we probably could have more fun talking about these traffic stoppers

KSU Monitoring Designs # 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 MONITORING DESIGNING MONITORING SURVEYS OVER TIMESURVEYS OVER TIME

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

TOPICSTOPICS

DESIGNING MONITORING DESIGNING MONITORING SURVEYS OVER TIMESURVEYS OVER TIME

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


OUTLINEOUTLINEOUTLINEOUTLINE Anatomy Of Sampling Studies Of EcologicalAnatomy Of Sampling Studies Of Ecological

Responses Through Time Responses Through Time Collaborator = Tony Olsen, EPA, WEDCollaborator = Tony Olsen, EPA, WED http://www.oregonstate.edu/instruct/st571/urquhart/anatomy/index.http://www.oregonstate.edu/instruct/st571/urquhart/anatomy/index.

htmhtm Urquhart, N.S. (1981). Anatomy of a study. HortScience 16:621-627.

Elaboration on Elaboration on Survey Designs – GRTS – Work of Don StevensSurvey Designs – GRTS – Work of Don Stevens Temporal Designs Temporal Designs

Power to detect trend – joint with Tom KincadePower to detect trend – joint with Tom Kincade Uses components of varianceUses components of variance

Current work = estimating varianceCurrent work = estimating variance Work of Sarah Williams, finishing MS this monthWork of Sarah Williams, finishing MS this month


A CONTEXTA CONTEXTA CONTEXTA CONTEXT

“EMAP-TYPE“EMAP-TYPE SITUATIONS” SITUATIONS” EMAPEMAP = US EPA’S = US EPA’S EEnvironmental nvironmental MMonitoring and onitoring and AAssessment ssessment PProgramrogram

Estimate status, changes, and trends in selected Estimate status, changes, and trends in selected indicators of our nation’s ecological resources indicators of our nation’s ecological resources on a regional scale with known confidence. on a regional scale with known confidence.

Estimate status, changes, and trends in the Estimate status, changes, and trends in the extent and geographic coverage of our nation’s extent and geographic coverage of our nation’s ecological resources on a regional scale with ecological resources on a regional scale with known confidence. known confidence.

Describe associations between indicators ofDescribe associations between indicators of anthropogenic stress and indicators of anthropogenic stress and indicators of condition. condition.


WHO MUST COMMUNICATEWHO MUST COMMUNICATEWHO MUST COMMUNICATEWHO MUST COMMUNICATE

Ecologists & Other BiologistsEcologists & Other Biologists

StatisticiansStatisticians

GeographersGeographers

Geographic Information SpecialistsGeographic Information Specialists

Information ManagersInformation Managers

Quality Assurance PersonnelQuality Assurance Personnel

Managers, at Various LevelsManagers, at Various Levels


““SAMPLING”SAMPLING” ““SAMPLING”SAMPLING”

A WORD OF MANY MEANINGSA WORD OF MANY MEANINGS

A statistician often associates it with survey samplingA statistician often associates it with survey sampling

An ecologist may associate it with the An ecologist may associate it with the selection of local sites or material selection of local sites or material

A laboratory scientist may associate it with the selection A laboratory scientist may associate it with the selection of material to be analyzed from the material of material to be analyzed from the material

suppliedsupplied

Common general meaning, varied specific meaningsCommon general meaning, varied specific meanings


THE SPECIAL NEEDTHE SPECIAL NEEDTHE SPECIAL NEEDTHE SPECIAL NEED

Communication Demands a Distinction BetweenCommunication Demands a Distinction Between The local process of evaluating a response, andThe local process of evaluating a response, and The statistical selection of a sampling unit, The statistical selection of a sampling unit,

for example,for example, A lakeA lake A point on a steamA point on a steam A point in vegetationA point in vegetation

The terms The terms Response design Response design Sampling design or survey designSampling design or survey design

Can be used to make this distinctionCan be used to make this distinction


BASIC ROLESBASIC ROLESBASIC ROLESBASIC ROLES

Survey Design Tells Us Where To Go to Survey Design Tells Us Where To Go to Collect Sample Information or MaterialCollect Sample Information or Material

Response Design Tells Us What To Do Response Design Tells Us What To Do Once We Get ThereOnce We Get There

But These Two Components Exist in a But These Two Components Exist in a Broader ContextBroader Context


