Download STARMAP - Colorado State University`s Department of Statistics

Colorado State University’s
EPA-FUNDED PROGRAM ON
SPACE-TIME AQUATIC RESOURCE
MODELING and ANALYSIS PROGRAM
(STARMAP)
Jennifer A. Hoeting and N. Scott Urquhart
Associate Professor and Senior Research Scientist
Department of Statistics
Colorado State University
Fort Collins, CO 80523-1877
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STARMAP FUNDING
Space-Time Aquatic Resources Modeling and Analysis Program
The work reported here today was developed under the STAR
Research Assistance Agreement CR-829095 awarded by the
U.S. Environmental Protection Agency (EPA) to Colorado
State University. This presentation has not been formally
reviewed by EPA. The views expressed here are solely
those of presenters and STARMAP, the Program they
represent. EPA does not endorse any products or
commercial services mentioned in these presentation.
This research is funded by
U.S.EPA – Science To Achieve
Results (STAR) Program
Cooperative
# CR - 829095
Agreement
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Overview of Presentation
1. EPA’s Request for Applications (RFA)
2. CSU’s Response = STARMAP
3. A summary of some of the goals and recent
accomplishments of the four STARMAP projects
4. Opportunities for Cooperation
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EPA’s REQUEST FOR APPLICATIONS
(RFA)
Content Requirements
• Research in Statistics
Directed toward using, in part, data gathered by probability
surveys of the “EMAP-sort.”
•
Training of “future generations” of environmental
statisticians
•
Outreach to the states and tribes
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EPA’s REQUEST FOR APPLICATIONS
(RFA) - continued
•
Major Administrative Requirement
“… each of the two programs established will involve
collaborative research at multiple, geographically diverse
sites.”
•
Two Programs:
1. Oregon State University:
Design-based/model assisted survey methodology
2. Colorado State University:
Spatial and temporal modeling, incorporating
hierarchical survey design, data analysis, modeling
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RESPONSE to RFA from CSU
•
Institutions:
 Colorado State University
o Department of Statistics
o Natural Resources Ecology Lab
 Oregon State University
 Including work at
o
o
o
o
o
Iowa State University
University of Alaska, Fairbanks
University of Washington
Southern California Coastal Water Research Project (SCCWRP)
Water Quality Technology, Inc
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STARMAP Overview
Goals of STARMAP:
• Develop statistical methods for aquatic resources
• Extend current methods for sampling design and
modeling
• Emphasize spatio-temporal data: spatially explicit
data collected over time
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STARMAP Overview
•
•
•
Most statistical techniques taught in graduate
statistics classes assume that the observations are
uncorrelated
Reality: aquatic resources that are nearby in space
are typically more similar than those far apart
STARMAP aims to
1. Develop sampling methods to enhance EMAP designs
2. Develop statistical methods which make the best use of
the all available current data
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STARMAP
Types of available data
• A response of interest
 A probability sample in a region, e.g., 305(b)
 Some purposefully chosen points in the region
 Spatially “intensive” points near some of the observation
locations
 Response may be multivariate
• Predictors
 Some at observation locations only
 Some at whatever density desired from GIS
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STARMAP PROJECTS
1. Combining Environmental Data Sets
2. Local Estimation
3. Indicator Development
4. Outreach
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STARMAP PROJECT 1:
COMBINING ENVIRONMENTAL DATA SETS
Project leader: Jennifer Hoeting,
CSU Department of Statistics
Two of the goals of the project:
1. Develop models and methodology for modeling
aquatic resource data
2. Enhance EMAP designs
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STARMAP PROJECT 1:
A closer look at one of the projects
Goal 1: Develop models and methodology for modeling aquatic
resource data
•
Challenges:


•
Spatially explicit, but incomplete coverage over space
Form of the response
Example: Compositional data


