Colorado State University

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Colorado State Universitys EPA-FUNDED PROGRAM
ONSPACE-TIME AQUATIC RESOURCEMODELING 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 FUNDINGSpace-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.

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Overview of Presentation

• EPAs Request for Applications (RFA)
• CSUs Response STARMAP
• A summary of some of the goals and recent
  accomplishments of the four STARMAP projects
• Opportunities for Cooperation

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EPAs 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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EPAs 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
• Oregon State University
• Design-based/model assisted survey methodology
• 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
• Department of Statistics
• Natural Resources Ecology Lab
• Oregon State University
• Including work at
• 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
• Develop sampling methods to enhance EMAP designs
• Develop statistical methods which make the best
  use of the all available current data

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STARMAPTypes 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

• Combining Environmental Data Sets
• 2. Local Estimation
• Indicator Development
• 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
• Develop models and methodology for modeling
  aquatic resource data
• 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 dataMotivating 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 dataSampling locations
for Mid-Atlantic Highlands Region
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Modeling compositional dataDiscrete
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 gt 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 dataRandom 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 dataRandom 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

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Modeling compositional data Example Chain Graph
b
a
c
d
e

• 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
  pairs 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
  cross-categorized according to 2 discrete
  variables

• Pollution tolerance
• Intolerant
• Intermediate
• Tolerant

• Habit
• Column species
• Benthic species

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Modeling compositional data Stream Covariates

• Environmental covariates values were measured at
  each site for the following covariates
• 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)

• Edge exclusion determined from 95 HPD intervals
  for b parameters and off-diagonal elements of ?Ø.

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Modeling compositional dataA 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)
• Accurate maps of environmental measures around
  San Diegos 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
• Develop techniques for small area estimation
• Develop methods to estimate the cumulative
  distribution function
• 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
• Develop and determine landscape indicators for
  analyses of EMAP data
• 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
• Classification of perennial versus non-perennial
  streams
• Estimation of regional indicators of taxa
  richness
• 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
• Identify and establish statistical needs of
  states, tribes and local agencies
• Prepare content material relevant to target
  audience

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STARMAP PROJECT 4 Outreach

• Learning Materials for Aquatic Monitoring
• Individualized interface
• Images can vary by geographic context
• Content varies by responsibility level
• Supports language variation
• Browser based
• Also available on a CD ROM
• Avoid internet delays for learners at remote
  sites in the field
• Customizable environment
• Materials are under active development
• Interface initial materials tested late last
  summer by monitoring personnel in state agencies,
  Region 10 and NGOs
• Anticipate video taping of EMAP training session
  in Corvallis later this month material to be
  included in How to Monitor
• 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
• Planning studies
• Site selection
• Analyses

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STARMAPTraining 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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STARMAPTraining future environmental
statisticians

• Colorado State Universitys 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
• Like at sites 100s of meters apart to few km
• Or which include spatial locations and were
  collected over a long time frame (gt 5 time
  points)
• Identified several such possible sets at EMAP
  Conference
• Involvement in Evolving Learning Materials
• Testing
• Suggestions
• Case studies
• 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!