AN IMPORTANT DISTINCTIONAN IMPORTANT DISTINCTIONAN IMPORTANT DISTINCTIONAN IMPORTANT DISTINCTION

Monitoring StrategyMonitoring Strategy

ConceptualConceptual

Impacted by objectivesImpacted by objectives

Addressable without regard to the inference strategyAddressable without regard to the inference strategy

Inference StrategyInference Strategy Places to evaluate the responsePlaces to evaluate the response

Relation between points evaluated and the populationRelation between points evaluated and the population Ie, the basis for inferenceIe, the basis for inference


SAMPLING STUDIES OF ECOLOGICAL RESPONSES

THROUGH TIME HAVE

SAMPLING STUDIES OF ECOLOGICAL RESPONSES

THROUGH TIME HAVE Monitoring StrategyMonitoring Strategy

Universe modelUniverse model

Statistical populationStatistical population

Domain designDomain design

Response designResponse design

Inference StrategyInference Strategy Survey designSurvey design

Temporal designTemporal design

Quality assurance designQuality assurance design

These componentsexist regardless of the inference strategy

These componentsexist for any monitoring strategy


The UNIVERSE MODELThe UNIVERSE MODEL

Reality (Universe): Ecological Entity Within a DefinedReality (Universe): Ecological Entity Within a DefinedGeographic Area to be MonitoredGeographic Area to be Monitored

Model of the Universe:Model of the Universe: Development of monitoring approach requires construction of Development of monitoring approach requires construction of

a model for the universea model for the universe

Elements Of The Universe Model: Set of Entities Elements Of The Universe Model: Set of Entities Composing the Entire Universe of ConcernComposing the Entire Universe of Concern


The UNIVERSE MODELThe UNIVERSE MODELThe UNIVERSE MODELThe UNIVERSE MODEL

Population Description And Its Sampling RequirePopulation Description And Its Sampling RequireDefinition Of the “Units” in the PopulationDefinition Of the “Units” in the Population

Discrete units:Discrete units: Lakes may be viewed this wayLakes may be viewed this way Individual trees can be viewed this way, tooIndividual trees can be viewed this way, too

Continuous structure in space of some dimension:Continuous structure in space of some dimension: 2-SPACE: Forests or Agroecosystems2-SPACE: Forests or Agroecosystems 1-SPACE: Streams1-SPACE: Streams 3-SPACE: Groundwater3-SPACE: Groundwater


A CONTINUOUS MODEL FOR STREAMSA CONTINUOUS MODEL FOR STREAMSStrahler OrdersStrahler Orders

A CONTINUOUS MODEL FOR STREAMSA CONTINUOUS MODEL FOR STREAMSStrahler OrdersStrahler Orders

Third Order

First Orders

First Orders

First Order

First Orders

Second Order

Second Order

SecondOrder


The STATISTICAL POPULATIONThe STATISTICAL POPULATIONThe STATISTICAL POPULATIONThe STATISTICAL POPULATION

The Collection of Units (as modeled)The Collection of Units (as modeled) Over Some Region of Definition Over Some Region of Definition SpatialSpatial TemporalTemporal Spatial and TemporalSpatial and Temporal

Population Definition Could Include Features Population Definition Could Include Features Which Depend on Response ValuesWhich Depend on Response Values

EX: acid sensitive streams at upper elevationsEX: acid sensitive streams at upper elevations


The DOMAIN DesignThe DOMAIN DesignThe DOMAIN DesignThe DOMAIN Design Specifies Subpopulations or “Domains” Specifies Subpopulations or “Domains”

of Special Interestof Special Interest

May Specify Meaningful Comparisons BetweenMay Specify Meaningful Comparisons BetweenDomainsDomains

Similar to “planned comparisons” in experimental designSimilar to “planned comparisons” in experimental design situations situations

Domain design may depend in response valuesDomain design may depend in response values EX: Warm EX: Warm VersusVersus Cold Water Lakes Cold Water Lakes


The RESPONSE DESIGNThe RESPONSE DESIGNThe RESPONSE DESIGNThe RESPONSE DESIGN

The Response Design SpecifiesThe Response Design Specifies The process of obtaining a responseThe process of obtaining a response

At an individual element (site)At an individual element (site) Of the resourceOf the resource During a single monitoring periodDuring a single monitoring period

