Weighting Adjustments for Estimates of Coho Salmon Abundance When Survey Sites are Missing At Random

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Weighting Adjustments for Estimates of Coho
Salmon Abundance When Survey Sites are Missing At
RandomLeigh Ann Harrod, Virginia Lesser, Breda
Munoz-HernandezOregon State University,
Department of StatisticsAugust 12, 2003
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The research described in this presentation has
been funded by the U.S. Environmental Protection
Agency through the STAR Cooperative Agreement
CR82-9096-01 National Research Program on
Design-Based/Model-Assisted Survey Methodology
for Aquatic Resources at Oregon State
University. It has not been subjected to the
Agency's review and therefore does not
necessarily reflect the views of the Agency, and
no official endorsement should be inferred.
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Project Goal

• To develop a users manual for environmental
  scientists working with probability surveys that
  include nonresponding units
• The manual will include
• Methods to determine type of nonresponse
• Ignorable
• Missing-completely-at-random (MCAR)
• Missing-at-random (MAR)
• Non-ignorable
• Approaches to deal with nonresponse
• Examples of nonresponse adjustment approaches
  with sample data sets

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Topics Covered

• Data description
• Assessment of missing-at-random data assumption
• Assessment of significance of auxiliary data as
  class adjustment variables
• Presentation of two estimators
• Nonresponse simulation

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Data description

• Oregon Department of Fish and Wildlife (ODFW) and
  the EPA cooperate to monitor coho salmon spawner
  and juvenile populations and coho habitat
• Measures of spawner abundance are obtained at
  each selected site
• Adult coho spawner surveys include sites that
  cannot be surveyed due to landowner denial of
  access or environmental factors

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Missing Sites for Which Landowner Access Was
Obtained
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Are these unsurveyed sites missing-at-random?

• The nonresponse is ignorable if the response
  probabilities depend on auxiliary variables but
  not the response
• Juvenile coho survey data are available for a
  subset of coho spawner survey sites
• ODFW biologists feel that spawner and juvenile
  abundances are highly and positively correlated
• Coho juvenile survey responses are used as a
  covariate in a logistic model to predict the
  probability that a spawner site is surveyed

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Evaluation of the missing-at-random assumption
for spawner survey sites for which landowner
access is obtained

• 108 sites over 4 years were available for both
  juvenile and spawner surveys
• Neither juvenile frequency nor juvenile density
  were significant in the logistic regression model
  of the spawner survey probability within any
  survey year
• Given the biological assumption that juvenile and
  spawner abundances are highly correlated, we will
  assume that spawner abundance does not differ
  between surveyed and unsurveyed sites
• Therefore, we assume the sites are
  missing-at-random

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Class adjustment variables

• Auxiliary information that is available for both
  surveyed and unsurveyed sites is examined for
  association with response rates
• For the ODFW spawner survey data, the Monitoring
  Area and Number of Owners are examined for
  modeling nonresponse

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ODFW Auxiliary Variables

• The Monitoring Areas (MAs) are the
  mutually-exclusive geographic land units
  containing the major coastal watersheds in Oregon
• MAs are used as strata in the sample selection
• The number of landowners is categorized as

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Spawner Means by Monitoring Area and Number of
Owners
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Assessing Class Adjustment Variables

• ANOVA is used to determine if response means for
  surveyed sites differ within levels of the
  auxiliary variables
• Response rates do differ significantly by Number
  of Owners (p0.008), Monitoring Area (p0.032),
  and for the interaction of Number of Owners by
  Monitoring Area (p0.027).
• Both variables will be used for adjustments for
  all years

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Weighting Class Adjustment

• Sites within a weighting class have more similar
  characteristics than as compared to the
  population as a whole
• The sampling weights of surveyed sites are
  adjusted so that the surveyed sites more closely
  represent the selected sample

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Weighting Class Adjustment Assumptions

• Within a weighting class, the probability that a
  site is surveyed does not depend on the response
  of interest (data are missing-at-random).
• The probability of response is the same within
  each weighting class.
• Information on class membership for surveyed and
  unsurveyed sites is available.
• There is at least one respondent in each class.

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Weighting Class Adjustment Calculations
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Unadjusted Estimates
Weighting Class Adjustment Estimates
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Poststratification Adjustment

• Similar to the weighting class adjustment except
  that population counts are used to adjust the
  weights
• If the same adjustment class variables are used,
  the variance of the poststratification adjustment
  estimator is smaller than for the weighting class
  adjustor.

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Poststratification Adjustment Assumptions

• The probability of response is the same within
  each weighting class.
• Within a poststratification class, the
  probability that a site is surveyed does not
  depend on the response of interest.
• The population size within each weighting class
  is known.
• There is at least one respondent in each class.

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Poststratification Adjustment Calculations
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Unadjusted Estimates
Poststratification Adjustment Estimates
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Nonresponse Simulation

• For each year, 5 to 50 of the surveyed sites
  were randomly dropped and estimates were computed
• The simulations generated 1000 random samples and
  corresponding estimates and variances
• The means of the simulated values are plotted
  against the nonresponse rate
• The weighting adjusted estimators and variances
  are compared to the estimator that does not
  account for nonresponse

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Means of the Simulated Estimates of the 1998
Adult Coho Spawner Abundance Estimates with
Adjustments by Monitoring Area and Number of
Owners
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Means of the Simulated Standard Errors of the
1998 Adult Coho Spawner Abundance Estimates with
Adjustments by Monitoring Area and Number of
Owners
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Future work

• Prepare and finalize manual on handling missing
  data in environmental surveys
• Obtain auxiliary information for juvenile and
  habitat surveys and apply the same techniques
• Model the response probability with logistic
  regression and adjust the inclusion probability
  with estimated response probabilities
• Discuss the feasibility of making extra attempts
  to sample unsurveyed sites. If possible,
  investigate other estimates to incorporate the
  double sample.

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References

• Cochran, W. G. (1977). Sampling Techniques. New
  York Wiley.
• Lessler, J.T. and Kalsbeek, W.D. (1992).
  Nonsampling Error in surveys. New York Wiley.
• Oh, H.L. and Scheuren, F.J. (1983). Weighting
  adjustment for unit nonresponse. In Incomplete
  Data in Sample Surveys, W.G. Madow, I. Olkin, and
  D.B. Rubin (eds), 143-184. New York Academic
  Press.
• Thompson, S.K. (1992). Sampling. New York
  Wiley.