HBI), (3) Family Index of Biotic Integrity (FIBI), and (4)
Ephemeroptera, Plecoptera, Trichoptera (EPT) index for macroinvertebrates were used in order to
assess the biological integrity of riverine ecosystems. The IBI evaluates the species richness,
abundance and trophic composition of fish communities and ranges from zero (lowest score) to
100 (highest score) (Karr, 1981; Kerans and Karr, 1994; Herman and Nejadhashemi, 2015).
Meanwhile, the HBI quantifies the response of macroinvertebrates species to organic pollutants
and ranges from zero to 10, where higher values mean more degradation by organic pollutants
(Hilsenhoff, 1987). The FIBI is the third index used in this study and measures the response of
70

macroinvertebrates communities to industrial pollutants by quantifying species’ composition in
family taxonomic groups with scores ranging from zero (lowest score) to 45 (highest score)
(Woznicki et al., 2015). The sensitivity of the three macroinvertebrate orders of Ephemeroptera
(mayflies), Plecoptera (stoneflies), and Trichoptera (caddisflies), known as EPT taxa, to local
instream degradations are evaluated by positive EPT scores where zero scores represent the highest
degradation (Lenat, 1988; Woznicki et al., 2015).
The Michigan Department of Environmental Quality (MDEQ) has quantified the fish index
(IBI) and the three macroinvertebrate indices (HBI, FIBI, and EPT) for 193 and 262 monitoring
sites within the Saginaw River Basin, respectively (MDEQ, 1997; Seelbach and Wiley, 1997).
These monitoring sites are shown in Figure 8. However, since there are 13,831 stream segments
in the Basin, stream health models need to be developed for both fish and macroinvertebrate
indices to estimate the overall biological conditions of streams beyond the monitoring sites.
5.2.3. Socioeconomic/Physiographic Indices
Socioeconomic indices representing concentrated disadvantages are commonly used for
environmental justice assessments (Sampson et al., 2008). In this study, sixteen frequently used
indices for population, age, race, housing, education, and income disadvantages assessment are
taken into account and are listed in Table 13 (Brulle and Pelow, 2006; Bullard et al., 2008;
Sampson et al., 2008; Lin and Morefield; 2011).

71

Table 13. Socioeconomic/Physiographic indices
ID

S1

Category

Type of
aggregation

S2

Water
Ratio
access
Population Ratio

S3
S4

Age

S5

Percentage
Percentage
Percentage

S6

Race

Percentage

S7

Household Percentage

S8

Percentage

S9

Average

S10
S11
S12

Education

Count
Percentage
Percentage

S13

Income

Percentage

S14

S15

Average

Aggregate

S16

Percentage

S17

Percentage

Indicator description
County
Drainage density (m-1)
Population density
(people/mi2)
Land area (%)
Population under 18 years
old (%)
Population of or over 65
years old (%)
African American
population (%)
Households with female
householder (no husband
present) (%)
Households with living
alone householder (%)
Household size
(people/household)
Household units (No.)
Occupied housing units (%)
Population of or over 25
years old with less than
high school education (%)
Families with income
below poverty level (%)
Household income ($
adjusted with 2010
inflation)
Household income ($
adjusted with 2010
inflation)
Households with public
assistance income (%)
Unemployed population of
and over 16 years old (%)

4.76×10-4

Average values
Census
Block
tract
group
8.257×10-4
9.85×10-4

75.31

368.57

350.57

88.93

97.12

97.07

22.16

23.65

23.46

16.76

14.36

14.98

3.56

8.62

6.88

10.48

12.65

11.79

26.53

25.25

24.93

2.44
61.77×103
78.98

2.51
1632.00
87.612

2.52
592.44
88.52

13.35

12.01

11.57

11.50

12.30

11.53

55.06×103

59.52×103

60.02×103

38.23×108

86.10×106

31.78×106

3.46

3.88

3.55

50.08

48.36

47.77

These indices are obtained from the U.S. Census Bureau for three census levels of county,
census tract and block group (U.S. Census Bureau, 2010). The Saginaw River Basin overlaps with
21, 393, and 1076 census units of counties (Figure 9 (a)), census tracts (Figure 9(b)), and block
groups (Figure 9(c)) respectively. In addition to sixteen socioeconomic indices, one physiographic
index called drainage density was also used to quantify the relative distance of population under
72

study to waterbodies. Drainage density was calculated as the ratio of the total length of streams in
a census unit (of county, census tract, or block group) to the unit area.

Figure 9. Census units of (a) counties, (b) census tracts, and (c) block groups overlapping
with the Saginaw River Basin

5.2.4. Modeling Process
Figure 10 illustrates the modeling process used to predict the stream health indices beyond
the monitoring sites and the analysis conducted for the stream health based environmental justice
assessments. A hydrologic/water quality model was initially setup, calibrated, and validated for
the study area to estimate streamflow and water quality parameters (including sediment, total
nitrogen, and total phosphorus loads) for each stream segment on a daily time- step. The estimated
flow and water quality parameters were used as inputs to the MATLAB Hydrological Index Tool
(MHIT) that calculates ecologically relevant water quality and water quantity parameters (Abouali
et al., 2016a). These parameters quantify the magnitude, frequency, duration, timing, and rate of
change in flow and water quality parameters that can affect aquatic ecosystems (Poff et al., 1997;
Henriksen et al., 2006). MHIT outputs were then used to develop stream health predictive models.
For this purpose, a two-phase approach (Abouali et al., 2016b) was implemented, in which (1)
Partial Least Square Regression (PLSR) was used to predict the initial stream health indices and
73

their associated errors, and then (2) a fuzzy logic approach (e.g. ANFIS) was used to estimate the
modified stream health indices based on the initial estimations and associated errors. Having the
four predicted stream health measures along with 17 socioeconomic and physiographic indices at
three census levels of county, census tract and block group, the individual correlations among
indices were evaluated and the stream health based environmental justice models were developed.
Since these two datasets are in different spatial units (one at the stream level, and one at the census
levels), scale adjustment was conducted first, in which weighted average scores based on stream
lengths falling in each census unit were used as their associated stream health scores.

Figure 10. The overall modeling processes

74

5.2.4.1. Hydrological/Water Quality Modeling
The Soil and Water Assessment Tool (SWAT) was used to develop a hydrologic/water
quality model for the study area. SWAT is a physically based and semi-distributed watershed and
water quality model developed by U.S. Department of Agriculture-Agricultural Research Service
(USDA-ARS) in order to evaluate the impact of land management practices on water quantity and
water quality (Arnold et al., 1998). SWAT delineates a watershed into subwatersheds with unique
stream segments passing through them, while each subwatershed can be divided into several
Hydrologic Response Units (HRUs) based on similarity in landuse, soil, and slope variations
within the region (Neitsch et al., 2011). In this study, a pre-delineated watershed developed by
Michigan Institute of Fisheries Research was used in which the study area was divided into 13,831
subwatersheds with unique HRUs. The developed SWAT model was then calibrated based on
three statistical criteria including 1) Nash-Sutcliffe efficiency (NSE), 2) Percent bias (PBIAS), and
3) root mean square error-observations standard deviation ratio (RSR) (Moriasi et al., 2007). NSE
ranges from one (optimum value) to minus infinity, PBIAS ranges from minus infinity to infinity
(with optimum value of zero), and RSR ranges from zero (optimum value) to infinity (Moriasi et
al., 2007). For both streamflow and water quality components, NSE above 0.5, and RSR below
0.7 are called satisfactory. While satisfactory range of PBIAS varies based on variable, where
absolute PBIASs below 25, 55, and 70 are called satisfactory for streamflow, sediment, and
nutrients respectively (Moriasi et al., 2007). Streamflow was calibrated and validated based on
daily streamflow data collected by the U.S. Geological Survey (USGS) for nine monitoring
stations within the region, while water quality (including sediment, total nitrogen, and total
phosphorus) loads were calibrated and validated based on monthly observations provided by the
U.S. EPA (Daneshvar et al., 2017). All three statistical criteria were met for streamflow (NSEs

75

ranging from 0.54 to 0.80, PBIASs ranging from 16.34 to -1.53, and RSRs ranging from 0.68 to
0.45) and water quality (NSEs ranging from 0.57 to 0.75, PBIASs ranging from 35.52 to 10.00,
and RSRs ranging from 0.65 to 0.50), components calibration and validation (Daneshvar et al.,
2017). The calibrated SWAT model was then used to evaluate streamflow, sediment, total
nitrogen, and total phosphorus loads for all stream segments on a daily basis.
5.2.4.2. Stream Health Model Development
5.2.4.2.1. One-Phase Approach
Fuzzy Logic and ANFIS models developed by Einheuser et al. (2012; 2013a) were used in
former stream health based environmental justice studies by Sanchez et al. (2014; 2015), and
Daneshvar et al. (2016). These techniques are commonly used for ecological modeling (Woznicki
et al., 2016a), however their inputs are limited due to computational resources and finite ecological
observations (Hamaamin et al., 2013). Therefore, parameter selection must be conducted first to
limit models’ inputs (Woznicki et al., 2015). Einheuser et al. (2012; 2013a) used Spearman’s rank
correlation to find the most significant water quantity and water quality parameters with respect to
stream health measures, which reduced the number of inputs to four for each macroinvertebrates
index (Einheuser et al., 2012), and five for the fish index (Einheuser et al., 2013a). Selected input
parameters for this approach are listed in Table B1.
5.2.4.2.2. Two-Phase Approach
To address the drawback of limited input parameters, a two-phase approach (Abouali et
al., 2016b) was used in this study, where during the first phase, all input parameters will be used
to estimate the stream health index and associated error, while during the second phase, ANFIS
will use these two predictions as inputs to estimate the final stream health score.

76

PLSR was used for the first phase to project both the inputs and outputs into a mutually
orthogonal coordinate system. PLSR is able to use all input parameters and unlike regular linear
regressions, it is not affected by multicollinearity that may exist among input parameters.
Therefore, all 171 ecologically relevant hydrologically indices introduced by Poff et al. (1997) in
addition to the 78 water quality parameters representing annual and seasonal averages and
coefficients of variations were used as input parameters for the first phase. These PLSR predictions
of stream health indices and their associated errors were used as inputs for the ANFIS models in
the second phase. Table B1 summarizes the two-phase input parameters.
During the second phase, two different sets of stream health predictive models were
developed, one set for all streams and then another set for different stream groups. Based on the
river continuum concept (Vannote et al., 1980), instream species characteristics vary across
different stream sizes that can be classified into three major groups of headwater (stream orders 13), medium (stream orders 4-7), and large (stream orders 7-10) streams. The maximum stream
order within the Saginaw River Basin is 7 (Figure 8), therefore two stream groups of headwater
streams (orders 1-3), and medium and large streams (orders 4-7) were defined and different stream
health predictive models were developed for each group. Then the set of stream health predictive
models with a better performance was used to calculate the four stream health measures for all
13,831 stream segments.
5.2.5. Data Analysis
Scatter plot matrices were developed for each census level in which histograms, pairwise
distributions, and pairwise correlation coefficients were evaluated for all indices including the four
stream health measures and the seventeen socioeconomic/physiographic indicators. Spearman’s
ranking was used for pairwise correlation coefficients evaluation (Lehmann and D’Abrera, 1998).