Response: What Will Be Determined on an ElementResponse: What Will Be Determined on an Element Needs to be responsive to the objectives of the Needs to be responsive to the objectives of the

monitoring activitymonitoring activity


The INFERENCE STRATEGYThe INFERENCE STRATEGYThe INFERENCE STRATEGYThe INFERENCE STRATEGY

Is The Basis For Scientific Inference Is The Basis For Scientific Inference Provides The Connection Between Objectives and Provides The Connection Between Objectives and

the Monitoring Strategy the Monitoring Strategy Monitoring Strategy Usually Must Rely On Monitoring Strategy Usually Must Rely On

Obtaining Information on a Subset Of All Possible Obtaining Information on a Subset Of All Possible Elements in the UniverseElements in the Universe

Specifies Which Elements of the Universe Will HaveSpecifies Which Elements of the Universe Will HaveResponses Determined on ThemResponses Determined on Them

Can Be Based on EitherCan Be Based on Either Judgment selection of unitsJudgment selection of units

Inferential validity rests on knowledge of relation between the universe and Inferential validity rests on knowledge of relation between the universe and the units evaluated the units evaluated

– Why do a study if you know this much about the population?Why do a study if you know this much about the population?

Probability selection of unitsProbability selection of units The focus hereThe focus here


The SURVEY DesignThe SURVEY DesignThe SURVEY DesignThe SURVEY Design

Probability Based Survey Designs are Probability Based Survey Designs are Considered HereConsidered Here

May Be Somewhat Limited To Sedentary ResourcesMay Be Somewhat Limited To Sedentary Resources

Positive Features -- As An Observational StudyPositive Features -- As An Observational Study Permit clear statistical inference to Permit clear statistical inference to

well-defined populationswell-defined populations Measurements often can be made in natural settings,Measurements often can be made in natural settings,

giving to greater realism to resultsgiving to greater realism to results


The SURVEY DESIGN - The SURVEY DESIGN - CONTINUEDCONTINUEDThe SURVEY DESIGN - The SURVEY DESIGN - CONTINUEDCONTINUED

DisadvantagesDisadvantages Limited control over predictor variablesLimited control over predictor variables Restricts causative inferenceRestricts causative inference Usually will produce inaccessible sampling pointsUsually will produce inaccessible sampling points

Good - for inferenceGood - for inference Bad - for logisticsBad - for logistics


The TEMPORAL DesignThe TEMPORAL DesignThe TEMPORAL DesignThe TEMPORAL Design

The TEMPORAL DESIGN specifies theThe TEMPORAL DESIGN specifies the pattern of revisits to sites selected by the pattern of revisits to sites selected by the Survey Design Survey Design

Sampled population units are partitioned into oneSampled population units are partitioned into one (degenerate case) or more PANELS. (degenerate case) or more PANELS.

Each population unit in the same panel has theEach population unit in the same panel has the same temporal pattern of revisits. same temporal pattern of revisits.

Panel definition could be probabilistic or Panel definition could be probabilistic or systematic systematic

Several temporal designs follow after a briefSeveral temporal designs follow after a briefdiscussion of the rest of the Anatomy, and a bit discussion of the rest of the Anatomy, and a bit

ononsite selection.site selection.


QUALITY ASSURANCE DESIGNQUALITY ASSURANCE DESIGNQUALITY ASSURANCE DESIGNQUALITY ASSURANCE DESIGN

Defines Those Activities IntendedDefines Those Activities Intended to Provide Data of Known Quality: to Provide Data of Known Quality:

Blind duplicatesBlind duplicates Accepted chemical standards, etcAccepted chemical standards, etc

Can Provide Valid Estimates of the Variance Of PureCan Provide Valid Estimates of the Variance Of PureMeasurement ErrorMeasurement Error


ON SITE SELECTIONON SITE SELECTIONON SITE SELECTIONON SITE SELECTION

Systematically Selected SitesSystematically Selected Sites Good for means & totals, but do not support Good for means & totals, but do not support

design-based estimate of variancedesign-based estimate of variance Probably OK for large areas like national forests, Probably OK for large areas like national forests, Systematic designs can systematically miss things that Systematic designs can systematically miss things that

have a natural layout.have a natural layout. EX: Triangular grid (deliberately skewed) in early EMAP got EX: Triangular grid (deliberately skewed) in early EMAP got

fowled up with fowled up with

– Coastline in the NortheastCoastline in the Northeast

– The canal network in FloridaThe canal network in Florida

– Lakes east of the Cascade Mountain Range in OregonLakes east of the Cascade Mountain Range in Oregon

How to select spatially balanced, but random sites?How to select spatially balanced, but random sites?


