NPS Conference 2006 # 1 WE PROBABLY COULD HAVE MORE FUN TALKING ABOUT THESE TRAFFIC STOPPERS.

NPS Conference 2006 # 1

WE PROBABLY COULD HAVE MORE WE PROBABLY COULD HAVE MORE FUN TALKING ABOUT THESE FUN TALKING ABOUT THESE

TRAFFIC STOPPERSTRAFFIC STOPPERS

WE PROBABLY COULD HAVE MORE WE PROBABLY COULD HAVE MORE FUN TALKING ABOUT THESE FUN TALKING ABOUT THESE

TRAFFIC STOPPERSTRAFFIC STOPPERS


WHO CLEARLY HAVE WHO CLEARLY HAVE THE RIGHT OF WAY!THE RIGHT OF WAY!

BUT…BUT…


DESIGNING SURVEYS OVER DESIGNING SURVEYS OVER TIMETIME

(PANEL (PANEL SURVEYS)SURVEYS)VARIANCE, POWER and RELATED VARIANCE, POWER and RELATED

TOPICSTOPICS

DESIGNING SURVEYS OVER DESIGNING SURVEYS OVER TIMETIME

(PANEL (PANEL SURVEYS)SURVEYS)VARIANCE, POWER and RELATED VARIANCE, POWER and RELATED

TOPICSTOPICS

N. Scott UrquhartN. Scott UrquhartSenior Research ScientistSenior Research ScientistDepartment of StatisticsDepartment of Statistics

Colorado State UniversityColorado State UniversityFort Collins, CO 80527-1877Fort Collins, CO 80527-1877


BRIEF COMMENTS ON MONITORINGBRIEF COMMENTS ON MONITORINGBRIEF COMMENTS ON MONITORINGBRIEF COMMENTS ON MONITORING

Monitoring is a long-term endeavor for most Monitoring is a long-term endeavor for most (living) natural resources(living) natural resources

Think of it as a legacy for your grandchildren

Many of you have tried to use solid data someoneMany of you have tried to use solid data someoneelse gathered, but documented poorly.else gathered, but documented poorly.

Much good data “dies” when the person who gathered it dies or retires!

Monitoring data requires three things to retain itsMonitoring data requires three things to retain itsvalue:value:

Metadata Storage in a retrievable, maintained, data system Backed up – safe from fires, floods, or earthquakes


SHORT OUTLINE OF THE REST OF SHORT OUTLINE OF THE REST OF THIS TALKTHIS TALK

SHORT OUTLINE OF THE REST OF SHORT OUTLINE OF THE REST OF THIS TALKTHIS TALK

Inference Perspectives & monitoringInference Perspectives & monitoring

Trend, Variance Structures, and Power to Detect TrendTrend, Variance Structures, and Power to Detect Trend

Panels and Panel StructuresPanels and Panel Structures

Putting it all together = Power Curves Putting it all together = Power Curves {and standard errors of estimated current status}{and standard errors of estimated current status}

Status Estimates from Data Over YearsStatus Estimates from Data Over Years


INFERENCE PERSPECTIVESINFERENCE PERSPECTIVESINFERENCE PERSPECTIVESINFERENCE PERSPECTIVES

Design BasedDesign Based Inferences rest on the probability structure

incorporated in the sampling plan Completely defensible; very minimal assumptions Limiting relative to using auxiliary information

Model AssistedModel Assisted Uses models to complement underlying sampling

structure Has opportunities for use of auxiliary information

Model Based (eg: spatial statistics)Model Based (eg: spatial statistics) Ignores sampling plan Defensibility lies in defense of model


APPROACH OF THIS PRESENTATIONAPPROACH OF THIS PRESENTATIONAPPROACH OF THIS PRESENTATIONAPPROACH OF THIS PRESENTATION

Use tools from the arena ofUse tools from the arena of Model-assisted and Model-based analyses

To study the performance of To study the performance of Design based & Model-assisted analyses