77

Bivariate maps were also developed to identify area of high priority concerning environmental
justice. In the case of stream health, the area was divided into three classes of high, medium, and
low quality using the four biological factors. However, for the socioeconomic indicators, the Jenks
natural break method (Jenks, 1967) was used first and then summed to identify the overall area of
concern. These two maps were overlapped to identify communities that are vulnerable regarding
the environmental justice issue.
To

evaluate

spatial

dependencies

among

stream

health

measures

and

socioeconomic/physiographic indices, the spatial Conditional Autoregressive (CAR) technique
(Banerjee et al., 2014) was used to develop stream health based environmental justice models.
Equation (17) represent the general form of CAR model used in this study
𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 (𝑀𝐼 − 𝛾𝐼 𝑊𝐼 )−1 ) ; 𝑖 = 1,2, … , 𝐼 census units

(17)

in which, 𝑌𝑖 and 𝑋𝑖 represent the stream health measure and the corresponding 𝑝 covariates vector
for the 𝑖th census unit (e.g. county, census tract, or block group). Spatial neighborhood
dependencies for the 𝐼 census units are represented by 𝑊𝐼 , and the number of neighbors are listed
as diagonal entries of the 𝑀𝐼 matrix. Variation and spatial dependency are also measured by 𝜏𝐼2
and 𝛾𝐼 respectively.
In order to assess the significance of spatial dependency, two simplified forms of the spatial
CAR model were also developed as follows:
(i)

Assuming 𝛾𝐼 = 0, means no spatial dependence while the residual variance is
weighted by the number of neighbors. This simplifies the spatial model to a
weighted regression model as shown in Equation (18):
𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 𝑀𝐼−1 ) ;

78

𝑖 = 1,2, … , 𝐼 census units

(18)

(ii)

While setting 𝛾𝐼 = 0 and 𝑀𝐼 = 𝐼𝐼 , the identity matrix, means no spatial information
is implemented and the spatial model will be simplified to an ordinary regression
model as shown in Equation (19):
𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 𝐼𝐼 ) ;

𝑖 = 1,2, … , 𝐼 census units

(19)

These three forms of spatial, weighted regression, and ordinary regression were used to
develop single level (with no random effect) and multilevel (with random effect) models at three
census levels of county, census tract, and block group.
5.2.5.1.Single Level (With no Random Effect) Models
Assuming = 1,2, … , 𝐼 , 𝑗 = 1,2, … , 𝐽 , and 𝑘 = 1,2, … , 𝐾 represents the number of counties,
census tracts, and block groups respectively. The single level (with no random effect) CAR models
at the three census levels are presented as follow:
𝑌𝑖 = 𝑋𝑖 𝛽 + 𝜀𝑖 ,

𝜺 ~ 𝑁(0, 𝜏𝐼2 𝐷𝐼 (𝛾𝐼 )),

𝑖 = 1,2, … , 𝐼

(20-1)

𝑌𝑗 = 𝑋𝑗 𝛽 + 𝜀𝑗 ,

𝜺 ~ 𝑁(0, 𝜏𝐽2 𝐷𝐽 (𝛾𝐽 )),

𝑗 = 1,2, … , 𝐽

(20-2)

𝑌𝑘 = 𝑋𝑘 𝛽 + 𝜀𝑘 ,

𝜺 ~ 𝑁(0, 𝜏𝐾2 𝐷𝐾 (𝛾𝐾 )),

𝑘 = 1,2, … , 𝐾

(20-3)

Where using full forms of 𝐷𝐼 (𝛾𝐼 ) = (𝑀𝐼 − 𝛾𝐼 𝑊𝐼 )−1, 𝐷𝐽 (𝛾𝐽 ) = (𝑀𝐽 − 𝛾𝐽 𝑊𝐽 )−1, and 𝐷𝐾 (𝛾𝐾 ) =
(𝑀𝐾 − 𝛾𝐾 𝑊𝐾 )−1 resulted in spatial models development while 𝐷𝐼 (𝛾𝐼 ) = 𝑀𝐼−1 , 𝐷𝐽 (𝛾𝐽 ) = 𝑀𝐽−1 ,
and 𝐷𝐾 (𝛾𝐾 ) = 𝑀𝐾−1 implementations resulted in weighted regression models at three census levels
of county, census tract, and block group respectively. Ordinary regression models are also
developed by setting 𝐷𝐼 (𝛾𝐼 ) = 𝐼𝐼 , 𝐷𝐽 (𝛾𝐽 ) = 𝐼𝐽 , and 𝐷𝐾 (𝛾𝐾 ) = 𝐼𝐾 for the three levels of county,
census tract, and block group respectively.
5.2.5.2.Multilevel (With Random Effect) Models
Since the three census levels of county, census tract, and block group are nested, the total
number of census tracts is 𝐽 = ∑𝐼𝑖=1 𝐽𝑖 where 𝐽𝑖 is the number of census tracts in the 𝑖th county, and
79

𝐽

𝑖
the total number of block groups is 𝐾 = ∑𝐽𝑗=1 𝐾𝑗 = ∑𝐼𝑖=1 ∑𝑗=1
𝐾𝑗 where, 𝐾𝑗 is the number of block

groups in the 𝑗th census tract. To assess the nested effect of aggregated data at different spatial
levels, multilevel (with random effect) models were also developed for the census tract and block
group levels as follows:
(1) Multilevel (with random effect) models at the census tract level
Implementation of the random effects of data collected at the census tract and county levels
resulted in the following form of the spatial CAR model at the census tract level:
𝑌𝑖𝑗 = 𝑋𝑖𝑗 𝛽 + 𝑢𝑖 + 𝜀𝑖𝑗 ,

𝜺 ~ 𝑁(0, 𝜏𝐽2 𝐷(𝛾𝐽 )), 𝒖 ~ 𝑁(0, 𝜏𝐼2 𝐷(𝛾𝐼 ))
𝑗 = 1,2, … , 𝐽𝑖 ,

(21)

𝑖 = 1,2, … , 𝐼

where, 𝑢 and 𝜀 represent the residual terms at two levels of county and census tract,
respectively. 𝐷(𝛾𝐼 ) and 𝐷(𝛾𝐽 ) can be either be in spatial, weighted regression, or ordinary
regression form and their combination will result in 3×3=9 different multilevel (with random
effect) models.
(2) Multilevel (with random effect) models at the block group level
Implementation of the random effects of data collected at the block group, census tract, and
county levels resulted in the development of the following form of the spatial CAR model at
the block group level:
𝑌𝑖𝑗𝑘 = 𝑋𝑖𝑗𝑘 𝛽 + 𝑢𝑖 + 𝑣𝑖𝑗 + 𝜀𝑖𝑗𝑘 ,
𝜺 ~ 𝑁(0, 𝜏𝐾2 𝐷(𝛾𝐾 )),
𝑘 = 1,2, … 𝐾𝑗 ,

(22)

𝒗 ~ 𝑁 (0, 𝜏𝐽2 𝐷(𝛾𝐽 )) ,
𝑗 = 1,2, … , 𝐽𝑖 ,

𝒖 ~ 𝑁(0, 𝜏𝐼2 𝐷(𝛾𝐼 )),
𝑖 = 1,2, … , 𝐼

where, 𝑢, 𝑣, and 𝜀 represent the residual terms at the three levels of county, census tract, and
block group, respectively. Combinations of the three forms of spatial, weighted regression, and
ordinary regression implementation of 𝐷(𝛾𝐼 ), 𝐷(𝛾𝐽 ), and 𝐷(𝛾𝐾 ) will result in the development
80

of 3×4×4-3=45 multilevel (with random effect) models, while only one of 𝐷(𝛾𝐼 ) or 𝐷(𝛾𝐽 ) can
be zero (not both) at the same time.
For both the single level (with no random effect) and multilevel (with random effect)
analysis, Markov chain Monte Carlo (MCMC) was used to estimate parameters. Six chains with
different initial values were used for each model and were run for 6,000 iterations. The last 1,000
samples after convergence for each chain were then used as posterior samples. Deviance
Information Criterion (DIC4) was used for model comparison (Celeux et al., 2006), which
measures both model simplicity and model fit at the same time and models with lower DICs are
preferred.
5.3. Results and Discussion
5.3.1. Stream Health Indices
Tables 14 and B2 present the coefficient of determination (R2) and root-mean-square error
(RMSE) of current (two-phase approach) and former (one-phase approach) developed stream
health predictive models. Comparison of the stream health model performances when all streams
were used for development of the predictive model reveals that the two-phase approach, used in
this study, has outperformed the former predictive models for all four stream health measures
within all streams. The Fish index (IBI) has the highest improvement compared to previous
approach where a R2 of 0.89 and RMSE of 7.56 are achieved compared to the former R2 of 0.48
and RMSE of 16.37. This shows that incorporating larger sets of ecologically relevant water
quantity and water quality parameters (249), and combining the two methods of PLSR and ANFIS
resulted in more accurate predictions of stream health measures rather than just using the onephase fuzzy logic model with a few water quantity and water quality parameters (4 to 5), especially

81

for fish that are highly sensitive to ecologically relevant flow parameters (Poff and Zimmerman,
2010).
The next two columns of Tables 14 and B2 summarize the performance of the stream health
predictive models developed for two stream classes of “Headwater streams” and “Medium and
large streams”. Results show that for all stream health indices, models developed for the two
classes have better performances (with R2 values ranging from 0.90 to 0.97) than models developed
for all streams combined (with R2 values ranging from 0.70 to 0.89). For instance, R2 values of
0.97 and 0.91 were achieved for the EPT predictive models for the two stream classes instead of
the 0.72 obtained for the EPT predictive model for all streams combined. This is due to the fact
that species are often found in specific stream classes and have different responses to stressors
(McManamay et al., 2014; Herman et al., 2015). So distinct models for different stream classes
are preferred to models that are developed for all streams especially for macroinvertebrate indices
(HBI, FIBI, and EPT) that are more sensitive to local impairment than fish (Kerans and Karr,
1994).
Table 14. Comparison of coefficient of determination of developed stream health predictive
models
Stream
One-phase
Two-phase approach
health
approach
measures
All streams
All streams
Headwater streams
IBI
0.48*
0.89****
0.90****
HBI
0.57**
0.83***
0.91***
**
***
FIBI
0.50
0.70
0.94***
**
***
EPT
0.54
0.72
0.97***
*
This data was obtained from Einheuser et al. (2013a)
**
This data was obtained from Einheuser et al. (2012)
***
This data was obtained from Daneshvar et al. (2017)
****
Results obtained from this study

Medium and large streams
0.96****
0.97***
0.94***
0.91***

The new developed stream health predictive models for two stream classes were then used
to simulate the four stream health indices beyond the sampling points (Figure B1) and their
predictions are compared with the one-phase approach by calculating the absolute percent of
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change in prediction (Nejadhashemi et al., 2011) as shown in Table 15. Results show that HBI
scores have the lowest deviation from the results obtained in the one-phase approach where 71.2%
of headwater streams and 91.1% of medium and large streams have less than a 25% change in
scores. Meanwhile, the highest changes are found in the IBI prediction for headwater streams
where 38.8% of streams in this class have more than a 75% change in score prediction. High
changes in the IBI scores prediction reveals the high dependency of the fish index on ecologically
relevant water quantity and water quality parameters (Poff and Zimmerman, 2010). While the HBI
is less sensitive to these parameters due to the fact that it measures the response of aquatic species
to organic pollutants (Hilsenhoff, 1987).
Table 15. Absolute percent of change in the stream health measures prediction between oneand two-phase approaches
Stream health
measure
IBI
HBI

FIBI
EPT

Stream classes
Headwater streams
Medium and large streams
Headwater streams
Medium and large streams
Headwater streams
Medium and large streams
Headwater streams
Medium and large streams

< 25%
31.3%
58.0%
71.2%
91.1%
42.4%
54.6%
44.5%
40.7%

Absolute percent of change
25% - 50% 50% - 75%
17.0%
12.9%
24.0%
6.7%
22.6%
4.4%
7.8%
0.6%
18.9%
14.5%
19.3%
12.4%
12.3%
11.0%
27.1%
15.8%

> 75%
38.8%
11.2%
1.8%
0.5%
24.2%
13.6%
32.2%
16.4%

5.3.2. Variables Distribution and Pairwise Correlations
Figures 11, B2, and B3 present the correlation matrices for all indices including the four
stream health measures (IBI, HBI, FIBI, and EPT), and the seventeen socioeconomic and
physiographic variables (S1 to S17) at three levels of county, census tract, and block group
respectively. The diagonals of the matrices represent the indices distribution, while upper and
lower parts represent pairwise correlation coefficients and scatterplots respectively. Modified
stream health indices prediction has changed their distribution, correlation with each other and
correlation with independent variables (S1 to S17).
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Figure 11. Correlation matrix of indices at the county level. The diagonal represents the
scatterplots, while lower level and upper levels represent pairwise distributions and
correlation coefficients, respectively. Boldfaced numbers represent significant correlation
coefficients at the 0.05 level. Red and blue values represent positive and negative significant
correlation coefficients with absolute value above 0.7 at 0.05 level
Compared to the previous study (Daneshvar et al., 2016) that used one-phase stream health
modeling approach to construct the environmental justice models, stream health indices
distribution are more consistent among three levels of county, census tract and block group, while
there was inconsistency among stream health scores distribution at county level compared to
census tract and block group levels in the previous study. For example, using the results from the
one-phase approach, EPT had right skewness at the county level, and left skewness at the census
tract and block group levels, while using the results from the two-phase approach, EPT scores have
close to normal distributions with slight skewness to the left among all three census levels (Figures