GENERALIZED RANDOM TESSELLATION GENERALIZED RANDOM TESSELLATION STRATIFIED (GRTS) DESIGNSTRATIFIED (GRTS) DESIGN


Due to Don Stevens – see referencesDue to Don Stevens – see references Allows Allows

A continuous population modelA continuous population model Variable density sampling by defined areasVariable density sampling by defined areas Accommodates an “imperfect frame” = realityAccommodates an “imperfect frame” = reality Sequential addition of points while maintaining Sequential addition of points while maintaining

spatial balancespatial balance Differing measurementsDiffering measurements

Lots of points for inexpensive measuresLots of points for inexpensive measures A subset for more expensive measuresA subset for more expensive measures A further subset for very expensive measuresA further subset for very expensive measures Implemented in Southern California BightImplemented in Southern California Bight




Two GIS-based implementationsTwo GIS-based implementations EMAP R code operates on ARC “Shape” files, and EMAP R code operates on ARC “Shape” files, and

returns points therereturns points there Begin at http://www.epa.gov/nheerl/arm/Begin at http://www.epa.gov/nheerl/arm/ http://www.epa.gov/nheerl/arm/designpages/monitdesign/monitoring_design_info.htmhttp://www.epa.gov/nheerl/arm/designpages/monitdesign/monitoring_design_info.htm http://www.epa.gov/nheerl/arm/documents/design_doc/psurvey.design_2.2.1.ziphttp://www.epa.gov/nheerl/arm/documents/design_doc/psurvey.design_2.2.1.zip

STARMAP – Dave TheobaldSTARMAP – Dave Theobald RRQRR operates completely in ArcGISRRQRR operates completely in ArcGIS

http://www.nrel.colostate.edu/projects/starmap/rrqrr_index.htmhttp://www.nrel.colostate.edu/projects/starmap/rrqrr_index.htm

Both Allow Variable (spatial) Sampling RatesBoth Allow Variable (spatial) Sampling Rates Generally much better than stratificationGenerally much better than stratification (We can talk about this more if you want)(We can talk about this more if you want)


Urquhart, N.S. and T.M Kincaid (1999). Designs for detecting trend from repeated surveys of ecological resources. Journal of Agricultural, Biological and Environmental Statistics 4: 404 - 414.

Urquhart, N.S. and T.M Kincaid (1999). Designs for detecting trend from repeated surveys of ecological resources. Journal of Agricultural, Biological and Environmental Statistics 4: 404 - 414.

Initially presented at the invited conference Initially presented at the invited conference Environmental Monitoring Surveys Over TimeEnvironmental Monitoring Surveys Over Time, held , held at the University the Washington, Seattle, in 1998at the University the Washington, Seattle, in 1998

Initially presented at the invited conference Initially presented at the invited conference Environmental Monitoring Surveys Over TimeEnvironmental Monitoring Surveys Over Time, held , held at the University the Washington, Seattle, in 1998at the University the Washington, Seattle, in 1998

THE FOLLOWING MATERIAL WAS THE FOLLOWING MATERIAL WAS ADAPTED FROMADAPTED FROM

THE FOLLOWING MATERIAL WAS THE FOLLOWING MATERIAL WAS ADAPTED FROMADAPTED FROM


MOTIVATING SITUATIONMOTIVATING SITUATIONMOTIVATING SITUATIONMOTIVATING SITUATION

In 1986 Oregon Department of Fisheries andIn 1986 Oregon Department of Fisheries andWildlife Sought a “One Time” ProbabilityWildlife Sought a “One Time” ProbabilitySampling Design To Survey Coastal Salmon. Sampling Design To Survey Coastal Salmon.

They Used It In 1990.They Used It In 1990. It showed earlier estimates of salmon returns to spawnIt showed earlier estimates of salmon returns to spawn

to have been grossly overstated.to have been grossly overstated. Consequence: continue to repeat an available design.Consequence: continue to repeat an available design.

