jennifer a. hoeting and n. scott urquhart associate professor and senior research scientist

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Colorado State University’s Colorado State University’s EPA-FUNDED PROGRAM ONEPA-FUNDED PROGRAM ON

SPACE-TIME AQUATIC RESOURCESPACE-TIME AQUATIC RESOURCEMODELING and ANALYSIS PROGRAMMODELING and ANALYSIS PROGRAM

(STARMAP) (STARMAP)

Colorado State University’s Colorado State University’s EPA-FUNDED PROGRAM ONEPA-FUNDED PROGRAM ON

SPACE-TIME AQUATIC RESOURCESPACE-TIME AQUATIC RESOURCEMODELING and ANALYSIS PROGRAMMODELING and ANALYSIS PROGRAM

(STARMAP) (STARMAP)

Jennifer A. Hoeting and N. Scott Urquhart

Associate Professor and Senior Research ScientistDepartment of Statistics

Colorado State UniversityFort Collins, CO 80523-1877

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STARMAP FUNDINGSTARMAP FUNDINGSpace-Time Aquatic Resources Modeling and Analysis ProgramSpace-Time Aquatic Resources Modeling and Analysis Program

STARMAP FUNDINGSTARMAP FUNDINGSpace-Time Aquatic Resources Modeling and Analysis ProgramSpace-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 AchieveResults (STAR) ProgramCooperativeAgreement

# CR - 829095

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Overview of PresentationOverview of PresentationOverview of PresentationOverview 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 APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA)(RFA)

EPA’s REQUEST FOR APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA)(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 APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA) (RFA) - continued- continued

EPA’s REQUEST FOR APPLICATIONSEPA’s REQUEST FOR APPLICATIONS(RFA) (RFA) - continued- 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 methodology2. Colorado State University:

Spatial and temporal modeling, incorporating hierarchical survey design, data analysis, modeling

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RESPONSE to RFA from CSURESPONSE to RFA from CSURESPONSE to RFA from CSURESPONSE to RFA from CSU

• Institutions: Colorado State University

o Department of Statistics o Natural Resources Ecology Lab

Oregon State University

Including work at o Iowa State Universityo University of Alaska, Fairbankso University of Washington o Southern California Coastal Water Research Project (SCCWRP)o Water Quality Technology, Inc

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STARMAP OverviewSTARMAP OverviewSTARMAP OverviewSTARMAP 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 OverviewSTARMAP OverviewSTARMAP OverviewSTARMAP 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 to1. Develop sampling methods to enhance EMAP designs2. Develop statistical methods which make the best use of

the all available current data

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STARMAPSTARMAPTypes of available dataTypes of available data

STARMAPSTARMAPTypes of available dataTypes 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 PROJECTSSTARMAP PROJECTSSTARMAP PROJECTSSTARMAP PROJECTS

1. Combining Environmental Data Sets

2. Local Estimation

3. Indicator Development

4. Outreach

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STARMAP PROJECT 1: STARMAP PROJECT 1: COMBINING ENVIRONMENTAL DATA SETSCOMBINING ENVIRONMENTAL DATA SETS

STARMAP PROJECT 1: STARMAP PROJECT 1: COMBINING ENVIRONMENTAL DATA SETSCOMBINING 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: STARMAP PROJECT 1: A closer look at one of the projectsA closer look at one of the projects

STARMAP PROJECT 1: STARMAP PROJECT 1: A closer look at one of the projectsA 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:Modeling compositional data:Motivating ProblemMotivating Problem

Modeling compositional data:Modeling compositional data:Motivating ProblemMotivating 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:Modeling compositional data:Sampling locations for Sampling locations for

Mid-Atlantic Highlands Region Mid-Atlantic Highlands Region

Modeling compositional data:Modeling compositional data:Sampling locations for Sampling locations for

Mid-Atlantic Highlands Region Mid-Atlantic Highlands Region

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Modeling compositional data:Modeling compositional data:Discrete Compositions and Probability ModelsDiscrete Compositions and Probability Models

Modeling compositional data:Modeling compositional data:Discrete Compositions and Probability ModelsDiscrete Compositions and Probability Models

• Compositional data are multivariate observations

Z = (Z1,…,ZD) subject to the constraints that iZi = 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:Modeling compositional data:Random effects discrete regression modelRandom 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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• 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

f

f G~

MVN , f G

0ε

0

if is not complete in

if is complete in

REDR

2

exp fcdf c d c

Mm

f dm ff d m f

f | , , x

, x

y x x ε y x

y x y

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Modeling compositional data: Modeling compositional data: Example Chain GraphExample Chain Graph