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11, B2, and B3). This means that the new developed stream health scores are less sensitive to
stream health score aggregation and more consistent at the different census levels.
The same consistency among the three levels exists in pairwise correlations, where
correlation coefficients have the same sign at all three levels, while in the previous study
correlation coefficients at the county level showed opposite correlations compared to the census
tract and block group levels (Tables 16-18). For the new developed stream health scores, HBI had
negative correlations with IBI, FIBI, and EPT at all three levels, while these three had positive
correlations with each other. This is also in agreement with their definitions, where higher values
of IBI, FIBI, and EPT represent better stream health condition, while for HBI it is reversed
(Woznicki et al., 2016b). Besides that, pairwise correlation coefficients for each pair are almost
the same at all three census levels, which again reveals that the new developed stream health scores
are not as sensitive to aggregation at different spatial levels.
Table 16. Comparison of pairwise correlations among stream health indices at the county
level. (Blue upper right values represent correlations among the new developed stream health
indices using a two-phase approach, while red lower left values are correlations reported by
Daneshvar et al. (2016) using a one-phase approach)
IBI
0.042
-0.33
-0.23

-0.69
HBI
-0.34
-0.29

0.46
-0.28
FIBI
0.12

0.59
-0.36
0.78
EPT

Table 17. Comparison of pairwise correlations among stream health indices at the census
tract level. (Blue upper right values represent correlations among the new developed stream
health indices using a two-phase approach, while red lower left values are correlations
reported by Daneshvar et al. (2016) using a one-phase approach)
IBI
-0.31
0.21
0.32

-0.40
HBI
-0.40
-0.29

0.27
-0.42
FIBI
0.24

85

0.48
-0.50
0.38
EPT

Table 18. Comparison of pairwise correlations among stream health indices at the block
group level. (Blue upper right values represent correlations among the new developed stream
health indices using a two-phase approach, while red lower left values are correlations
reported by Daneshvar et al. (2016) using a one-phase approach)
IBI
-0.23
0.16
0.20

-0.37
HBI
-0.40
-0.18

0.30
-0.40
FIBI
0.14

0.41
-0.45
0.40
EPT

5.3.3. Identifying High Priority Area
Figure 12 shows the area of concern for stream health and socioeconomic aspects using bivariate
maps at three census levels of county, census tract, and block group. Overall, the highest spatial
variations are found at the block group (Figure 12-c), while aggregations in upper levels (census
and county) smoothed these variations, especially at the county level (Figure 12-a). Considering
spatial variations at the block group level, northern regions of the watershed that are mainly
dominated by forests and less affected by human activities have the best conditions for both stream
health and socioeconomic indicators. Moving to the watershed outlet, both stream health, and
socioeconomic measures are declined. In general, the central region has been identified as the most
vulnerable area. This highly populated area (Bay city and Flint) suffers from low water quality
condition and dense concentration of vulnerable communities. Such analysis for other regions
enables policymakers to identify areas that have higher priority for resources allocation.

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Figure 12. Bivariate map of overall stream measures and their predictors across Saginaw
River Basin at (a) county, (b) census tract, and (c) block group levels
5.3.4. Single Level (with No Random Effect) Stream Health Based Environmental
Justice Regression Models
Tables B3 to B14 summarize the outputs of the three single level (with no random effect)
regression models (including spatial, weighted regression, and ordinary regression) developed for
the four stream health measures of IBI, HBI, FIBI, and EPT at three levels of county, census tract
and block group. DICs of the developed models are also shown in Table 19 and lower DICs
(representing better performances) for each of the four stream health measures at all three census
levels are boldfaced.
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Table 19. DICs of single level (with no random effect) regression models (Boldfaced values
indicate best selected models with lower DICs)
Stream
County
Census tract
health
S
WR
OR
S
WR
OR
index
IBI
156.50 158.74 156.65
2623.42 2786.37 2767.44
HBI
22.47 22.08 21.72
452.75 577.96 567.20
FIBI 102.85 105.09 102.42
1984.03 2090.95 2081.21
EPT
91.50 94.33 91.56
1378.87 1501.52 1503.99
S: Spatial; WR: Weighted Regression; OR: Ordinary regression

Block group
S

WR

OR

5964.52
1139.18
4491.20
3301.39

6454.62
1488.91
4865.83
3602.18

6403.28
1463.87
4836.51
3589.46

Similar to the previous study using one-phase approach (Daneshvar et al., 2016), spatial
models had better performances (with lower DICs) than the two non-spatial models at the census
tract and block group levels, while at the county level, the DICs of the three models are close and
in some cases (e.g. HBI), non-spatial models had slightly lower DICs than the spatial model. In
other words, spatial models are preferred at the census tract and block group levels, while at the
county level there is no major preference.
Comparison of significant parameters selected for each model also resulted in the same
conclusion. For each regression model (Tables B3 to B14), significant parameters, meaning that
their range does not cover zero, are boldfaced. Table 20 summarizes all significant parameters for
the three regression models developed for each of the four stream health measures.
Like the previous study (Table B15), all three models of spatial, weighted regression, and
ordinary regression had similar significant parameters at the county level, while moving to census
tract and block group, fewer and different parameters were identified as significant for the spatial
models than the two non-spatial models. For instance, three independent variables of S2
(population density), S16 (households with public assistance income), and S17 (unemployed
population over 16 years old), were significant for EPT prediction by all three regression models
at the county level. Meanwhile, at the census tract, S1 (drainage density) and S11 (percentage of

88

occupied housing units), and at the block group only S1 were significant for spatial models.
Meanwhile for the two non-spatial models, significant parameters were S6 (percentage of African
American population) and S11 at the census tract, and S1, S5 (percentage of population of or over
65 years old), S6, and S11 at the block group levels. This is also in agreement with the former
study (Daneshvar et al., 2016), showing that spatial dependencies are lost at the county level, while
census tract and block group levels can capture spatial dependencies among variables. In summary,
three models of spatial, weighted regression, and ordinary regression had similar performance at
the county level. While spatial models are preferred to the two non-spatial forms at the census tract
and block group levels with fewer number of significant parameters.
Table 20. Significant parameters of new developed single level (with no random effect)
regression models
Index Census
level
IBI
County
Census tract
Block group

Spatial

Weighted regression

Ordinary regression

S1, S3
S5, S9, S11
S6, S8, S10, S17

S1, S3
S1, S3, S5, S11
S2, S3, S5, S6, S11,
S12

S1, S3
S1, S3, S5, S11
S1, S3, S5, S6, S11,
S12

HBI

County
Census tract
Block group

S1
-

S1
S1, S6, S11, S13
S2, S8, S10, S11

S1
S6, S11, S13
S2, S4, S6, S10, S11

FIBI

County
Census tract
Block group

S2, S7, S16, S17
S1, S11, S16
S1, S2, S6

S2, S7, S16, S17
S1, S3, S5, S11, S12
S1, S2, S3, S5, S6, S11

S2, S7, S16, S17
S1, S3, S5, S11, S12
S1, S2, S3, S5, S6,
S11

EPT

County
Census tract
Block group

S2, S16, S17
S1, S11
S1

S2, S16, S17
S6, S11
S1, S5, S6, S11

S2, S16, S17
S6, S11
S1, S5, S6, S11

However, comparison of current significant parameters (Table 20) with those from the
previous study (Table B15) reveals that modified stream health scores used the two-phase
approach resulted in much fewer and somehow different significant parameters for the same
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regression model. Overall, 115 significant parameters are identified for all regression modes
(Tables B3 to B14), while this number was 171 in the former study (Daneshvar et al., 2016).
Especially at the county level, the number of significant parameters have drastically dropped
compared to the previous study. For instance, nine independent parameters (S1, S3, S7, S11, S12,
S13, S14, S16, and S17) identified by all regression models developed for the IBI at the county level

has reduced to only two parameters (S1, S3). This shows that using the two-phase approach
modified the regression models and removed redundancies that existed before, especially at the
county level. This is also in agreement with the pairwise correlation results that showed that the
new developed stream health scores improved the correlations at the county level while in the
former study using the one-phase approach, aggregated stream health scores at the county level
showed opposite correlations compared to the census tract and block group levels.
5.3.5. Multilevel (with Random Effect) Stream Health Based Environmental Justice
Regression Models
The combination of the three residual forms of spatial, weighted regression, and ordinary
regression for data collected at the three census levels (county, census tract, and block group)
resulted in 48 multilevel (with random effect) models among the three levels. Table B16
summarizes the DICs of these models and the lowest DICs are boldfaced. The county level is the
coarsest level used in this study with no nested upper level, so only three regression models
(spatial, weighted regression, and ordinary regression) are developed for each stream health
measure at this level. Similar to the single level analysis, there is no major preference among the
three models developed for each stream health measure at the county level, and the three DICs are
very close (<2%). Meanwhile, at the census tract and block group levels considering the nested
effect of data collected at upper levels, the models’ predictability outperformed the single level

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analysis. For both census tract and block group analysis, combinations of spatial models at the
finest resolution and a mix of spatial and non-spatial models for nested upper levels resulted in
lower DICs compared to the single level models.
Table 21 summarizes the DICs of best selected single level and multilevel models
developed for the four stream health based environmental justice analysis. Multilevel models have
much lower DICs compared to the single level models at the same level, especially in the block
group level where much lower DICs are achieved for the multilevel models compared to the single
level models (ranging from 23% to 120% decrease in DICs). This is also in agreement with
Daneshvar et al (2016) results showing that multilevel models had better performance than single
level models.
Table 21. DICs of the best selected regression models for the census tract and block group
levels
Stream health
index
IBI
HBI
FIBI
EPT

Census tract
Single level
Multilevel
2623.42
2545.98
452.75
374.58
1984.03
1907.28
1378.87
1302.31

Block group
Single level
Multilevel
5964.52
4575.22
1139.18
-232.51
4491.20
3012.60
3301.39
1951.01

Meanwhile, the significant parameters of the best selected models are different from the
former study using a single-phase approach. Table 22 summarizes the significant parameters of
the best selected models for each of the four stream health measures at all three census levels.
Similar to the previous study, both single level and multilevel models had the same
significant parameters. This shows that considering the nested effect of data collected in upper
levels does not change the significant parameters, while at the same time considering the nested
effect of aggregated data at different levels will improve the model prediction. However, a totally
different trend in significant parameters selected was observed in this study. Table 22 shows that
for the fish index (IBI), only two significant parameters (S1, and S3) are selected at the county
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level, while moving to the census tract and block group levels resulted in a change in significant
parameters selected as well as an increase in the total number of parameters selected to three (S5,
S9, and S11), and four (S6, S8, S10, and S17) for the census tract and block group levels
respectively. However, the trend is the opposite for the other three other macroinvertebrate indices
(HBI, FIBI, and EPT). For instance, three significant parameters (S2, S16, and S17) are selected
at the county level, while moving to the census tract and block group levels resulted in a change
in significant parameters selected as well as a decrease in the total number of parameters selected
to only two (S1, and S11), one (S1) for the census tract and block group levels respectively.
Table 22. Significant parameters (in black) for the best-selected stream health based
environmental justice models (Boldfaced values indicate repeated indices from Daneshvar et
al. (2016), while red indices are those from Daneshvar et al. (2016) that are eliminated with
the new approach)
Census
level
County