How Good Is The Repeated Use Of Such a DesignHow Good Is The Repeated Use Of Such a DesignFor Estimating Trend?For Estimating Trend?


CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS

General: Power for Trend DetectionGeneral: Power for Trend Detection Planned revisits are far superior to obtaining revisitsPlanned revisits are far superior to obtaining revisits

from random “hits”from random “hits”

Year Variance: Power Deteriorates Fast asYear Variance: Power Deteriorates Fast asIncreasesIncreases

Site Variance:Site Variance: No problem with revisit designs.No problem with revisit designs. Without revisits it increases residual variance.Without revisits it increases residual variance.

Sampling Rate: Power Increases with Sampling Rate: Power Increases with Sampling Rate (No surprise!)Sampling Rate (No surprise!)

YEAR2


EVALUATION CONTEXTEVALUATION CONTEXTEVALUATION CONTEXTEVALUATION CONTEXT

General Perspective General Perspective Finite population samplingFinite population sampling But model assistedBut model assisted

A generalization of the “error analysis” perspective of A generalization of the “error analysis” perspective of samplers samplers

ButBut recognizing realities of natural resource sampling recognizing realities of natural resource sampling

Specific PerspectiveSpecific Perspective Finite population, like of stream segments.Finite population, like of stream segments. Response exists continuously in time, or at least forResponse exists continuously in time, or at least for

reoccurring blocks of time.reoccurring blocks of time. Take independent samples at different points in timeTake independent samples at different points in time

(during an “index window”)(during an “index window”)


EVALUATION CONTEXTEVALUATION CONTEXT(CONTINUED)(CONTINUED)

EVALUATION CONTEXTEVALUATION CONTEXT(CONTINUED)(CONTINUED)

Model:Model: Sites (or stream segments) = a random effect Sites (or stream segments) = a random effect Years = a random effect, but may contain trendYears = a random effect, but may contain trend Residual = a random effectResidual = a random effect

Specific evaluation timeSpecific evaluation time Variation introduced by collection protocolVariation introduced by collection protocol Crew effect, if present Crew effect, if present

– (often present for large surveys)(often present for large surveys) “ “Measurement error” - broadly interpretedMeasurement error” - broadly interpreted


PANEL PLANS PANEL PLANS = “TEMPORAL DESIGNS”= “TEMPORAL DESIGNS”

PANEL PLANS PANEL PLANS = “TEMPORAL DESIGNS”= “TEMPORAL DESIGNS”

Sampled Population Units are Partitioned intoSampled Population Units are Partitioned intoOne (Degenerate Case) or More PanelsOne (Degenerate Case) or More Panels

Each population unit in the same panel has the sameEach population unit in the same panel has the sametemporal pattern of revisits.temporal pattern of revisits.

Panel definition could be probabilistic or systematicPanel definition could be probabilistic or systematic

Specific PlansSpecific Plans Always revisitAlways revisit Never revisit Never revisit repeated surveys repeated surveys Random revisits and other plansRandom revisits and other plans


TEMPORAL DESIGN #1:TEMPORAL DESIGN #1: ALWAYS REVISIT = ONE PANELALWAYS REVISIT = ONE PANEL

(This is Wayne Fuller’s “PURE PANEL”)(This is Wayne Fuller’s “PURE PANEL”)

TEMPORAL DESIGN #1:TEMPORAL DESIGN #1: ALWAYS REVISIT = ONE PANELALWAYS REVISIT = ONE PANEL

(This is Wayne Fuller’s “PURE PANEL”)(This is Wayne Fuller’s “PURE PANEL”)

TIME PERIOD ( ex: YEARS)PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ...