Modeling compositional data: Modeling compositional data: Example Chain GraphExample Chain Graph

• 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 Modeling compositional data: Fish Species Richness in the Mid-Atlantic HighlandsRichness in the Mid-Atlantic Highlands

Modeling compositional data: Fish Species Modeling compositional data: Fish Species Richness in the Mid-Atlantic HighlandsRichness 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:

1. Habit

• Column species

• Benthic species

2. Pollution tolerance

• Intolerant

• Intermediate

• Tolerant

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Modeling compositional data: Modeling compositional data: Stream CovariatesStream Covariates

Modeling compositional data: Modeling compositional data: Stream CovariatesStream Covariates

Environmental covariates: values were measured at each site for the following covariates

1. Mean watershed precipitation (m)2. Minimum watershed elevation (m) 3. Turbidity (ln NTU)4. Chloride concentration (ln eq/L)5. Sulfate concentration (ln eq/L)6. Watershed area (ln km2)

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Modeling compositional data: Modeling compositional data: Fish Species Functional GroupsFish Species Functional GroupsModeling compositional data: Modeling compositional data:

Fish Species Functional GroupsFish Species Functional Groups

Edge exclusion determined from 95% HPD intervals for parameters and off-diagonal elements of Ø

Posterior suggested chain graph for independence model (lowest DIC model)

Tolerance

Precipitation

Chloride

Elevation

Turbidity

Area

SulfateHabit

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Modeling compositional data:Modeling compositional data:A summary A summary

Modeling compositional data:Modeling compositional data:A summary 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: STARMAP PROJECT 1: Some Recent Accomplishments 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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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: STARMAP PROJECT 2: Local Inferences from Aquatic StudiesLocal Inferences from Aquatic Studies

STARMAP PROJECT 2: STARMAP PROJECT 2: Local Inferences from Aquatic StudiesLocal Inferences from Aquatic Studies

Project leader: Jay Breidt, CSU Department of Statistics

Goals: 1. Develop techniques for small area estimation2. Develop methods to estimate the cumulative distribution

function3. Methods to infer causality from non-experimental

spatially referenced data

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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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• 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: STARMAP PROJECT 3: Development and Evaluation of Aquatic IndicatorsDevelopment and Evaluation of Aquatic Indicators

STARMAP PROJECT 3: STARMAP PROJECT 3: Development and Evaluation of Aquatic IndicatorsDevelopment 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 data2. Develop better GIS tools for relevant agencies

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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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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 PointsLaramie Foothills Study Area and Sample PointsLaramie Foothills Study Area and Sample PointsLaramie Foothills Study Area and Sample Points

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Photo interpretation points displayed with predicted current condition map

Photo interpretation points displayed with predicted current condition map

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STARMAP PROJECT 4: STARMAP PROJECT 4: OUTREACHOUTREACH

STARMAP PROJECT 4: STARMAP PROJECT 4: OUTREACHOUTREACH

Project leader: Scott Urquhart, CSU Department of Statistics

Project goals:1. Identify and establish statistical needs of states, tribes

and local agencies2. Prepare content material relevant to target audience

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STARMAP PROJECT 4: STARMAP PROJECT 4: OutreachOutreach

STARMAP PROJECT 4: STARMAP PROJECT 4: OutreachOutreach

• Learning Materials for Aquatic Monitoring1. Individualized interface

o Images can vary by geographic contexto Content varies by responsibility levelo Supports language variation

2. Browser basedo Also available on a CD ROM

• Avoid internet delays for learners at remote sites & in the field• Customizable environment

3. Materials are under active developmento Interface & initial materials tested late last summer by monitoring

personnel in state agencies, Region 10 and NGOso 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: STARMAP PROJECT 4: Recent Accomplishments Recent AccomplishmentsSTARMAP PROJECT 4: STARMAP PROJECT 4: Recent Accomplishments 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 studieso Site selection o Analyses

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STARMAPSTARMAPTraining future environmental statisticiansTraining 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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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 COOPERATIONOPPORTUNITIES FOR COOPERATIONOPPORTUNITIES FOR COOPERATIONOPPORTUNITIES FOR COOPERATION

• GIS-based GRTS site selection• New analysis needs• We are looking for aquatic environmental data sets

Which are spatially intenseo 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 DOINGCHECK OUT WHAT WE ARE DOINGCHECK OUT WHAT WE ARE DOINGCHECK 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!

jennifer a. hoeting and n. scott urquhart associate professor and senior research scientist

Documents

data analysis

modeling aquatic resource

explicit data

collaborative research

sampling design

temporal modeling

starmap projectsopportunities

todevelop sampling methods