WHY?WHY? Without models,

performance evaluations need simulation (Steve

Garman’s topic)

Before substantial data have been gatheredBefore substantial data have been gathered Minimal basis for values to enter into simulation studies


STATUS & TRENDS OVER TIME STATUS & TRENDS OVER TIME IN ECOLOGICAL RESOURCES IN ECOLOGICAL RESOURCES

OF A REGIONOF A REGION

MAJOR POINTSMAJOR POINTS

STATUS & TRENDS OVER TIME STATUS & TRENDS OVER TIME IN ECOLOGICAL RESOURCES IN ECOLOGICAL RESOURCES

OF A REGIONOF A REGION

MAJOR POINTSMAJOR POINTS

Regional trend Regional trend site trend site trend Detection of trend requires substantial elapsed timeDetection of trend requires substantial elapsed time

Regional OR intensive site

Almost all indicators have substantial patterns inAlmost all indicators have substantial patterns intheir variabilitytheir variability

Design to capitalize on this; don’t fight it.

Minimize effect of site variability with plannedMinimize effect of site variability with plannedrevisits – specific plans will be illustratedrevisits – specific plans will be illustrated

Design tradeoffs: TREND Design tradeoffs: TREND vs vs STATUSSTATUS


REGIONAL TREND REGIONAL TREND SITE TREND SITE TREND

The predominant theme of ecology:The predominant theme of ecology: Ecological processes How does a specific kind of ecosystem function

Energy flows Food webs Nutrient cycling

Most studies of such functions must be Temporally intensive

– What material goes from where to where? Consequently spatially restrictive

In this situation: Temporal trend = site trend


REGIONAL TREND REGIONAL TREND SITE TREND SITE TREND( - CONTINUED)( - CONTINUED)

The predominant theme of ecologyThe predominant theme of ecologyversusversus

A Substantial (any) Agency Focus:A Substantial (any) Agency Focus: All of an ecological resource

In an area or region Across all of the variability present there

For Example, National Park ServiceFor Example, National Park Service All riparian areas in Olympic National Park All riparian areas in National Parks in the

coastal Northwest


TREND ACROSS TIME - What is it?TREND ACROSS TIME - What is it?

Any response which changes across time in a Any response which changes across time in a generally generally

Increasing or Decreasing

Manner shows trendManner shows trend Monotonic change is not essential.

If trend of this sort is present, If trend of this sort is present, it WILL BE detectable as linear trend.it WILL BE detectable as linear trend.

This does NOTNOT mean trend must be linear (examples follow)

Any specified form is detectable Time = years, here


TREND ACROSS TIME - What is it?TREND ACROSS TIME - What is it?(continued)(continued)

TREND = YES

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TREND DETECTION REQUIRES TREND DETECTION REQUIRES SUBSTANTIAL ELAPSED TIMESUBSTANTIAL ELAPSED TIME

IT IS NEARLY IMPOSSIBLE TO DETECT IT IS NEARLY IMPOSSIBLE TO DETECT TREND IN LESS THAN FIVE YEARS. WHY?TREND IN LESS THAN FIVE YEARS. WHY?

2

2ˆ( )

( )i

vart t

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POPULATION VARIANCE: POPULATION VARIANCE:

YEAR VARIANCE:YEAR VARIANCE:

RESIDUAL VARIANCE:RESIDUAL VARIANCE:

2( )SITE

2( )YEAR

VARIANCE HAS A LOT OF STUCTUREVARIANCE HAS A LOT OF STUCTUREIMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE

2( )RESIDUAL


HOW SHOULD YOU ESTIMATE HOW SHOULD YOU ESTIMATE VARIANCE?VARIANCE?


Alternatives:Alternatives: Designed-based

Horwitz-Thompson – extremely variable = don’t use Local Neighborhood Variance Estimator (NBH) – Stevens

– Gives estimate of variance something like residual component of variance, only

– Power nearly impossible to evaluate in this context

Model-assisted Linear models – Urquhart & Courbois (& Williams, now) Gives estimates of site, year and residual variances

Which should you use?