1 X X X X X X X X X X X X X


TEMPORAL DESIGN #2:TEMPORAL DESIGN #2: NEVER REVISIT = NEW PANEL EACH YEARNEVER REVISIT = NEW PANEL EACH YEAR

(INDEPENDENT SURVEYS IN A LARGE POPULATION)(INDEPENDENT SURVEYS IN A LARGE POPULATION)

TEMPORAL DESIGN #2:TEMPORAL DESIGN #2: NEVER REVISIT = NEW PANEL EACH YEARNEVER REVISIT = NEW PANEL EACH YEAR

(INDEPENDENT SURVEYS IN A LARGE POPULATION)(INDEPENDENT SURVEYS IN A LARGE POPULATION)

TIME PERIOD ( ex: YEARS)PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X


TEMPORAL DESIGN #3:TEMPORAL DESIGN #3: ROTATING PANEL like NASSROTATING PANEL like NASS

TEMPORAL DESIGN #3:TEMPORAL DESIGN #3: ROTATING PANEL like NASSROTATING PANEL like NASS

TIME PERIOD ( ex: YEARS)PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 1 X X X X X 2 X X X X X 3 X X X X X 4 X X X X X 5 X X X X X 6 X X X X X 7 X X X X X 8 X X X X X 9 X X X X X


TEMPORAL DESIGN #3:TEMPORAL DESIGN #3:

ROTATING PANELROTATING PANELTEMPORAL DESIGN #3:TEMPORAL DESIGN #3:

ROTATING PANELROTATING PANEL

A Rotating Panel Design Is The Temporal DesignA Rotating Panel Design Is The Temporal DesignUsed By The National Agricultural StatisticalUsed By The National Agricultural StatisticalService (US - “NASS”)Service (US - “NASS”)

This Temporal Design Is “Connected” In The This Temporal Design Is “Connected” In The Experimental Design SenseExperimental Design Sense

It is fairly well suited for estimation “status,” It is fairly well suited for estimation “status,” But not nearly particularly powerful for detecting trend But not nearly particularly powerful for detecting trend

over intermediate time spansover intermediate time spans


TEMPORAL DESIGN:TEMPORAL DESIGN: SERIALLY ALTERNATINGSERIALLY ALTERNATING

(ORIGINAL EMAP)(ORIGINAL EMAP)

TEMPORAL DESIGN:TEMPORAL DESIGN: SERIALLY ALTERNATINGSERIALLY ALTERNATING

(ORIGINAL EMAP)(ORIGINAL EMAP)

This Temporal Design Is “Unconnected” in theThis Temporal Design Is “Unconnected” in the Experimental Design Sense. Experimental Design Sense.

TIME PERIOD ( ex: YEARS)PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 1 X X X X 2 X X X 3 X X X 4 X X X


TIME PERIOD ( ex: YEARS)PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ... 1 X X X X 2 X X X 3 X X X

4 X X X1A X X X X X1B X X X X X…2A X X X X…

TEMPORAL DESIGN #5:TEMPORAL DESIGN #5: AUGMENTED SERIALLY ALTERNATINGAUGMENTED SERIALLY ALTERNATING(CURRENTLY USED BY EMAP FOR SURFACE WATERS)(CURRENTLY USED BY EMAP FOR SURFACE WATERS)

TEMPORAL DESIGN #5:TEMPORAL DESIGN #5: AUGMENTED SERIALLY ALTERNATINGAUGMENTED SERIALLY ALTERNATING(CURRENTLY USED BY EMAP FOR SURFACE WATERS)(CURRENTLY USED BY EMAP FOR SURFACE WATERS)

This Temporal Design Is “Connected” in theThis Temporal Design Is “Connected” in theExperimental Design Sense.Experimental Design Sense.


NUMBERS OF OCCURENCES

YEAR N = 240 N = 600PANEL 1 2 3 … SAMPLE 1 SAMPLE 2 SAMPLE 1 SAMPLE 2

1 X 37 36 46 482 X 38 35 46 483 X 35 34 46 494 X X 9 9 6 65 X X 12 10 6 56 X X 11 11 6 5

7 X X X 2 5 2 1NO

VISIT96 100 442 438

TEMPORAL DESIGN #6:TEMPORAL DESIGN #6: RANDOM PANELS RANDOM PANELS

TEMPORAL DESIGN #6:TEMPORAL DESIGN #6: RANDOM PANELS RANDOM PANELS


STATISTICAL MODELSTATISTICAL MODELSTATISTICAL MODELSTATISTICAL MODEL

Consider A Finite Population Of SitesConsider A Finite Population Of Sites {{SS1 1 , S, S2 2 , … , S, … , SN N } }

and a Time Series Of Response Values At Each Site:and a Time Series Of Response Values At Each Site:

A finite population of time seriesA finite population of time series Time is continuous, but suppose Time is continuous, but suppose

Only a sample can be observed in any year, andOnly a sample can be observed in any year, and Only during an index window of, say, 10% of a yearOnly during an index window of, say, 10% of a year

{ ( ), ( ), , ( )} ( )Y t Y t Y t Y tN1 2 and their average:


STATISTICAL MODEL -- IISTATISTICAL MODEL -- IISTATISTICAL MODEL -- IISTATISTICAL MODEL -- IIAGAIN CONSIDER THE UNDERLYING TIME SERIES

DURING AN INDEX WINDOW

and their averages: and

= var{

{ ( ), ( ), , ( )}

( ), ( ), ( ).

