A Comparison of Variance Estimates of Stream Network Resources

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A Comparison of Variance Estimates of Stream
Network Resources

• Sarah J. Williams
• Candidate for the degree of Master of Science
• Colorado State University
• Department of Statistics

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A Comparison of Variance Estimates of Stream
Network Resources

• Sarah J. Williams
• Candidate for the degree of Master of Science
• Colorado State University
• Department of Statistics

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Todays Outline

• The problem
• Two methods of variance estimation
• Local Area Neighborhood estimate
• Linear model and Components of Variance
• Comparing the two estimates
• Practical Implications

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Part 1 The Problem

• Surveys of aquatic resources provide challenges
  in sampling and also analysis

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Studies of aquatic resources need to have a
proper temporal design that will allow for trend
detection

• The revisit structure may be the most difficult
  part of the study to define
• Waterways are highly variable and volatile

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Studies of aquatic resources need to have a
proper spatial design that will preserve spatial
proximity

• Generalized Random Tessellation Stratified
  (GRTS) sample

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By using well planned panel designs researchers
achieve both of these very important objectives
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Part 2 Two methods of variance estimation

• Of course, there are many methods for estimating
  the variance of a sample
• Today, we will focus on two of these methods
• Local Area Neighborhood Estimate (NBH)
• Linear model components of variance

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Local Area Neighborhood Estimate

• Design-based
• Compares well to a Horvitz-Thompson estimate

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Mixed Linear Model and Components of Variance

• Why use this method?
• Design-based estimators have no inclusion of time
• Specifications of the study

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Mixed Linear Model and Components of Variance

In either case above we have that for a single
observation
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Part 3 Comparing the two methods
Coho Salmon of the Pacific Northwest
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The Oregon Plan for Salmon and Watersheds

• GRTS design (40 panels)
• 3-year salmon lifecycle
• Each monitoring area is a stratum

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The Data

• 35 responses of interest (Landscape habitat)
• 6 regions of interest
• 8 years available
• 1,535 site visits (1,055 distinct sites)

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Results and Conclusions

• As residual component of variance increases, so
  too does NBH
• As site component of variance increases, NBH
  decreases

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Results and Conclusions
Indicating that on average, the residual
component of variance is 0.63 times the NBH
estimate
Indicating that on average, the site component of
variance is 1.32 times the NBH estimate
It was also of interest to express the NBH
estimate as a linear combination of the residual
and site components of variance
This relation is forced through the origin.
Using interpretable as R2 shows moderate
strength of this relation
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What does it all mean? Practical Implications

• When is it appropriate to use the linear model
  method over the local area estimate of variance?
• The local estimate will capture all variance due
  to residual effect and we have seen that time
  variance is relatively negligible
• The results of this study show that the NBH
  accounts for roughly 60 -70 of variance due to
  site
• Note again, the inverse relationship of site
  variance with NBH
• This project is an intermediate step in the
  larger problem of accurately modeling trend of an
  environmental indicator

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Acknowledgements

• N. Scott Urquhart
• Don Stevens
• Tom Kincaid
• Kim Jones
• Oregon Department of Fisheries and Wildlife
• The work reported here was developed under the
  STAR Research Assistance Agreements CR-829095
  awarded to Colorado State University and
  CR-829096 awarded to Oregon State University by
  the U.S. Environmental Protection Agency (EPA).
  This presentation has not been formally reviewed
  by the EPA. The work done and views expressed
  here are solely those of the author and STARMAP.
  EPA does not endorse any products or commercial
  services mentioned in this report.
• Thank you for listening today

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Resources

• Hocking, R.R. Methods and Applications of Linear
  Models. Wiley, 2002
• Horvitz, D.G. and D.J. Thompson. 1952. A
  generalization of sampling without replacement
  from a finite universe. Journal of the American
  Statistical Association 47 663685.
• Sarndal, C., Swensson, B., and Wretman, J. Model
  Assisted Survey Sampling. Springer-Verlag, 1992.
• Stevens, D.L., and Olsen A.R. 1999. Spatially
  Restricted Surveys Over Time for Aquatic
  Resources. Journal of Agricultural, Biological
  and Environmental Statistics, Vol.4, No.4
  415-428.
• Stevens, D.L. 2003. Sampling Design and
  Statistical Analysis Methods for the Integrated
  Biological and Physical Monitoring of Oregon
  Streams. The Oregon Plan for Salmon and
  Watersheds.
• Stevens, D.L., and Olsen, A.R. 2003. Variance
  estimation for spatially balanced samples of
  environmental resources. Environmetrics,
  submitted.
• Strahler A.N. 1957. Quantitative analysis of
  watershed geomorphology. Transactions ofthe
  American Geophysical Union, 21, 913-920.
• Urquhart, N.S., Overton W.S., and Birkes D.S.
  1993. Comparing Sampling Designs for Monitoring
  Ecological Status and Trends Impact of Temporal
  Patterns. Statistics for the Environment,
  chapter 371-85.
• Urquhart, N.S., Paulsen, S.G. and Larsen, D.P.
  1998. Monitoring for policy-relevant regional
  trends over time. Ecological Applications, 8
  246-257.
• Urquhart, N.S., and Kincaid, T.M. 1999. Designs
  for detecting trend from repeated surveys of
  ecological resources. Journal of Agricultural,
  Biological and Environmental Statistics, 4
  404-414.
• The Oregon Plan for Watersheds and Salmon,
  Biennial Report, 2005.
• www.epa.gov/emap
• www.dfw.state.or.us
• Map obtained from http//nrimp.dfw.state.or.us/crl
  /default.aspx?PNGCAs