What proportion of the species of fish at a sample location are in
three pollution (or thermal) tolerance categories: intolerant,
intermediate, and tolerant?
Can we relate multiple compositions to environmental covariates in
a scientifically meaningful way?
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Modeling compositional data:
Motivating Problem
• Stream sites in the Mid-Atlantic region of the United
States were visited
 Response: For each site, each observed fish species was
cross categorized according to several traits
 Predictors: Environmental variables are also measured at
each site (e.g. precipitation, chloride concentration,…)
• How can we determine if collected environmental
variables affect species trait compositions (which
ones)?
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Modeling compositional data:
Sampling locations for
Mid-Atlantic Highlands Region
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Modeling compositional data:
Discrete Compositions and Probability Models
• Compositional data are multivariate observations
Z = (Z1,…,ZD) subject to the constraints that SiZi = 1
and Zi  0.
• Compositional data are usually modeled with the
Logistic-Normal distribution (Aitchison 1986).
 LN model defined for positive compositions only, Zi > 0
• Problem: With discrete counts one has a non-trivial
probability of observing 0 individuals in a particular
category
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Modeling compositional data:
Random effects discrete regression model
• Developed a new model: the random effects discrete
regression model
• Developed Bayesian methods to estimate the
parameters of this model
• Developed graphical models theory which allows for
statistically sound displays of the results
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Modeling compositional data:
Random effects discrete regression model
• Sampling of individuals occurs at many different
random sites, i = 1,…,S, where covariates are
measured only once per site
• Hierarchical model for individual probabilities:

f REDR  y | x   exp    x ,ε  


x
     y ,x  

f  c  d 
  
f 

0
εf ~ 

 MVN  0, S f
 d 
fcd

c

 f  dm y , x   x    f  y  

m2
f 

M
m
if f   is not complete in G

if f   is complete in G
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Modeling compositional data:
Example Chain Graph


c

d
•
Mathematical graphs are used to illustrate complex dependence relationships
in a multivariate distribution
•
A random vector is represented as a set of vertices, V .
•
Pairs of vertices are connected by directed or undirected edges depending on
the nature of each pair’s association
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Modeling compositional data: Fish Species
Richness in the Mid-Atlantic Highlands
•
91 stream sites in the Mid Atlantic region of the United
States were visited in an EPA EMAP study
•
Response composition: Observed fish species were crosscategorized according to 2 discrete variables:
1. Habit
2. Pollution tolerance
• Column species
• Intolerant
• Benthic species
• Intermediate
• Tolerant
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Modeling compositional data:
Stream Covariates
Environmental covariates: values were measured at
each site for the following covariates
1.
2.
3.
4.
5.
6.
Mean watershed precipitation (m)
Minimum watershed elevation (m)
Turbidity (ln NTU)
Chloride concentration (ln meq/L)
Sulfate concentration (ln meq/L)
Watershed area (ln km2)
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Modeling compositional data:
Fish Species Functional Groups
Posterior suggested chain graph for independence model (lowest
DIC model)
Precipitation
Habit
Elevation
Area
Turbidity
Sulfate
Tolerance
Chloride
Edge exclusion determined from 95% HPD intervals for 
parameters and off-diagonal elements of Ø.
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Modeling compositional data:
A summary
The Random Effects Discrete Regression Model
• Allows for multivariate composition response
• Provides a statistically defensible graphical model
interpretation
• Offers measures of uncertainty and inferences not
available using other techniques for species trait and
related analyses
• Allows for predictions at unobserved locations
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STARMAP PROJECT 1:
Some Recent Accomplishments
Goal 1: Develop models and methodology for modeling aquatic
resource data
Other projects aimed at goal 1:
• Models for radio telemetry habitat association data
 Radio-tagged fish are monitored over time
 Goal: extend existing models to account for seasonal changes in fish
habitat types
• Model selection for geo-statistical models
 When predicting a continuous response , which covariates are best?
 Does spatial correlation affect model selection (YES!)
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STARMAP PROJECT 1:
Some Recent Accomplishments
Goal 2: Enhance EMAP designs
• How should EMAP-type sampling be intensified to
estimate spatial correlation?
 Current context – City of San Diego and Southern
California Coastal Water Research Project (SCCWRP)
o Accurate maps of environmental measures around San Diego’s
oceanic sewage outfall
• How to Get From 305(b) Survey Results to Identify
303(d) Sites?
 STARMAP organized a morning of talks on this topic at
the recent EMAP Conference
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STARMAP PROJECT 2:
Local Inferences from Aquatic Studies
Project leader: Jay Breidt,
CSU Department of Statistics
Goals:
1. Develop techniques for small area estimation
2. Develop methods to estimate the cumulative distribution
function
3. Methods to infer causality from non-experimental
spatially referenced data
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STARMAP PROJECT 2:
Some Recent Accomplishments
Goal 1: Small area estimation