Census
tract

Block
group

Model type

IBI

HBI

FIBI

EPT

Single level

S1, S3, S7, S11,
S12, S13, S14,
S16, S17

S1, S2, S3,
S5, S10, S13,
S17

S2, S3, S6, S7,
S10, S15, S16,
S17

S1, S2, S3, S5,
S8, S9, S15, S16,
S17

Single level

S5, S9, S11, S16

S3

Multilevel

S5, S9, S11, S16

S3

S1, S2, S10, S11,
S16
S1, S2, S10, S11,
S16

S1, S4, S5, S7,
S9, S11
S1, S4, S5, S7,
S9, S11

Single level

S2, S6, S7, S8,
S10, S16, S17
S2, S6, S7, S8,
S10, S16, S17

S1, S16

S1, S2, S5, S6,
S7
S1, S2, S5, S6,
S7

S1

Multilevel

S1, S16

S1, S17

The same trend of reduction is significant parameters is observed for the HBI and FIBI
when moving from county, to census tract and block group levels, respectively. This dissimilarity
in the trend of significant parameters among fish and macroinvertebrate indices can be explained
by the fact that fish indices measure large scale impacts, while macroinvertebrates are responding
to local stressors (Flinders et al., 2008; Paller et al., 2014; Herman and Nejadhashemi, 2015).
Therefore, for the IBI (fish index) less significant parameters are selected at the county level
92

compared to the two detailed spatial levels of census tract and block group. Meanwhile for
macroinvertebrate indices that are sensitive to local stressors, more parameters are selected as
significant at the coarser resolution compared to finer census levels. This trend was not observed
in the former study by Daneshvar et al. (2016). For instance, six significant parameters (S2, S3,
S6, S10, S15, and S17) were reported for the FIBI at the county level, while at the census tract
level the number of significant parameters was reduced to two (S2, and S10), and again increased
to four (S2, S5, S6, and S7) at the block group level (Daneshvar et al., 2016). Therefore, the
modified stream health scores using the two-phase approach improved model performances not
only in terms of DICs, but also with regard to the type and number of significant parameters
required for stream health based environmental justice models development. This is especially true
for the county level where the number of significant parameters was drastically reduced from 9, 6,
6, and 6, to 2, 1, 4, and 3 for IBI, HBI, FIBI, and EPT, respectively. Therefore, using more accurate
stream health indicators when developing the environmental justice models can help with
mitigating redundancy among predictors while revealing more meaningful relationships.
5.4. Conclusion
The goal of this study was to assess the relative importance of parameter estimation in
stream health based environmental justice model development. The results showed that
incorporating ecologically relevant water quantity and water quality parameters and using a twophase approach will provide more reliable and consistent stream health predictions that are less
sensitive to aggregation at different census levels. Besides that, comparison of significant
parameters selected for the development of stream health based environmental justice models for
one- and two-phase approaches revealed that the modified stream health indices improve stream

93

health based environmental justice models’ performance by reducing redundancies especially at
the county level.
In addition, more meaningful spatial dependencies were observed among fish and
macroinvertebrate indices and socioeconomic/physiographic components using the improved
stream health models, where more significant parameters were selected at the finest level (block
group) compared to the coarsest level (county) for fish index, while the trend was opposite for
macroinvertebrate indices. Finally, in order to better evaluate the robustness of the developed
techniques in this study, it is recommended that future studies will be implemented in other regions
with different socioeconomic and physiographic characteristics.

94

6. CONCLUSIONS
This research study enhanced the existing framework for environmental justice studies with
respect to stream health. Four stream health indices evaluating response of fish and
macroinvertebrates to instream stressors were used for stream health assessment. Meanwhile, in
order to capture the socioeconomic indices representing concentrated disadvantages of a
community, sixteen common indices from the U.S. Census Bureau in addition to one
physiographic index were used to assess the environmental justice conditions within the study
area. In this study, the role of spatial levels in stream health based environmental justice studies
was evaluated. In addition, the significance of parameters estimation on the newly developed
stream health based environmental justice models was assessed. The following conclusions were
made based on the two conducted research studies:


Pairwise correlation was highly sensitive to level of aggregation, especially for social
parameters, where more than 30 significant correlations with absolute correlation
coefficient above 0.7 were found at the county level. Whereas at the census tract and block
group levels, this number drastically reduced to three.



Single level analysis of stream health based environmental justice models revealed that in
general county level models are not able to capture spatial dependencies among stream
health measures and their predictors. Meanwhile, spatial dependencies were seen at the
census tract and block group levels.



Three developed forms of spatial, weighted regression, and ordinary regression models had
quite similar performances at the county level, while at the census tract and block group
levels, spatial models were preferred (with lower DICs).

95



The highest spatial dependencies were found at the block group level, where spatial models
had the lowest DICs compared to two non-spatial models.



In general, multilevel models that incorporate the nested effect of data collected at upper
levels had lower DICs than single level models. Significant parameters required for both
single level and multilevel models were almost the same. That revealed that multilevel
models perform better than the single level models.



Summary of study 1: Incorporation of the spatial level of socioeconomic factors will
improve the predictability of the stream health based environmental justice studies.



Incorporating ecologically relevant water quantity and water quality parameters, using the
two-phase modeling approach, and stream order grouping enhanced the predictability of
the stream health models. Using the new two-phase approach resulted in coefficient of
determinations above 0.9 for all stream health measures. In contrast, the highest coefficient
of determination for the one-phase approach was 0.57.



Comparison of one- and two-phase approaches of stream health modeling showed an
improvement of model predictability of stream health scores by 25% for almost half of the
streams in the study area. However, improvement for the HBI predictor model was
minimum compared to other indices. This is because the HBI evaluates the response of
aquatic ecosystems to organic pollutants; and therefore it is less sensitive to ecologically
relevant hydrologic and water quality parameters than other macroinvertebrates and fish
indices.



In the two-phase stream health modeling approach and similar to the one-phase approach,
the most special dependencies among the stream health and the socioeconomic indices
exist at the block group level, while these dependencies are lost at the county level.

96



Using the two-phase approach and for all four stream health indices, spatial models had
better performances than non-spatial ones at the census tract and block group levels.
However at the county level, both spatial and non-spatial models had similar performances.



Evaluation of spatial correlations between stream health measures and their predictors at
three census levels showed block group data are able to capture vulnerable communities
with both low social and stream health status. However, aggregation of data in upper levels
smoothed these spatial variations especially at the county level.



Summary of study 2: improvement in the accuracy of biological indices predictions will
improve the overall performance of the stream health based environmental justice models.



Overall, using more accurate stream health predictive models provide robust and reliable
stream health predictions while improving the performance of environmental justice
models. We also observed more consistent responses at all three levels of study when more
accurate biological measures were used in study 2.



Studies such as this can help policy makers to better understand the complex
socioeconomic and environmental relationships. Also, using bivariate maps can help with
identification of vulnerable communities.

97

7. FUTURE RESEARCH RECOMMENDATIONS
The ultimate goal of this research is to identify the environmental inequality among different
social groups. This will help water resources managers to find the most suitable places to
implement conservation practices to expand environmental justice. This study improved our
understanding regarding the relationship between aquatic species and socioeconomic factors that
are key in detecting and modeling environmental justice concerning the health of streams.
However, additional works are needed including:

 This study was conducted in the Saginaw River Basin in Michigan. In order to evaluate
the reliability of the proposed methods, regional and national scale analysis of these types
of models are recommended. As a result, different and wider ranges of socioeconomic
and biological characteristics can be examined. The next step is extending analysis for the
entire Michigan. So far, hydrological datasets and models were created for all watersheds
in Michigan. Then all models will be calibrated and validated using flow and water quality
data at monitoring points. Once all hydrologic models are calibrated, their outputs are
going to be used to predict statewide stream health measures. These indices along with
existing socioeconomic/physiographic indices will be used to develop a statewide
environmental justice model.


In this study, one fish and three macroinvertebrate indices were used to examine the
overall health condition of the riverine systems. These indices were commonly used in
the Great Lakes region to evaluate stream health. However, different biological indices
are used in different regions of United States and around the world. Therefore, it is
recommended to establish similar types of relationships between other biological and

98

socioeconomic indices to assure the applicability of the proposed work at larger scales
and for different regions.


Socioeconomic indices that were used here are typically employed to perform
environmental justice studies. However, many of these indices can lose their predictive
ability when aggregated to large scales. Future research should identify and recommend
appropriate scales of use for different socioeconomic indices.



In this study, CAR models were used to evaluate the spatial dependencies among stream
health measures and socioeconomic indices. Future study should examine the
applicability of other techniques, such as spatial autoregressive models, to improve the
reliability and accuracy of the stream health based environmental justice models.

99

APPENDICES

100

APPENDIX A: Study One

Figure A1. Spearman ranks correlation matrix between dependent and independent
variables at the census tract level. Boldfaced value indicates significance at the
0.05 level and correlation less than 0.7, Boldfaced value in red indicates
significance at the 0.05 level and strongly positive correlation equal or above 0.7,
value in blue indicates significance at the 0.05 level and strongly negative
correlation equal or below -0.7

101

Figure A2. Spearman rank correlation matrix between dependent and independent
variables at the block group level. Boldfaced value indicates significance at the 0.05 level
and correlation less than 0.7, Boldfaced value in red indicates significance at the 0.05 level
and strongly positive correlation equal or above 0.7, value in blue indicates significance at
the 0.05 level and strongly negative correlation equal or below -0.7

102

Figure A3. EPT model residuals at: a) census tract single level (no random effect), b)
census tract level with multilevel (random) effect, c) block group single level (no
random effect), d) block group level with multilevel (nested random) effect

103

Figure A4. HBI model residuals at: a) census tract single level (no random effect), b)
census tract level with multilevel (random) effect, c) block group single level (no random
effect), d) block group level with multilevel (nested random) effect

104

Figure A5. FIBI model residuals at: a) census tract single level (no random effect), b)
census tract level with multilevel (random) effect, c) block group single level (no random
effect), d) block group level with multilevel (nested random) effect

105

Figure A6. IBI model residuals at: a) census tract single level (no random effect), b) census
tract level with multilevel (random) effect, c) block group single level (no random effect),
d) block group level with multilevel (nested random) effect

106

Table A1. Regression models for FIBI at census tract level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
14.76
-0.05
1.19
-0.26
-0.80
0.70
0.71
1.65
0.25
1.65
1.83
0.46
-0.14
0.35
1.40
-1.51
-0.65
0.30
96.5
0.93

Spatial
lower
12.54
-0.63
0.31
-0.86
-1.89
-0.16
-0.41
-0.05
-1.62
-0.43
0.33
-0.54
-1.03
-0.82
-0.03
-3.32
-1.62
-0.59
81.8
0.83
1943.58

upper
16.94
0.55
2.09
0.36
0.30
1.57
1.79
3.35
2.23
3.79
3.30
1.47
0.74
1.53
2.86
0.28
0.32
1.22
114.0
0.99

Ordinary regression
mean lower upper
14.68 14.13 15.22
0.07 -0.53
0.65
0.72 -0.24
1.69
-0.98 -1.57 -0.38
-1.44 -2.60 -0.31
0.80 -0.14
1.73
-0.18 -1.35
0.98
1.55 -0.31
3.44
-0.13 -2.27
1.98
2.34
0.10
4.64
2.44
0.79
4.09
0.91
0.01
1.79
0.13 -0.82
1.08
1.67
0.35
2.30
1.07 -0.51
2.65
-1.68 -3.69
0.30
-0.97 -2.14
0.22
0.39 -0.66
1.38
137.4 117.4 160.1
0
0
0
2011.64

107

Weighted regression
mean lower upper
14.82 14.25 15.38
0.23 -0.37 0.83
1.028 0.10 1.95
-0.82 -1.39 -0.24
-1.61 -2.77 -0.45
0.93 -0.07 1.92
-0.22 -1.33 0.89
1.78 -0.09 3.66
-0.02 -2.18 2.20
2.44
0.13 4.78
2.41
0.74 4.05
0.83 -0.08 1.72
0.17 -0.80 1.15
1.57 0.210 2.94
1.24 -0.45 2.89
-1.68 -3.73 0.42
-0.99 -2.12 0.10
0.23 -0.85 1.30
27.3
23.3 31.8
0
0
0
2030.37

Table A2. Regression models for EPT at census tract level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
5.86
-0.11
0.46
-0.04
1.16
-0.63
0.14
-1.36
-0.84
-1.65
-0.73
-0.04
0.24
0.31
-0.42
0.45
0.08
0.39
33.4
0.98

Spatial
lower
3.22
-0.46
-0.07
-0.42
0.48
-1.15
-0.50
-2.36
-1.95
-2.87
-1.59
-0.66
-0.29
-0.41
-1.28
-0.62
-0.47
-0.15
28.3
0.94
1606.74

upper
8.33
0.25
0.99
0.31
1.82
-0.10
0.76
-0.33
0.26
-0.41
0.12
0.57
0.77
0.10
0.44
1.51
0.64
0.92
39.1
0.998