We really aren’t sure, but this topic is underWe really aren’t sure, but this topic is underactive investigationactive investigation

Don Stevens and I are good friends, so this topicDon Stevens and I are good friends, so this topic isn’t a professional conflict. isn’t a professional conflict.

We both want to know the answer!

Results by Courbois (JABES, 2004) suggest this:Results by Courbois (JABES, 2004) suggest this: Unless response values and inclusion probabilities (p)

are highly correlated, they (p) can be ignored.

If this stands up, as I expect it to, practically, linear model estimates of components of variance will be fine.

Answer expected by summer.


(Continued)(Continued)


POPULATION VARIANCE: POPULATION VARIANCE:

Variation among values of an indicator (response) across all sites in a park or group of related parks, that is, across a population or subpopulation of sites

2( )SITE

IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE( - CONTINUED)( - CONTINUED)


YEAR VARIANCE: YEAR VARIANCE:

Concordant variation among values of an indicator (response) across years for ALLALL sites in a regional population or subpopulation

NOT variation in an indicator across years at a single site

Detrended remainder, if trend is present Effectively the deviation away from the trend line (or other

curve)

2( )YEAR

IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE( - CONTINUED II)( - CONTINUED II)


Residual component of varianceResidual component of variance

Has several contributors

Year*Site interaction This contains most of what ecologists would call year to year

variation, i.e. the site specific part

Index variation Measurement error Crew-to-crew variation

(minimize with well documented protocols and training)

Local spatial = protocol variation Short term temporal variation

IMPORTANT COMPONENTS OF VARIANCEIMPORTANT COMPONENTS OF VARIANCE( - CONTINUED - III)( - CONTINUED - III)

2( )RESIDUAL


SOURCE OF DATA FOR ESTIMATES SOURCE OF DATA FOR ESTIMATES OF COMPONENTS OF VARIANCEOF COMPONENTS OF VARIANCE

EMAP Surface Waters: EMAP Surface Waters: Northeast Lakes Pilot 1991 - 1994 Northeast Lakes Pilot 1991 - 1994

About 450 observationsAbout 450 observations Over four years Including about 350 distinct lakes Design allowed estimation of several residual

components Lakes illustrate what is generally referred to Lakes illustrate what is generally referred to

in this presentation as “sites.”in this presentation as “sites.” Similar patterns appear in other data sets

Both aquatic and terrestrial


COMPOSITION OF TOTAL VARIANCE - NE LAKES

0.00 0.20 0.40 0.60 0.80 1.00

Maximum Temperature

Ln( # rotifer taxa)

Ln( # zooplankton taxa)

Ln(Chlorophyll A)

Ln(Total Phosphorus)

Ln(Total Nitrogen)

Secchi Depth

pH(Closed system)

Ln(Chloride)

Ln(Conductance)

Acid Neutralizing Capacity

PROPORTION OF VARIANCE

RESIDUAL COMPONENT OF VARIANCE

LAKE COMPONENT OF VARIANCE

YEAR


ALL VARIABILITY IS OF INTERESTALL VARIABILITY IS OF INTEREST

The site component of variance is one of the majorThe site component of variance is one of the majordescriptors of the regional populationdescriptors of the regional population

The year component of variance often is small, tooThe year component of variance often is small, toosmall to estimate. It is a major enemy forsmall to estimate. It is a major enemy fordetecting trend over time.detecting trend over time.

If it has even a moderate size, “sample size” reverts to the number of years.

In this case, the number of visits and/or number of siteshas no practical effect.


ALL VARIABILITY IS OF INTERESTALL VARIABILITY IS OF INTEREST( - CONTINUED)( - CONTINUED)

Residual variance characterizes the inherentResidual variance characterizes the inherentvariation in the response or indicator.variation in the response or indicator.