Combining probability survey data with non-probability
data to make spatially-explicit predictions
Bayesian models to construct a set of ensemble estimates
to predict some response
Data not observed everywhere, but methods will provide
predictions over entire region along with estimates of
uncertainty
Current emphasis: characteristics of water quality for
Mid-Atlantic Highlands region
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STARMAP PROJECT 2:
Some Recent Accomplishments
• Goal 1: Developing and comparing different
methods for small area estimation
 Developing new semi-parametric methods
 Compared to parametric and non-parametric methods,
can optimize over the benefits of both
• Goal 2: Nonparametric regression estimators for
two-stage samples
 Incorporates auxiliary information available at the level
of the primary sampling unit
 Current emphasis: EMAP Northeast Lakes
• Presented results at recent EMAP conference
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STARMAP PROJECT 3:
Development and Evaluation of Aquatic Indicators
Project leader: Dave Theobald,
CSU Natural Resources Ecology Lab
Two of the project goals:
1. Develop and determine landscape indicators for analyses
of EMAP data
2. Develop better GIS tools for relevant agencies
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STARMAP PROJECT 3:
Some Recent Accomplishments
Goal 1: Develop and determine landscape indicators for
analyses of EMAP data
•
Developing predictors for stream size and flow status to
overcome limitations of the National Hydrological Database

•
Estimation of regional indicators of taxa richness


•
Classification of perennial versus non-perennial streams
Quantifying taxa richness in terms of rarity assessed by a fixed
count
Sampling macroinvertebrates: compositing and structure of
variance
Compiling indicators and additional GIS data coverage for
MAHA and Western Pilot Study
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STARMAP PROJECT 3:
Some Recent Accomplishments
Goals 2: Develop better GIS tools
•
•
•
•
Software for Generalized Random Tessellation
Stratified (GRTS) sampling
GRTS: Robust spatially balanced random sampling
Software implements the GRTS algorithm in
ARCVIEW
Software is in final testing stages
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Laramie Foothills Study Area and Sample Points
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Photo interpretation
points displayed with predicted current condition map
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STARMAP PROJECT 4:
OUTREACH
Project leader: Scott Urquhart,
CSU Department of Statistics
Project goals:
1. Identify and establish statistical needs of states, tribes
and local agencies
2. Prepare content material relevant to target audience
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STARMAP PROJECT 4:
Outreach
•
Learning Materials for Aquatic Monitoring
1. Individualized interface
o Images can vary by geographic context
o Content varies by responsibility level
o Supports language variation
2. Browser based
o Also available on a CD ROM
•
•
Avoid internet delays for learners at remote sites & in the field
Customizable environment
3. Materials are under active development
o Interface & initial materials tested late last summer by monitoring
personnel in state agencies, Region 10 and NGOs
o Anticipate video taping of EMAP training session in Corvallis later
this month; material to be included in “How to Monitor”
o See poster and reprint for more info
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STARMAP PROJECT 4:
Recent Accomplishments
• Content –






Monitoring Objectives
Methods for Site Selection
What/How to Monitor
How to Monitor = Field Operations
How to Summarize
Case Studies
o Planning studies
o Site selection
o Analyses
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STARMAP
Training future environmental statisticians
• Graduate students graduated
 1 Ph.D. + 1 affiliated student in landscape ecology
 4 M.S.
• Current graduate students
 6 Ph.D. students – including two in landscape ecology
 2 M.S. students
• Post doctoral fellows – one at present; seeking others
• Early career professionals
 3 young faculty
 2 agency employees
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STARMAP
Training future environmental statisticians
Colorado State University’s PRIMES program
• PRogram for Interdisciplinary Mathematics,
Ecology and Statistics,
• NSF IGERT program aimed at training graduate
students in this interdisciplinary area
• Works well with STARMAP as both have similar
goals
• Allows us to offer new classes and support students
in many ways
• Opportunities for visitors and joint research!
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OPPORTUNITIES FOR COOPERATION
•
•
•
GIS-based GRTS site selection
New analysis needs
We are looking for aquatic environmental data sets
 Which are spatially intense
o Like at sites 100s of meters apart to few km
 Or which include spatial locations and were collected over
a long time frame (> 5 time points)
 Identified several such possible sets at EMAP Conference
• Involvement in Evolving Learning Materials
 Testing
 Suggestions
 Case studies
o We could analyze some data for you to make these
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CHECK OUT WHAT WE ARE DOING
• STARMAP Web Site:
 http://www.stat.colostate.edu/starmap/
 This presentation will be posted there, soon.
• Team members here are …
• Questions Are Welcome!
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