Ordinary regression
mean lower upper
5.98
5.61
6.34
-0.35 -0.74 0.04
0.75
0.11
1.39
-0.98 -1.38 -0.59
0.83
0.04
1.60
-0.14 -0.79 0.49
-0.56 -1.34 0.19
-0.59 -1.82 0.62
-0.27 -1.71 1.16
-0.73 -2.25 0.79
-1.24 -2.32 -0.18
0.30 -0.30 0.88
0.77
0.12
1.40
0.71 -0.22 1.61
-0.76 -1.79 0.28
1.31
0.02
2.65
-0.41 -1.15 0.37
0.56 -0.14 1.24
60.6
51.8
70.4
0
0
0
1743.92

108

Weighted regression
mean lower upper
5.94
5.57
6.32
-0.29 -0.68
0.10
0.96
0.33
1.58
-1.10 -1.50 -0.70
0.86 0.070 1.65
-0.14 -0.79
0.49
-0.66 -1.43
0.13
-0.53 -1.78
0.73
-0.31 -1.75
1.15
-0.76 -2.31
0.78
-1.18 -2.28 -0.05
0.36 -0.25
0.95
1.05
0.39
1.71
0.51 -0.43
1.39
-0.67 -1.78
0.45
1.19 -0.21
2.58
-0.43 -1.18
0.33
0.70
0.01
1.43
12.4
10.6
14.5
0
0
0
1773.60

Table A3. Regression models for HBI at census tract level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
4.82
0.12
-0.15
0.18
0.09
-0.01
-0.22
0.12
-0.32
-0.47
-0.01
-0.13
-0.09
0.18
0.04
0.08
-0.05
-0.15
6.5
0.93

Spatial
lower
4.26
-0.03
-0.38
0.02
-0.20
-0.23
-0.50
-0.32
-0.81
-1.02
-0.37
-0.40
-0.32
-0.13
-0.33
-0.38
-0.29
-0.39
5.6
0.83
1062.41

upper
5.36
0.27
0.09
0.34
0.38
0.22
0.07
0.56
0.17
0.07
0.38
0.13
0.14
0.49
0.41
0.55
0.20
0.09
7.7
0.99

Ordinary regression
mean lower upper
4.82
4.68
4.95
0.15 -0.01 0.30
-0.16 -0.40 0.09
0.50
0.35
0.65
0.19 -0.10 0.50
-0.18 -0.42 0.06
0.06 -0.23 0.36
0.10 -0.38 0.59
-0.29 -0.85 0.26
-0.65 -1.23 -0.06
0.01 -0.41 0.45
-0.28 -0.50 -0.04
-0.34 -0.60 -0.10
-0.17 -0.51 0.18
0.01 -0.40 0.42
-0.02 -0.54 0.49
0.04 -0.25 0.34
-0.08 -0.35 0.17
9.1
7.8
10.6
0
0
0
1124.94

109

Weighted regression
mean lower upper
4.83
4.69
4.97
0.14 -0.02 0.29
-0.26 -0.50 -0.01
0.49
0.34
0.65
0.20 -0.10 0.51
-0.19 -0.44 0.07
0.09 -0.20 0.38
0.05 -0.44 0.54
-0.30 -0.88 0.27
-0.67 -1.28 -0.07
0.03 -0.38 0.46
-0.25 -0.48 -0.02
-0.40 -0.66 -0.15
-0.08 -0.44 0.28
-0.03 -0.46 0.40
0.01 -0.53 0.53
0.05 -0.24 0.34
-0.10 -0.38 0.17
1.9
1.6
2.2
0
0
0
1151.03

Table A4. Regression models for IBI at census tract level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

Spatial
mean lower
49.25 46.55
0.28 -0.52
-0.85 -2.02
0.02 -0.84
0.58 -0.93
-0.77 -2.00
-0.12 -1.60
1.54 -0.77
-1.51 -4.13
-1.21 -4.07
-1.98 -3.96
-0.89 -2.25
0.73 -0.53
0.19 -1.44
-1.25 -3.21
2.28 -0.21
-2.21 -3.50
0.73 -0.51
180.7 153.2
0.92
0.82
2146.73

upper
52.09
1.07
0.41
0.88
2.11
0.41
1.38
3.85
1.09
1.56
0.01
0.47
1.94
1.81
0.76
4.63
-0.89
1.96
212.9
0.99

Ordinary regression
mean lower upper
49.27 48.51 50.03
0.45 -0.35 1.26
-0.74 -2.12 0.59
-1.07 -1.90 -0.26
0.12 -1.46 1.72
-0.97 -2.26 0.32
-1.03 -2.65 0.56
1.18 -1.38 3.71
-1.39 -4.37 1.56
-0.83 -3.96 2.33
-2.17 -4.36 0.02
-0.09 -1.30 1.14
1.38
0.08
2.71
1.01 -0.86 2.87
-2.34 -4.48 -0.15
3.34
0.59
6.04
-2.32 -3.92 -0.71
0.81 -0.59 2.19
257.6 219.7 301.7
0
0
0
2217.03

110

Weighted regression
mean lower upper
49.30 48.53
50.07
0.46 -0.36
1.27
-0.48 -1.76
0.78
-1.15 -1.98
-0.31
0.36 -1.27
1.98
-1.14 -2.48
0.23
-0.76 -2.41
0.82
0.55 -2.13
3.15
-1.54 -4.61
1.57
-1.22 -4.41
1.97
-1.96 -4.20
0.32
0.10 -1.13
1.30
1.50
0.14
2.85
0.32 -1.58
2.18
-2.47 -4.74
-0.11
3.11
0.31
5.92
-1.77 -3.35
-0.16
1.11 -0.37
2.63
52.9
45.2
61.9
0
0
0
2247.36

Table A5. Regression models for FIBI at block group level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
14.55
0.301
0.98
-0.09
-0.06
0.51
0.72
0.98
-0.42
0.46
-0.01
-0.33
0.14
-0.31
0.17
0.10
-0.06
0.11
95.55
0.97

Spatial
lower
12.44
-0.07
0.50
-0.50
-0.70
0.001
0.08
0.16
-1.37
-0.65
-0.65
-0.91
-0.28
-0.83
-0.55
-0.72
-0.52
-0.33
86.16
0.93
4370.06

upper
16.62
0.67
1.47
0.30
0.58
1.00
1.40
1.78
0.52
1.52
0.61
0.24
0.56
0.22
0.90
0.92
0.40
0.56
106.9
0.99

Ordinary regression
mean lower upper
14.43 14.03 14.82
0.59
0.17
1.01
0.82
0.29
1.36
-0.44 -0.85 -0.03
-0.75 -1.51 -0.02
0.37 -0.22 0.95
-0.35 -1.02 0.31
0.61 -0.31 1.55
-1.39 -2.54 -0.24
0.41 -0.94 1.72
0.37 -0.42 1.17
0.13 -0.39 0.66
0.07 -0.43 0.58
0.80
0.11
1.47
-0.16 -1.04 0.71
-0.05 -1.11 1.02
-0.13 -0.71 0.45
0.30 -0.24 0.84
158.7 143.3 175.5
0
0
0
4622.94

111

Weighted regression
mean lower upper
14.57 14.14 14.99
0.53
0.08
0.99
0.86
0.31
1.41
-0.57 -1.03 -0.11
-1.30 -2.13 -0.49
0.75
0.10
1.39
-0.17 -0.86
0.49
0.96 -0.04
2.00
-1.09 -2.31
0.15
1.17 -0.27
2.65
0.42 -0.46
1.28
0.30 -0.26
0.86
-0.14 -0.69
0.43
0.60 -0.12
1.33
-0.51 -1.49
0.51
0.08 -1.09
1.28
-0.08 -0.69
0.52
0.18 -0.43
0.79
34.9 31.53 38.77
0
0
0
4744.49

Table A6. Regression models for EPT at block group level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

Spatial
mean lower
5.51
4.03
-0.12 -0.33
-0.02 -0.29
0.02 -0.20
0.13 -0.22
-0.12 -0.40
0.08 -0.26
-0.19 -0.64
-0.05 -0.56
-0.16 -0.74
0.15 -0.19
-0.09 -0.42
0.16 -0.07
0.05 -0.26
0.27 -0.13
-0.30 -0.76
0.22 -0.03
-0.24 -0.48
29.30 26.37
0.98
0.95
3505.78

upper
6.97
0.08
0.24
0.25
0.48
0.16
0.45
0.26
0.47
0.44
0.50
0.23
0.40
0.35
0.69
0.15
0.47
0.01
32.61
0.996

Ordinary regression
mean lower upper
5.59 5.362 5.82
-0.25 -0.50 -0.01
-0.17 -0.49 0.16
-0.72 -0.97 -0.48
0.23 -0.20 0.66
-0.19 -0.54 0.14
0.12 -0.27 0.50
0.05 -0.51 0.61
0.29 -0.39 0.97
0.11 -0.69 0.91
0.19 -0.27 0.65
0.10 -0.22 0.41
0.23 -0.08 0.54
0.18 -0.22 0.57
0.27 -0.26 0.77
-0.34 -0.93 0.29
0.16 -0.18 0.50
-0.01 -0.32 0.31
55.32 49.86 61.25
0
0
0
3844.15

112

Weighted regression
mean lower upper
5.63
5.37
5.88
-0.27 -0.54 -0.01
-0.13 -0.45 0.19
-1.08 -1.35 -0.82
0.39 -0.13 0.80
-0.21 -0.60 0.17
0.11 -0.28 0.52
-0.11 -0.71 0.49
0.38 -0.36 1.14
0.06 -0.80 0.96
0.14 -0.36 0.63
0.23 -0.11 0.58
0.32 -0.02 0.67
0.15 -0.28 0.57
0.18 -0.39 0.75
-0.34 -1.04 0.36
0.20 -0.16 0.57
0.09 -0.26 0.44
12.03 10.86 13.32
0
0
0
3956.94

Table A7. Regression models for HBI at block group level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

mean
5.01
-0.11
-0.07
0.04
0.09
-0.01
-0.01
0.05
-0.04
-0.22
0.08
0.05
-0.01
0.04
0.12
-0.13
-0.12
-0.01
5.90
0.95

Spatial
lower
4.60
-0.20
-0.19
-0.06
-0.06
-0.13
-0.16
-0.16
-0.28
-0.49
-0.07
-0.09
-0.12
-0.09
-0.06
-0.34
-0.24
-0.12
5.31
0.91
2305.94

upper
5.38
-0.02
0.05
0.14
0.25
0.12
0.15
0.25
0.18
0.04
0.24
0.20
0.09
0.18
0.30
0.07
-0.01
0.09
6.58
0.99

Ordinary regression
mean lower upper
5.015 4.92
5.10
-0.07 -0.18 0.03
0.01 -0.12 0.14
0.34
0.24
0.44
0.20
0.02
0.38
-0.06 -0.20 0.08
0.08 -0.08 0.24
0.10 -0.13 0.33
-0.13 -0.40 0.15
-0.50 -0.82 -0.18
0.05 -0.15 0.24
-0.01 -0.14 0.12
-0.03 -0.16 0.10
-0.10 -0.26 0.05
0.13 -0.08 0.34
-0.07 -0.32 0.19
-0.17 -0.31 -0.03
-0.01 -0.15 0.12
9.33
8.42 10.35
0
0
0
2528.70

113

Weighted regression
mean lower upper
4.99
4.89
5.09
-0.07 -0.18 0.04
0.02
-0.11 0.15
0.43
0.33
0.54
0.24 0.045 0.44
-0.10 -0.25 0.06
0.04
-0.12 0.21
0.11
-0.14 0.36
-0.29 -0.59 0.02
-0.71 -1.06 -0.36
0.03
-0.18 0.23
-0.04 -0.17 0.10
-0.06 -0.20 0.07
-0.13 -0.30 0.05
0.15
-0.08 0.38
-0.05 -0.33 0.23
-0.14 -0.28 0.01
0.03
-0.13 0.18
2.06
1.85
2.28
0
0
0
2651.31

Table A8. Regression models for IBI at block group level (boldfaced values indicates a
significant parameter at the 0.05 level)
Parameters
β0
β1
β2
β3
β4
β5
β6
β7
β8
β9
β10
β11
β12
β13
β14
β15
β16
β17
𝜏2
𝛾
DIC