But some of its subcomponents may contain But some of its subcomponents may contain useful management informationuseful management information

CREW EFFECTS ===> training VISIT EFFECTS ===> need to reexamine definition of

index (time) window or evaluation protocol MEASUREMENT ERROR ===> work on

laboratory/measurement problems


DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS

How do we detect trend in spite of all of thisHow do we detect trend in spite of all of thisvariation?variation?

Recall two old statistical “friends.”Recall two old statistical “friends.” Variance of a mean, and Blocking


DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS( - CONTINUED)( - CONTINUED)

VARIANCE OF A MEAN:VARIANCE OF A MEAN:

Where m members of the associated population have been randomly selected and their response values averaged.

Here the “mean” is a regional average slope, so "2" refers to the variance of an estimated slope ---

var meanm

( ) 2


DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS( - CONTINUED - II)( - CONTINUED - II)

ConsequentlyConsequently

BecomesBecomes

Note that the regional averaging of slopes has theNote that the regional averaging of slopes has thesame effect as continuing to monitor at one site same effect as continuing to monitor at one site

forfora much longer time period.a much longer time period.

var meanm

( ) 2

var regional mean slopem t ti

( )( )

1 2

2


DESIGN TRADE-OFFS: TREND DESIGN TRADE-OFFS: TREND vs vs STATUSSTATUS( - CONTINUED - III)( - CONTINUED - III)

Now, Now, 22, in total, frequently is large., in total, frequently is large.

If we take one regional sample of sites at one time,If we take one regional sample of sites at one time,and another at a subsequent time, the siteand another at a subsequent time, the sitecomponent of variance is included in component of variance is included in 22..

Enter the concept of blocking, familiar fromEnter the concept of blocking, familiar fromexperimental design.experimental design.

Regard a site like a block Periodically revisit a site The site component of variance vanishes from the

variance of a slope.


PANEL DESIGNSPANEL DESIGNSPANEL DESIGNSPANEL DESIGNS

Question: “ What kind of temporal design shouldQuestion: “ What kind of temporal design shouldyou use for National Parks?you use for National Parks?

A Panel is a Set of Sites which have the same A Panel is a Set of Sites which have the same Revisit ScheduleRevisit Schedule

Each panel ordinarily should have as good a spatial coverage as possible (GRTS)

You have many usable and defensible temporalYou have many usable and defensible temporaldesignsdesigns

Choose one which fits your needs and resources Evaluation tools are available, and demonstrated here


A SINGLE PANELA SINGLE PANELA SINGLE PANELA SINGLE PANEL

Conventional for trend detectionConventional for trend detection Not very good for statusNot very good for status (Call this design 1)(Call this design 1)

NUM NUM OBSOBS YEARYEAR

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 2020 2121

1111 XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX XX


AN “AUGMENTED” PANEL PLAN (Design 2)AN “AUGMENTED” PANEL PLAN (Design 2)AN “AUGMENTED” PANEL PLAN (Design 2)AN “AUGMENTED” PANEL PLAN (Design 2)

NUMNUM

OBSOBSYEARSYEARS

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 ……

5 X X X X X X X X X X X X X X X X X X X …

Add sites to the above annual revisit plane, asAdd sites to the above annual revisit plane, as


AN “AUGMENTED” PANEL PLAN (Design 2)AN “AUGMENTED” PANEL PLAN (Design 2)AN “AUGMENTED” PANEL PLAN (Design 2)AN “AUGMENTED” PANEL PLAN (Design 2)NUMNUM

OBSOBSYEARSYEARS

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 ……

5 X X X X X X X X X X X X X X X X X X X …

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A POSSIBLE NPS PANEL PLAN (Design 3) A POSSIBLE NPS PANEL PLAN (Design 3) A POSSIBLE NPS PANEL PLAN (Design 3) A POSSIBLE NPS PANEL PLAN (Design 3) NUMNUM

OBSOBSYEARSYEARS

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 ……

5 X X

5 X

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OBSOBSYEARSYEARS

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 ……

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11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515 1616 1717 1818 1919 ……

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WHY LOOK AT POWER?WHY LOOK AT POWER?WHY LOOK AT POWER?WHY LOOK AT POWER?