( )},

var{ ( )}

var{ ( ) ( ) ( ) ( )}

Y t Y t Y t

Y Y t Y

Y

Y t

Y t Y Y t Y

N

i

SITE i

YEAR

RESIDUAL i i

1 2

2

2

2


PART OF A TIME SERIESDURING AN INDEX WINDOW

5

10

15

20

3.4 3.5 3.6 3.7

YEARS

RE

SP

ON

SE

V

AL

UE

S E

D

UV|W| RESIDUAL

2


STATISTICAL MODEL -- IIISTATISTICAL MODEL -- IIISTATISTICAL MODEL -- IIISTATISTICAL MODEL -- III

{ ( )} { }

( ) ( ) ( )

~ ( , ), ~ ( , ), ~ ( , ),

Y t Yi

j

Y Y Y Y Y Y Y Y Y Y

Y S T E

S T E

i ij

ij i j ij i j

i j ij

i SITE j YEAR ij RESIDUAL

RST

where indexes sites

indexes "years"

and and

with these random variables otherwise uncorrelated.

0 0 02 2 2


STATISTICAL MODEL -- IVSTATISTICAL MODEL -- IVSTATISTICAL MODEL -- IVSTATISTICAL MODEL -- IV

If If PP Indexes Panels, Then Indexes Panels, Then Sites are nested in panels: Sites are nested in panels: pp( ( ii ) and ) and Years of visit are indicated by panel with Years of visit are indicated by panel with

nnpjpj > 0 or > 0 or nnpj pj = = 0 0

for panels visited or not visited in year for panels visited or not visited in year jj The vector of cell means ( of “visited” cells) has The vector of cell means ( of “visited” cells) has

a covariance matrix a covariance matrix

cov ( , , , )Y npj SITE YEAR RESIDUAL pjc h 2 2 2


STATISTICAL MODEL -- VSTATISTICAL MODEL -- VSTATISTICAL MODEL -- VSTATISTICAL MODEL -- V

Now Let X Denote a Regressor Matrix ContainingNow Let X Denote a Regressor Matrix Containinga Column Of 1’s and a Column of the Numbers a Column Of 1’s and a Column of the Numbers of the Time Periods Corresponding to the Filledof the Time Periods Corresponding to the FilledCells. The Second Elements ofCells. The Second Elements of

Contain an Estimate Of Trend and its Contain an Estimate Of Trend and its Standard Error.Standard Error.

and ( ' ) ' ,

cov( ) ( ' )

X X X Y

X X

1 1

1

1

1


Ability of a Panel Plan to Detect Trend Can BeAbility of a Panel Plan to Detect Trend Can BeExpressed As Power.Expressed As Power.

We Will Evaluate Power in Terms of Ratios ofWe Will Evaluate Power in Terms of Ratios ofVariance Components:Variance Components:

and ofand of

TOWARD POWERTOWARD POWERTOWARD POWERTOWARD POWER

0 2/ , ~ ( , )RESIDUAL N so approximately,

SITE RESIDUAL YEAR RESIDUAL2 2 2 2/ / and


A SIMULATION STUDY A SIMULATION STUDY TO MAKE POWER COMPARISONSTO MAKE POWER COMPARISONS

A SIMULATION STUDY A SIMULATION STUDY TO MAKE POWER COMPARISONSTO MAKE POWER COMPARISONS

n = 60n = 60 N = 60, 240, 600, 1200, 10,000N = 60, 240, 600, 1200, 10,000

==> Sampling rates of 100%, 25%, 10%, 5%, ~ 0%==> Sampling rates of 100%, 25%, 10%, 5%, ~ 0%