Spatial
mean lower
49.14 47.79
0.34 -0.29
-0.9 -1.75
-0.57 -1.26
-0.69 -1.75
-0.29 -1.13
-0.42 -1.45
1.74
0.38
-0.56 -2.16
0.39 -1.42
-0.38 -1.48
-0.37 -1.27
0.07 -0.66
0.5
-0.42
-0.93 -2.15
1.01 -0.38
-0.92 -1.71
0.15 -0.60
281.2 252.8
0.84
0.74
5120.12

upper
50.47
0.96
-0.08
0.08
0.36
0.57
0.67
3.11
1.07
2.197
0.69
0.50
0.83
1.43
0.32
2.45
-0.13
0.89
313.7
0.93

Ordinary regression
mean lower upper
48.98 48.4 49.56
0.81
0.19
1.43
-1.7 -2.51 -0.85
-0.94 -1.55 -0.34
-0.77 -1.87 0.34
-0.48 -1.37 0.36
-0.64 -1.6
0.38
1.00 -0.38 2.43
-1.19 -2.98 0.52
0.09 -1.94 2.06
-0.59 -1.81 0.59
0.17 -0.62 0.95
0.38 -0.41 1.20
1.35
0.35
2.38
-1.44 -2.77 -0.15
1.09 -0.48 2.69
-1.22 -2.09 -0.35
0.14 -0.66 0.94
354.2 319.4 393.2
0
0
0
5216.79

114

Weighted regression
mean lower upper
48.99 48.4
49.6
0.59
-0.05
1.21
-1.71 -2.51 -0.92
-1.14 -1.77
-0.5
-0.97 -2.17
0.21
-0.41 -1.36
0.52
-0.65 -1.66
0.33
0.86
-0.60
2.35
-1.09 -2.92
0.70
0.17
-1.95
2.24
-0.76 -2.00
0.51
0.36
-0.46
1.18
0.23
-0.56
1.04
1.43
0.40
2.45
-1.74 -3.14 -0.32
1.24
-0.47
2.96
-1.26 -2.11 -0.42
0.24
-0.63
1.11
71.6
64.7
79.3
0
0
0
5275.78

APPENDIX B: Study Two

Table B1. Input parameters used for stream health predictive models
Modeling
approach
Onephase

Stream health
Water quantity
measure
IBI*
2 indices including:
1 annual average of flow, and
1 stream segment gradient
HBI**

1 index of cross-sectional area

FIBI**

2 indices including:
1 annual average of flow, and
1 cross-sectional area

EPT**

2 indices including:
1 seasonal average of flow, and
1 cross-sectional area
TwoAll
171 indices introduced by Poff et
phase
al. (1997), including:
94 indices of magnitude,
14 indices of frequency,
44 indices of duration,
10 indices of timing, and
9 indices of rate of change in
flow.
*
This data was obtained from Einheuser et al. (2013a)
**
This data was obtained from Einheuser et al. (2012)

115

Water quality
3 indices including:
1 annual average of phosphorus, and
2 seasonal averages of nitrogen
concentrations
3 indices including:
2 annual averages of nitrogen, and
1 seasonal average of nitrogen
concentrations
2 indices including:
1 annual average of nitrogen, and
1 annual average of phosphorus
concentrations
2 annual average indices of nitrogen
concentration
78 indices, including:
1 annual average,
1 annual average of coefficient of
variation,
12 seasonal averages, and
12 seasonal averages of coefficient
of variations for sediment, total
nitrogen, and total phosphorus loads.

Table B2. Comparison of root-mean-square error of developed stream health predictive
models
Stream
One-phase
Two-phase
health
approach
approach
measures
All streams
All streams
Headwater streams
IBI
16.37*
7.56****
6.24****
**
***
HBI
0.45
0.27
0.21***
**
***
FIBI
5.46
4.14
1.71***
**
***
EPT
2.57
2.04
0.73***
*
This data was obtained from Einheuser et al. (2013a)
**
This data was obtained from Einheuser et al. (2012)
***
This data was obtained from Daneshvar et al. (2017)
****
Results obtained from this study

116

Medium and large streams
4.96****
0.11***
2.01***
1.10***

Table B3. Regression models for IBI at county level (Boldfaced values indicate significant
parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
45.15
-10.21
-28.10
13.04
-4.29
-6.13
5.22
-7.79
11.02
9.46
81.90
0.42
14.69
-3.24
10.70
-63.48
-6.27
1.53
181.19
-0.14

spatial
lower
41.25
-15.65
-88.45
2.99
-15.89
-22.34
-11.74
-23.15
-23.49
-33.63
-58.65
-12.59
-4.23
-18.23
-12.15
-163.35
-17.01
-15.43
56.99
-0.97
156.50

upper
49.14
-4.89
29.65
23.50
7.20
10.23
21.78
8.03
45.46
52.51
228.29
13.63
34.34
11.55
33.85
33.08
3.78
19.23
493.82
0.93

Weighted regression
mean
lower
upper
45.04
41.74
48.34
-10.44 -16.77
-4.32
-33.09 -96.69
29.10
14.07
3.34
24.65
-5.03
-18.38
8.02
-6.59
-27.57
14.07
4.30
-13.43
21.47
-6.71
-23.73
10.91
9.27
-28.02
47.25
6.92
-39.72
54.71
94.54
-49.31 240.04
1.24
-13.55
15.83
16.67
-4.22
37.40
-3.57
-17.06
10.34
11.06
-13.09
34.49
-71.27 -173.41 31.56
-6.36
-18.83
6.02
-0.75
-20.03
19.15
56.25
16.03 175.95
0.00
0.00
0.00
158.74

117

Ordinary regression
mean
lower
upper
45.20
42.20
48.26
-10.14 -15.55
-4.39
-28.48 -87.58
29.80
13.41
2.54
23.50
-4.24
-15.88
7.68
-6.30
-23.61
10.68
5.27
-11.23
22.16
-7.91
-24.59
8.25
11.14
-24.40
46.32
9.29
-35.75
52.58
82.46
-61.00
224.19
0.31
-13.22
13.93
14.99
-5.71
34.22
-3.73
-18.16
10.94
10.39
-13.25
32.44
-63.70 -162.81
35.06
-6.12
-16.76
4.93
1.20
-16.95
19.20
202.35
63.39
599.48
0.00
0.00
0.00
156.65

Table B4. Regression models for HBI at county level (Boldfaced values indicate significant
parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
4.96
0.28
1.77
-0.06
0.19
0.12
-0.29
0.38
0.60
0.65
-4.60
-0.06
-0.12
-0.22
-0.50
3.08
0.02
0.09
0.32
0.09

spatial
lower
4.76
0.04
-0.67
-0.50
-0.30
-0.59
-0.95
-0.28
-0.84
-1.17
-10.47
-0.62
-0.94
-0.82
-1.47
-1.01
-0.41
-0.63
0.10
-0.95
22.47

upper
5.17
0.51
4.15
0.37
0.66
0.80
0.39
1.05
2.03
2.39
1.26
0.48
0.68
0.37
0.41
7.09
0.47
0.81
0.96
0.96

Weighted regression
mean lower upper
4.95
4.83
5.07
0.28
0.04
0.51
1.98
-0.62
4.37
-0.07
-0.47
0.31
0.23
-0.26
0.73
0.12
-0.67
0.90
-0.21
-0.86
0.47
0.28
-0.42
0.98
0.64
-0.94
2.03
0.69
-1.19
2.40
-4.96 -10.52 0.79
-0.06
-0.62
0.50
-0.17
-0.95
0.56
-0.21
-0.75
0.32
-0.56
-1.50
0.39
3.25
-0.80
7.17
0.01
-0.45
0.48
0.15
-0.58
0.90
0.08
0.02
0.23
0.00
0.00
0.00
22.08

118

Ordinary regression
mean lower upper
4.95
4.83
5.08
0.27
0.05
0.50
1.73
-0.63
4.08
-0.06
-0.49
0.37
0.19
-0.30
0.67
0.10
-0.60
0.80
-0.28
-0.95
0.42
0.36
-0.29
0.99
0.61
-0.84
2.16
0.66
-1.12
2.52
-4.48 -10.20 1.40
-0.06
-0.60
0.50
-0.11
-0.89
0.71
-0.23
-0.85
0.37
-0.49
-1.46
0.48
2.99
-1.15
6.97
0.03
-0.43
0.46
0.10
-0.64
0.84
0.34
0.11
1.07
0.00
0.00
0.00
21.72

Table B5. Regression models for FIBI at county level (Boldfaced values indicate significant
parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
14.88
0.88
23.30
-0.49
0.61
-3.31
3.69
-5.04
4.12
6.30
-29.89
-0.72
3.93
0.67
-0.40
9.12
-4.28
7.45
14.21
-0.06

spatial
lower
13.64
-0.64
7.03
-3.30
-2.47
-8.05
-0.88
-9.59
-5.60
-5.36
-69.31
-4.44
-1.43
-3.30
-6.86
-18.98
-7.16
2.44
4.38
-0.97
102.85

upper
16.14
2.46
39.78
2.30
3.89
1.34
8.25
-0.57
13.87
18.41
10.77
2.83
9.19
4.71
6.14
36.11
-1.30
12.25
40.10
0.96

Weighted regression
mean lower upper
14.80 13.93 15.68
0.70
-0.98
2.32
22.64
5.90 39.48
-0.40
-3.26
2.58
0.58
-2.88
4.12
-3.63
-9.13
1.84
3.94
-0.77
8.48
-5.23 -10.04 -0.49
3.79
-6.66 14.43
5.75
-7.49 18.78
-28.71 -69.45 10.96
-0.49
-4.60
3.56
4.06
-1.37
9.46
0.89
-3.13
4.72
-0.35
-6.82
6.21
8.41
-19.97 37.58
-4.30
-7.58 -1.06
7.19
1.92 12.53
4.04
1.23 11.68
0.00
0.00
0.00
105.09

119

Ordinary regression
mean lower upper
14.89 14.00 15.73
0.87
-0.75
2.44
23.32
7.26 38.89
-0.38
-3.30
2.55
0.58
-2.75
3.90
-3.36
-7.97
1.25
3.71
-0.95
8.24
-5.07
-9.39 -0.62
4.39
-5.67 14.26
6.54
-5.96 18.74
-29.96 -68.95 9.27
-0.81
-4.60
2.87
4.03
-1.35
9.36
0.67
-3.26
4.77
-0.31
-6.99
6.28
9.02
-18.43 36.10
-4.35
-7.29 -1.42
7.42
2.66 12.25
15.47
4.99 46.06
0.00
0.00
0.00
102.42

Table B6. Regression models for EPT at county level (Boldfaced values indicate significant
parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
7.44
0.79
16.01
-0.99
0.95
-3.24
0.18
0.21
0.19
-0.69
-28.93
-1.55
1.11
0.29
-0.34
14.95
-2.88
5.18
8.58
-0.10

spatial
lower
6.56
-0.42
3.54
-3.25
-1.57
-6.88
-3.34
-3.12
-7.55
-10.00
-58.44
-4.32
-3.14
-2.82
-5.28
-6.99
-5.14
1.34
2.63
-0.96
91.50

upper
8.31
1.95
28.37
1.29
3.52
0.37
3.78
3.71
7.55
8.19
1.72
1.27
5.21
3.34
4.50
36.04
-0.54
9.01
25.85
0.94

Weighted regression
mean lower upper
7.35
6.70
8.01
0.73
-0.57
2.05
16.37
3.46 29.49
-0.89
-3.14
1.33
1.02
-1.73
3.81
-3.25
-7.52
0.93
0.59
-3.06
4.21
-0.18
-3.70
3.45
-0.02
-8.09
7.99
-1.01 -11.25 9.34
-29.22 -60.29 1.09
-1.31
-4.42
1.67
1.16
-3.19
5.50
0.42
-2.54
3.26
-0.59
-5.84
4.61
14.88 -6.91 37.13
-2.98
-5.60 -0.46
5.03
1.03
9.07
2.39
0.76
7.02
0.00
0.00
0.00
94.33