Power provides a tool for comparing various designs Power provides a tool for comparing various designs Looking at it does not imply that we have to conduct Looking at it does not imply that we have to conduct

tests of hypothesestests of hypotheses The computations displayed here use The computations displayed here use

A components of variance statistical model To evaluate the underlying variances of estimated slopes And the temporal design being considered

These computations are much more complex, andsuitable to your problems, than any of the web-available tools

Use of those tools here would commit “sins of pseudoreplication”!


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Design 1: One panel n = 11

POWER FOR DESIGNS 1 – 3, & 2A POWER FOR DESIGNS 1 – 3, & 2A WITH PARAMETER CONDITIONS BILLY GAVEWITH PARAMETER CONDITIONS BILLY GAVE

{large is good}{large is good}




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Design 2: Augmented, n = 5 + 6






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Design 3: A NPS proposal, n varies from 3 to 12






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Design 2A: Augmented n = 3 + 2 or 3






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STANDARD ERROR OF STATUS FOR DESIGNS 1 – 3, & 2ASTANDARD ERROR OF STATUS FOR DESIGNS 1 – 3, & 2AWITH PARAMETER CONDITIONS BILLY GAVEWITH PARAMETER CONDITIONS BILLY GAVE

{small is good}{small is good}




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Design 2A: augmented n = 3 + 2 or 3






DESIGN 3 – A PROPOSED NPS DESIGN 3 – A PROPOSED NPS TEMPORAL DESIGN??TEMPORAL DESIGN??

DESIGN 3 – A PROPOSED NPS DESIGN 3 – A PROPOSED NPS TEMPORAL DESIGN??TEMPORAL DESIGN??

Defensible design, given restrictions ofDefensible design, given restrictions of Field resources = # sites visited per year Need to split field resources across two type of

aquatic systems: Streams Wetlands


STATUS ESTIMATES STATUS ESTIMATES FROM DATA OVER YEARSFROM DATA OVER YEARS

STATUS ESTIMATES STATUS ESTIMATES FROM DATA OVER YEARSFROM DATA OVER YEARS

Idea: Idea: Estimate year effects, and Adjust all sites to the latest year Idea very similar to “adjusted treatment means”

in the analysis of covariance For example, if a line approximates the trend,For example, if a line approximates the trend,

The array of { Sitei + (yearnow – yearinitial)slope } Describes current status, accounting for documented

trend This approach extends to models other than lines.

Linkage of site revisits (=connectedness) is necessaryLinkage of site revisits (=connectedness) is necessaryto allow estimation of all differences in year effectsto allow estimation of all differences in year effects


This research is funded by

U.S.EPA – Science To AchieveResults (STAR) ProgramCooperativeAgreement

# CR - 829095

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 presenter and STARMAP, the Program he represents. EPA does not endorse any products or commercial services mentioned in this presentation.

FUNDING ACKNOWLEDGEMENT


RELATED INFORMATION ON THE WEBRELATED INFORMATION ON THE WEBRELATED INFORMATION ON THE WEBRELATED INFORMATION ON THE WEB

Web-available information from a graduate course in environmental Web-available information from a graduate course in environmental Sampling (ST571) I taught at OSUSampling (ST571) I taught at OSU

http://oregonstate.edu/instruct/st571/urquhart/index.html Environmental Sampling Anatomy Variable Probability Sampling Cost Effective Resource Allocation Sampling Macroinvertebrates Maps & Grids Spatial Sampling Support Regions Statistical Power - Concepts Power to Detect Trend in Ecological Resources Representative Sampling Statistical Aspects of Taxonomic Richness Sample Size to Estimate Taxonomic Richness Evaluating a Protocol for "Measuring" Physical Habitat