SITES

RESIDUAL

2

2 0, 1.875, 2.5

YEARS

RESIDUAL

2

2 0, 0.075, 0.15, 0.3


POWER FOR DETECTING TRENDSAMPLING A FINITE POPULATION OF SIZE N

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

N = 60, n = 60

SITES YEARS2 21875 0 000 . . and

ALWAYS REVISIT, or EMAP-LIKE



0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

N = 60, n = 60

SITES YEARS2 21875 . and 0.000, 0.075, 0.15, 0.30




0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

N = 60, n = 60





0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

N = 10,000, n = 60

N = 60, n = 60


NEVER REVISIT




0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

N = 600, n = 60

N = 10,000, n = 60

N = 60, n = 60

RANDOM REVISIT



NEVER REVISIT



0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

N = 600, n = 60

N = 10,000, n = 60

N = 60, n = 60

NEVER REVISIT



RANDOM REVISIT


POWER FOR DETECTING TREND:AS A FUNCTION OF TEMPORAL DESIGN

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

TIME ( = YEARS )

PO

WE

R f

or

TR

EN

D

14 & 5

23

ROTATING PANEL


CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS

General: Power for Trend DetectionGeneral: Power for Trend Detection Planned revisits are far superior to obtaining revisitsPlanned revisits are far superior to obtaining revisits

from random “hits”from random “hits”

Year Variance: Power Deteriorates Fast asYear Variance: Power Deteriorates Fast asIncreasesIncreases

Site Variance:Site Variance: No problem with revisit designs.No problem with revisit designs. Without revisits it increases residual variance.Without revisits it increases residual variance.

Sampling Rate: Power Increases with Sampling Rate: Power Increases with Sampling Rate (No surprise!)Sampling Rate (No surprise!)

YEAR2


CURRENT WORKCURRENT WORKCURRENT WORKCURRENT WORK Stevens D.L. Jr and A.R. Olsen (2003). Variance

estimation for spatially balanced samples of environmental resources. Environmetrics 14: 593-610.

Proposed a local estimator for variance. I have been using some variance component estimators.

How do these two approaches relate? Should one be used rather than the other?

MS Student – Sarah Williams Use local estimator for things like status measures

Because it includes some site variance Use components of variance for trend studies

Revisits to sites remove most of the effect of that component

Currently investigating variance component of trend And its impact on trend detection


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 represented. EPA does not endorse any products or commercial services mentioned in this presentation.

FUNDING ACKNOWLEDGEMENT


0.0606 0.0612 0.0618

020

40

0.0684 0.0703 0.0722 0.0791 0.0845 0.0899

0.0606 0.0612 0.0618

020

40

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0.0606 0.0612 0.0618

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N =

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N =

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N =

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00P

erce

ntP

erce

ntP

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Power Power Power

DISTRIBUTION OF SIMULATED POWER: 10 YEARSDISTRIBUTION OF SIMULATED POWER: 10 YEARSSITE VARIANCE = 1.875; YEAR VARIANCE:SITE VARIANCE = 1.875; YEAR VARIANCE:

0.30 0.10 0.075 0.30 0.10 0.075


0.30 0.10 0.075 0.30 0.10 0.075

RA

TE

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AT

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RA

TE

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0.139 0.144 0.148

020

40

0.208 0.222 0.237 0.302 0.342 0.382

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020

40

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020

40

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240

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600

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Power Power Power


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0.0606 0.0612 0.0618

020

40

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0.0606 0.0612 0.0618

020

40

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0.0606 0.0612 0.0618

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40

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N =

600

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00P

erce

ntP

erce

ntP

erce

nt

Power Power Power


0.30 0.10 0.075 0.30 0.10 0.075


0.30 0.10 0.075 0.30 0.10 0.075

RA

TE

= 2

5%R

AT

E =

5%

RA

TE

= 1

0%


0.139 0.144 0.148

020

40

0.208 0.222 0.237 0.302 0.342 0.382

0.139 0.144 0.148

020

40

0.208 0.222 0.237 0.302 0.342 0.382

0.139 0.144 0.148

020

40

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N =

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N =

600

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00P

erce

ntP

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ntP

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nt

Power Power Power


0.30 0.10 0.075 0.30 0.10 0.075


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RA

TE

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5%R

AT

E =

5%

RA

TE

= 1

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we probably could have more fun talking about these traffic stoppers

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