120

Ordinary regression
mean lower upper
7.43
6.77
8.09
0.78
-0.46
2.02
15.91
3.76 28.30
-0.94
-3.34
1.29
0.94
-1.46
3.44
-3.26
-6.98
0.42
0.24
-3.23
3.85
0.17
-3.40
3.76
0.28
-6.96
7.79
-0.63
-9.95
8.45
-29.02 -59.22 0.48
-1.57
-4.46
1.34
1.11
-3.17
5.47
0.28
-2.75
3.47
-0.30
-5.11
4.72
15.03
-5.39 36.06
-2.88
-5.12 -0.53
5.16
1.40
9.23
9.53
2.91 29.57
0.00
0.00
0.00
91.56

Table B7. Regression models for IBI at census tract level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

spatial
mean
lower upper
40.25 28.58 51.49
-0.15
-1.82
1.56
0.13
-2.37
2.64
-0.97
-2.65
0.77
2.37
-0.73
5.50
-4.68
-7.14
-2.22
-0.34
-3.43
2.65
0.76
-4.02
5.53
-1.39
-6.61
4.12
-6.03 -11.87 -0.05
-2.06
-6.23
2.05
-3.33
-6.20
-0.38
-0.87
-3.37
1.64
-2.56
-5.81
0.72
1.38
-2.66
5.42
-0.87
-5.94
4.14
-0.77
-3.44
1.94
1.35
-1.15
3.87
748.36 635.32 880.81
0.98
0.93
1.00
2623.42

Weighted regression
mean
lower
upper
40.87
39.06
42.64
-1.95
-3.84
-0.03
0.14
-2.81
3.08
-2.02
-3.85
-0.21
2.80
-0.90
6.47
-6.00
-9.17
-2.85
-3.00
-6.54
0.51
-0.22
-6.18
5.74
-0.30
-7.15
6.75
-4.69 -12.03
2.73
0.29
-5.00
5.51
-5.89
-8.80
-3.06
-2.46
-5.55
0.66
0.80
-3.52
5.13
3.21
-2.18
8.44
-2.86
-9.38
3.79
-3.06
-6.64
0.43
0.64
-2.79
4.05
275.47 234.80 320.85
0.00
0.00
0.00
2786.37

121

Ordinary regression
mean
lower
upper
40.46
38.72
42.18
-2.02
-3.92
-0.16
-0.02
-3.07
3.06
-2.11
-3.98
-0.21
3.04
-0.63
6.63
-6.07
-9.09
-3.11
-1.71
-5.44
1.97
-1.49
-7.41
4.52
-1.66
-8.47
5.02
-5.60
-12.70
1.73
0.49
-4.75
5.72
-5.90
-8.77
-3.10
-2.13
-5.14
0.90
1.51
-2.71
5.72
2.46
-2.57
7.47
-3.01
-9.37
3.29
-3.27
-6.97
0.50
-0.05
-3.41
3.10
1385.93 1184.42 1614.95
0.00
0.00
0.00
2767.44

Table B8. Regression models for HBI at census tract level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
5.23
0.00
-0.02
0.02
0.04
-0.01
0.08
-0.04
0.03
-0.02
0.12
0.03
0.00
-0.08
-0.01
-0.15
0.03
0.00
0.98
0.97

spatial
lower
4.83
-0.06
-0.11
-0.04
-0.08
-0.10
-0.03
-0.22
-0.16
-0.23
-0.03
-0.08
-0.09
-0.20
-0.15
-0.33
-0.06
-0.09
0.83
0.93
452.75

upper
5.61
0.07
0.08
0.08
0.15
0.08
0.18
0.13
0.22
0.20
0.27
0.13
0.09
0.04
0.14
0.04
0.13
0.09
1.15
1.00

Weighted regression
mean lower upper
5.22
5.16
5.28
0.07
0.00
0.13
0.04 -0.06
0.14
-0.03 -0.09
0.04
0.03 -0.09
0.16
0.05 -0.06
0.15
0.13
0.01
0.26
0.03 -0.17
0.23
0.01 -0.23
0.24
-0.08 -0.33
0.17
0.03 -0.14
0.21
0.18
0.09
0.28
0.06 -0.05
0.17
-0.18 -0.33 -0.04
-0.08 -0.25
0.10
-0.06 -0.29
0.16
0.06 -0.07
0.18
0.06 -0.05
0.18
0.32
0.27
0.37
0.00
0.00
0.00
577.96

122

Ordinary regression
mean lower upper
5.23 5.17
5.29
0.06 0.00
0.13
0.05 -0.05 0.16
-0.02 -0.09 0.05
0.03 -0.10 0.16
0.05 -0.06 0.15
0.13 0.01
0.26
-0.01 -0.21 0.19
0.00 -0.24 0.24
-0.08 -0.33 0.17
0.02 -0.16 0.19
0.21 0.11
0.31
0.05 -0.06 0.16
-0.21 -0.37 -0.06
-0.09 -0.26 0.08
-0.05 -0.26 0.17
0.10 -0.02 0.23
0.09 -0.03 0.20
1.66 1.42
1.93
0.00 0.00
0.00
567.20

Table B9. Regression models for FIBI at census tract level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
12.81
0.88
-0.11
0.52
-0.37
-0.54
-0.90
1.62
-1.79
-1.63
-1.33
-1.28
-0.47
0.48
0.55
1.10
-1.32
0.51
107.96
0.95

spatial
lower upper
9.90
15.63
0.25
1.49
-1.09
0.86
-0.11
1.16
-1.56
0.84
-1.47
0.38
-2.07
0.26
-0.20
3.41
-3.80
0.22
-3.88
0.59
-2.87
0.25
-2.37
-0.18
-1.42
0.47
-0.75
1.72
-0.98
2.06
-0.77
3.03
-2.32
-0.31
-0.48
1.47
92.13 126.42
0.88
0.99
1984.03

Weighted regression
mean lower upper
12.76 12.15 13.37
0.98
0.33
1.64
-1.04 -2.06
0.01
1.29
0.65
1.94
-0.27 -1.53
1.03
-1.40 -2.46 -0.31
-1.18 -2.44
0.05
1.25
-0.81
3.30
-1.16 -3.60
1.27
-1.10 -3.64
1.44
-0.42 -2.16
1.39
-2.03 -2.99 -1.05
-1.51 -2.63 -0.45
-0.21 -1.72
1.31
0.23
-1.58
2.05
-0.03 -2.29
2.15
-0.93 -2.15
0.29
0.67
-0.51
1.80
32.81 27.99 38.47
0.00
0.00
0.00
2090.95

123

Ordinary regression
mean
lower upper
12.71 12.11 13.30
0.98
0.32
1.64
-0.86
-1.92
0.21
1.25
0.58
1.90
-0.39
-1.67
0.93
-1.26
-2.30
-0.24
-0.88
-2.15
0.39
1.23
-0.84
3.37
-1.67
-4.09
0.71
-1.33
-3.86
1.23
-0.53
-2.38
1.34
-2.22
-3.21
-1.22
-1.26
-2.34
-0.19
-0.13
-1.62
1.37
0.30
-1.47
2.05
0.21
-2.02
2.43
-1.14
-2.39
0.15
0.58
-0.57
1.69
170.00 145.41 197.76
0.00
0.00
0.00
2081.21

Table B10. Regression models for EPT at census tract level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
5.80
0.38
0.22
0.20
-0.32
-0.21
-0.06
0.18
-0.05
0.00
-0.13
-0.51
0.01
-0.02
0.04
0.18
-0.19
0.06
16.64
0.98

spatial
lower
4.08
0.13
-0.13
-0.06
-0.78
-0.59
-0.52
-0.52
-0.85
-0.86
-0.74
-0.93
-0.38
-0.52
-0.57
-0.58
-0.59
-0.32
14.19
0.93
1378.87

upper
7.58
0.63
0.60
0.46
0.15
0.15
0.40
0.89
0.75
0.85
0.47
-0.08
0.38
0.47
0.65
0.90
0.21
0.44
19.55
1.00

Weighted regression
mean lower upper
5.91
5.67
6.16
0.16
-0.10 0.42
0.25
-0.16 0.66
-0.01
-0.27 0.26
-0.34
-0.87 0.17
-0.29
-0.72 0.15
-0.68
-1.20 -0.17
0.00
-0.86 0.83
-0.06
-1.04 0.93
0.29
-0.73 1.31
0.07
-0.64 0.80
-1.05
-1.44 -0.66
0.10
-0.33 0.53
0.44
-0.17 1.04
0.31
-0.42 1.06
0.11
-0.78 1.01
-0.50
-1.01 0.01
0.02
-0.45 0.51
5.41
4.62
6.33
0.00
0.00
0.00
1501.52

124

Ordinary regression
mean lower upper
5.83 5.57
6.08
0.10 -0.17
0.37
0.15 -0.31
0.60
-0.01 -0.29
0.26
-0.34 -0.87
0.20
-0.29 -0.72
0.15
-0.62 -1.16 -0.09
-0.10 -0.96
0.75
-0.21 -1.21
0.78
0.19 -0.86
1.26
0.06 -0.68
0.80
-1.05 -1.46 -0.64
0.08 -0.36
0.53
0.49 -0.14
1.11
0.13 -0.59
0.87
0.21 -0.71
1.12
-0.44 -0.98
0.11
0.01 -0.46
0.47
29.10 24.82 34.08
0.00 0.00
0.00
1503.99

Table B11. Regression models for IBI at block group level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameter
s
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

spatial
mean
39.00
0.79
-1.18
-0.63
0.36
-0.98
-3.86
1.77
2.89
0.68
-2.14
-0.79
-1.02
-0.50
-0.46
1.82
0.88
1.54

lower
27.53
-0.30
-2.60
-1.81
-1.48
-2.48
-5.74
-0.61
0.13
-2.55
-4.00
-2.52
-2.25
-2.01
-2.57
-0.57
-0.47
0.24

810.55
0.99

731.39
0.97
5964.52

Weighted regression
upper
49.97
1.88
0.24
0.53
2.23
0.44
-1.90
4.14
5.61
3.78
-0.31
0.90
0.21
1.03
1.67
4.20
2.21
2.83
901.9
7
1.00

mean
39.39
-1.43
-2.07
-2.97
0.96
-3.25
-4.30
0.30
2.59
0.27
-1.60
-4.19
-2.52
0.18
-0.73
1.03
-0.31
1.42
353.4
6
0.00

lower upper
38.01 40.73
-2.87
0.04
-3.81
-0.30
-4.42
-1.50
-1.68
3.53
-5.34
-1.21
-6.49
-2.19
-2.91
3.59
-1.30
6.53
-4.31
5.00
-4.37
1.15
-5.94
-2.39
-4.29
-0.72
-2.11
2.50
-3.87
2.51
-2.70
4.83
-2.24
1.61
-0.53
3.37
318.9 392.2
7
1
0.00
0.00
6454.62

125

Ordinary regression
mean
39.31
-1.63
-1.72
-2.70
1.90
-2.82
-3.97
-0.30
2.03
-0.47
-1.46
-3.81
-2.18
0.41
-0.58
0.68
0.13
1.23
1765.4
5
0.00

lower
38.00
-3.03
-3.51
-4.08
-0.63
-4.79
-6.22
-3.38
-1.82
-4.96
-4.10
-5.55
-3.85
-1.87
-3.51
-2.85
-1.79
-0.59
1593.5
3
0.00
6403.28

upper
40.61
-0.21
0.08
-1.34
4.34
-0.89
-1.76
2.83
5.85
3.91
1.21
-2.05
-0.45
2.65
2.34
4.25
2.10
3.04
1952.2
8
0.00

Table B12. Regression models for HBI at block group level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

mean
5.23
-0.03
-0.04
-0.01
-0.02
-0.01
0.03
-0.02
0.05
0.01
-0.02
-0.01
-0.03
0.05
0.03
-0.01
0.00
0.01
1.19
0.98

spatial
lower
4.94
-0.07
-0.10
-0.05
-0.09
-0.07
-0.04
-0.11
-0.06
-0.10
-0.09
-0.08
-0.08
-0.01
-0.05
-0.10
-0.05
-0.04
1.07
0.95
1139.18

upper
5.52
0.01
0.01
0.04
0.05
0.04
0.10
0.07
0.15
0.13
0.05
0.06
0.02
0.11
0.11
0.08
0.05
0.05
1.33
1.00