Also see: Also see: http://www.stat.colostate.edu/starmap/http://www.stat.colostate.edu/starmap/ Also see NPS I&M site, from Port Angeles meeting, 2003Also see NPS I&M site, from Port Angeles meeting, 2003


VISUALIZING LINES AND VISUALIZING LINES AND YEAR EFFECTSYEAR EFFECTS

VISUALIZING LINES AND VISUALIZING LINES AND YEAR EFFECTSYEAR EFFECTS

N. Scott UrquhartN. Scott UrquhartSTARMAPSTARMAP

Colorado State UniversityColorado State UniversityFort Collins, Co 80523-1877Fort Collins, Co 80523-1877


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WHAT WE SEE – NO LINES & WHAT WE SEE – NO LINES & NO DECOMPOSITIONNO DECOMPOSITION



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A LINEA LINEA LINEA LINE


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A LINE WITH YEAR EFFECTSA LINE WITH YEAR EFFECTSA LINE WITH YEAR EFFECTSA LINE WITH YEAR EFFECTS


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A LINE WITH YEAR EFFECTS & A LINE WITH YEAR EFFECTS & ANNUAL RESIDUALSANNUAL RESIDUALS

A LINE WITH YEAR EFFECTS & A LINE WITH YEAR EFFECTS & ANNUAL RESIDUALSANNUAL RESIDUALS


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A LINE WITH ONLY ANNUAL A LINE WITH ONLY ANNUAL RESIDUALS SHOWNRESIDUALS SHOWN

A LINE WITH ONLY ANNUAL A LINE WITH ONLY ANNUAL RESIDUALS SHOWNRESIDUALS SHOWN


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A LINE WITH ANNUAL RESIDUALSA LINE WITH ANNUAL RESIDUALS& END MARKERS& END MARKERS

A LINE WITH ANNUAL RESIDUALSA LINE WITH ANNUAL RESIDUALS& END MARKERS& END MARKERS


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A LINE WITH YEAR EFFECTS, A LINE WITH YEAR EFFECTS, JIGGERED RESIDUALS & END JIGGERED RESIDUALS & END

MARKERSMARKERS

A LINE WITH YEAR EFFECTS, A LINE WITH YEAR EFFECTS, JIGGERED RESIDUALS & END JIGGERED RESIDUALS & END

MARKERSMARKERS


A REALITYA REALITYA REALITYA REALITY

With a single siteWith a single site The year effect And residual effect Can not be separated

But with several sitesBut with several sites These effects can be separated

Following figures show the patternsFollowing figures show the patterns


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TWO LINESTWO LINESTWO LINESTWO LINES


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TWO LINES WITH YEAR EFFECTSTWO LINES WITH YEAR EFFECTSTWO LINES WITH YEAR EFFECTSTWO LINES WITH YEAR EFFECTS


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TWO LINES WITH YEAR EFFECTS & TWO LINES WITH YEAR EFFECTS & JIGGERED RESIDUALSJIGGERED RESIDUALS

TWO LINES WITH YEAR EFFECTS & TWO LINES WITH YEAR EFFECTS & JIGGERED RESIDUALSJIGGERED RESIDUALS


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TWO LINES WITH YEAR EFFECTS & TWO LINES WITH YEAR EFFECTS & JIGGERED RESIDUALS – ONLY SOME YEARSJIGGERED RESIDUALS – ONLY SOME YEARS

TWO LINES WITH YEAR EFFECTS & TWO LINES WITH YEAR EFFECTS & JIGGERED RESIDUALS – ONLY SOME YEARSJIGGERED RESIDUALS – ONLY SOME YEARS


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NPS Conference 2006 # 1 WE PROBABLY COULD HAVE MORE FUN TALKING ABOUT THESE TRAFFIC STOPPERS.

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Transcript of NPS Conference 2006 # 1 WE PROBABLY COULD HAVE MORE FUN TALKING ABOUT THESE TRAFFIC STOPPERS.