Weighted regression
mean lower upper
5.23
5.18
5.27
0.01 -0.04
0.06
-0.10 -0.16 -0.03
-0.02 -0.07
0.03
-0.08 -0.17
0.01
0.03 -0.04
0.10
0.07 -0.01
0.15
0.07 -0.04
0.19
0.14
0.00
0.28
0.05 -0.12
0.22
-0.10 -0.19 -0.01
0.10
0.04
0.17
-0.02 -0.08
0.05
0.01 -0.07
0.09
-0.05 -0.16
0.05
0.07 -0.06
0.20
0.01 -0.06
0.08
0.02 -0.05
0.09
0.43
0.38
0.47
0.00
0.00
0.00
1488.91

126

Ordinary regression
mean lower upper
5.23
5.18
5.28
0.02 -0.03 0.07
-0.10 -0.17 -0.04
-0.01 -0.06 0.04
-0.10 -0.19 -0.01
0.01 -0.06 0.08
0.08
0.01
0.16
0.06 -0.05 0.17
0.11 -0.03 0.24
0.03 -0.13 0.19
-0.09 -0.19 0.00
0.11
0.04
0.17
-0.03 -0.09 0.03
0.02 -0.06 0.09
-0.05 -0.15 0.05
0.07 -0.05 0.19
0.02 -0.05 0.09
0.03 -0.03 0.09
2.21
1.99
2.45
0.00
0.00
0.00
1463.87

Table B13. Regression models for FIBI at block group level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

spatial
mean
lower
upper
12.95 10.09
15.63
0.76
0.36
1.14
-0.55
-1.07
-0.02
-0.01
-0.44
0.43
0.16
-0.52
0.86
-0.52
-1.07
0.00
-0.74
-1.44
-0.05
0.15
-0.71
1.06
-0.94
-1.97
0.06
-0.79
-1.97
0.36
-0.25
-0.93
0.43
-0.16
-0.82
0.48
0.23
-0.23
0.69
0.10
-0.46
0.69
-0.28
-1.05
0.51
0.52
-0.39
1.41
0.04
-0.46
0.54
0.04
-0.43
0.52
111.26 100.11 123.76
0.98
0.95
1.00
4491.20

Weighted regression
mean lower upper
12.74 12.27 13.20
1.02
0.55
1.50
-0.72
-1.31
-0.15
0.69
0.21
1.18
0.02
-0.86
0.90
-0.96
-1.66
-0.28
-1.11
-1.87
-0.38
-0.30
-1.40
0.81
-0.89
-2.24
0.48
-0.36
-1.92
1.22
0.15
-0.77
1.04
-1.42
-2.02
-0.79
-0.43
-1.04
0.18
-0.20
-0.98
0.58
-0.08
-1.15
0.95
-0.16
-1.42
1.12
-0.04
-0.69
0.60
0.37
-0.32
1.05
41.16 37.09 45.62
0.00
0.00
0.00
4865.83

127

Ordinary regression
mean
lower
upper
12.88
12.44
13.31
0.77
0.27
1.25
-0.68
-1.30
-0.03
0.51
0.03
1.00
0.25
-0.63
1.09
-0.76
-1.42
-0.09
-1.13
-1.90
-0.36
-0.21
-1.30
0.87
-1.07
-2.38
0.24
-0.36
-1.90
1.16
0.23
-0.69
1.14
-1.22
-1.82
-0.59
-0.33
-0.94
0.29
-0.18
-0.94
0.59
-0.15
-1.15
0.87
-0.17
-1.38
1.06
-0.11
-0.77
0.56
0.43
-0.20
1.05
211.86 191.23 235.16
0.00
0.00
0.00
4836.51

Table B14. Regression models for EPT at block group level (Boldfaced values indicate
significant parameters at the 0.05 level)
Parameters
𝛽0
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
𝛽10
𝛽11
𝛽12
𝛽13
𝛽14
𝛽15
𝛽16
𝛽17
𝜏2
𝛾
DIC

spatial
mean lower
5.85
4.70
0.32
0.14
0.09 -0.15
-0.03 -0.23
0.04 -0.27
-0.14 -0.38
-0.17 -0.48
-0.15 -0.54
0.02 -0.43
0.01 -0.51
-0.07 -0.38
-0.16 -0.44
0.15 -0.06
-0.05 -0.31
-0.08 -0.43
0.11 -0.28
0.02 -0.20
0.07 -0.14
22.32 20.13
0.98
0.95
3301.39

upper
7.01
0.49
0.33
0.16
0.34
0.11
0.15
0.24
0.49
0.52
0.24
0.11
0.36
0.21
0.28
0.52
0.24
0.28
24.85
1.00

Weighted regression
mean lower upper
5.87
5.68
6.07
0.27
0.06
0.47
0.14 -0.12
0.39
-0.18 -0.39
0.02
-0.05 -0.43
0.33
-0.33 -0.64 -0.03
-0.44 -0.77 -0.13
-0.43 -0.90
0.05
-0.33 -0.92
0.25
0.03 -0.66
0.69
0.31 -0.09
0.72
-0.69 -0.96 -0.43
0.14 -0.12
0.40
0.13 -0.20
0.46
0.16 -0.29
0.62
-0.31 -0.86
0.25
-0.17 -0.45
0.10
0.23 -0.06
0.51
7.44
6.72
8.24
0.00
0.00
0.00
3602.18

128

Ordinary regression
mean lower upper
5.82
5.63
6.01
0.22
0.02
0.43
0.10 -0.17
0.38
-0.11 -0.32
0.09
0.04 -0.33
0.41
-0.29 -0.58
-0.01
-0.52 -0.85
-0.19
-0.44 -0.90
0.04
-0.32 -0.91
0.25
0.01 -0.67
0.66
0.27 -0.14
0.67
-0.75 -1.01
-0.49
0.10 -0.16
0.37
0.20 -0.13
0.55
0.08 -0.36
0.51
-0.23 -0.76
0.30
-0.17 -0.46
0.12
0.19 -0.08
0.45
39.16 35.32 43.48
0.00
0.00
0.00
3589.46

Table B15. Significant parameters of former developed single level (with no random effect)
regression models (adapted from Daneshvar et al. (2016))
Index
IBI

HBI

Census level
County

Census tract

Spatial
S1, S3, S7, S11,
S12, S13, S14, S16,
S17
S16

Block group

S2, S7, S16

S3, S12, S14, S15,
S16
S2, S3, S13, S14, S16

S2, S3, S5, S10,
S13, S17
S3
S1, S16

S2, S3, S5, S10, S13,
S17
S2, S3, S9, S11,S12
S3, S9

S2, S3, S5, S10,
S13, S17
S3, S9, S11,S12
S3, S9, S16

Census tract

S2, S3, S6, S10,
S15, S17
S2, S10

S2, S3, S6, S10, S15,
S17
S3, S4, S9, S10, S13

Block group

S2, S5, S6, S7

S1, S2, S3, S4, S5

S2, S3, S6, S10,
S15, S17
S3, S4, S9, S10,
S11, S13
S1, S2, S3, S4, S8,
S13

Census tract

S1, S3, S5, S8, S9,
S15
S4, S5, S7, S9

Block group

-

S1, S3, S5, S8, S9,
S15
S2, S3, S4, S10, S12,
S17
S1, S3

County
Census tract
Block group

FIBI

EPT

County

County

Weighted regression
S1, S3, S7, S11, S12,
S13, S14, S16, S17

129

Ordinary regression
S1, S3, S7, S11,
S12, S13, S14, S16,
S17
S3, S12, S14, S15,
S16
S1, S2, S3, S13,
S14, S16

S1, S3, S5, S8, S9,
S15
S2, S3, S4, S10,
S12, S15
S1, S3

Table B16. DICs of multilevel models with random effect (boldfaced values represent best
models at each census level)
Census
level
County

IBI

HBI

FIBI

EPT

County

Census tract

Block group

157.05
155.21
159.36

21.66
21.26
20.66

102.72
103.02
104.73

91.66
92.10
92.91

S
WR
OR

-

-

Census tract

2623.40
2767.23
2786.39
2545.98
2693.09
2758.83
2547.84
2738.06
2711.38
2577.94
2797.10
2778.78

452.17
566.99
578.36
374.99
519.87
532.41
374.58
518.64
531.05
398.04
520.75
533.68

1984.62
2080.73
2090.36
1911.28
2051.87
2127.92
1907.28
2120.23
2128.32
1939.60
2117.31
2124.73

1378.67
1503.45
1500.95
1303.82
1494.41
1492.62
1302.31
1496.95
1495.14
1332.71
1495.01
1494.39

S
S
S
WR
WR
WR
OR
OR
OR

S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR

-

Block group

5963.90
4771.02
4760.74
5209.03
5891.49
4638.39
4668.49
5101.30
5891.27
4748.95
4582.47
5196.39
5917.26
4750.03
4575.22
5124.94
6402.57
6310.63
5278.24
5647.59
6349.00
4981.45
5215.06

1138.60
-14.54
-147.77
424.34
1059.42
-58.75
-178.71
331.39
1061.49
-168.91
-185.82
326.04
1085.44
27.82
-232.51
335.07
1463.68
1154.37
1384.96
1367.25
1367.86
1074.26
1282.79

4490.49
3157.34
3477.51
5199.75
4414.88
3995.43
3012.60
5664.51
4414.31
4891.46
3067.69
5669.20
4448.66
3156.61
3178.86
5707.52
4835.85
5978.36
5248.37
6153.98
4820.98
5076.34
5250.74

3301.54
2728.20
2179.16
3085.80
3227.68
2549.41
2567.20
3286.72
3225.52
1951.01
2218.64
3677.82
3253.57
3936.86
1976.94
3457.36
3588.55
4228.37
4448.53
4427.92
3515.08
4147.85
4368.86

S
S
S
S
WR
WR
WR
WR
OR
OR
OR
OR
S
S
S

S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR

S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
WR
WR
WR
WR
WR
WR
WR

130

Table B16. (cont’d)
6552.89 1269.07
6148.93
4346.66
6352.81 1368.25
4822.64
3522.26
8141.82 1075.42
5901.44
4150.88
5110.65 1284.42
4404.15
4379.42
5649.36 1269.91
6150.23
4358.68
6403.09 1365.45
4819.88
3520.87
5244.83 1099.75
5930.90
4181.62
5096.33 1281.20
4384.33
4374.62
5561.06 1266.87
6149.38
4354.36
6454.18 1488.14
4865.62
3601.96
5255.03 1211.91
5999.84
4264.16
5174.01 1431.45
4433.10
4483.43
6617.13 1436.20
6192.67
4481.22
6451.08 1396.14
4837.30
3530.47
5058.44 1134.36
5205.39
4194.31
5132.75 1331.21
5295.58
4402.44
6613.27 1337.35
6178.11
4401.13
6405.06 1397.41
4839.72
3537.43
5204.89 1132.23
5923.58
4192.28
5287.24 1333.95
4448.26
4410.71
6788.09 1340.97
6180.55
4408.32
6456.93 1393.59
4837.34
3536.58
5170.98 1154.58
5953.40
4223.69
6308.15 1330.46
5317.24
4408.29
6652.80 1335.65
6175.45
4407.38
S: Spatial; WR: Weighted Regression; OR: Ordinary regression

131

S
WR
WR
WR
WR
OR
OR
OR
OR
S
S
S
S
WR
WR
WR
WR
OR
OR
OR
OR

OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR
S
WR
OR

WR
WR
WR
WR
WR
WR
WR
WR
WR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR
OR

Figure B1. Predicted stream health indices for Saginaw River Basin: (a) IBI, (b) HBI, (c)
FIBI, (d) EPT using the two-phased approach (data for sections b, c, and d are adapted
from Daneshvar et al. (2017))

132

Figure B2. Correlation matrix of indices at the census tract level. The diagonal
represents the scatterplots, while lower level and upper levels represent pairwise
distributions and correlation coefficients, respectively. Boldfaced numbers represent
significant correlation coefficients at the 0.05 level. Red and blue values represent
positive and negative significant correlation coefficients with absolute value above 0.7 at
0.05 level

133

Figure B3. Correlation matrix of indices at the block group level. The diagonal
represents the scatterplots, while lower level and upper levels represent pairwise
distributions and correlation coefficients, respectively. Boldfaced numbers represent
significant correlation coefficients at the 0.05 level. Red and blue values represent
positive and negative significant correlation coefficients with absolute value above 0.7 at
0.05 level

134

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