Multiscale Analysis: Options for Modeling PresenceAbsence of Bird Species

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Multi-scale Analysis Options for
ModelingPresence/Absence of Bird Species
Kathryn M. Georgitis1, Alix I. Gitelman1, and
Nick Danz2 1 Statistics Department, Oregon State
University 2 Natural Resources Research
Institute University of Minnesota-Duluth
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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 Program on Designs and Models for
Aquatic Resource Surveys 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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Talk Overview

• Ecological Question of Interest
• Western Great Lakes Breeding Bird Study
• Interesting Features of our Example
• Options for Modeling Species Presence/Absence
• (1) Separate Models for Each Spatial Extent
• (2) One Model for all Spatial Extents
• (3) Model using Functionals of Explanatory
  Variables
• (4) Graphical Model

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Ecological Question of Interest

• How does the relationship between landscape
  characteristics and presence of a bird species
  change with scale?
• What scale is the most useful in terms of
  understanding bird presence/absence?

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Concentric Circle Sampling Design

1000m
500m
100 m
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Western Great Lakes Breeding Bird Study

• Response Variable
• Presence/Absence of Pine Warbler
• Explanatory Variables
• land cover within 4 different spatial extents
• Ten land cover types

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Interesting Features of the Data

• Correlation between Explanatory Variables

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Correlation Between Pine and Oak-Pine Measured at
Different Scales
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Relationship between Land Cover Variables and
Spatial Extent
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Options for Modeling Presence/Absence of Pine
Warbler

• (1) Separate Models for Each Spatial Extent
• (2) One Model for all Spatial Extents
• (3) Model using Functionals of Explanatory
  Variables
• (4) Bayesian Network (Graphical) Model

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Option 1 Separate Models Approach

• (100m) M1 log(p(1-p)-1) C1b1
  
• (500m) M5 log(p(1-p)-1) C5b5
• (1000m) M10 log(p(1-p)-1) C10b10
  
• (5000m) M50 log(p(1-p)-1) C50b50
• where
• Y denotes n-length vector of binary response
  with Pr(Yi1) pi,
• C1 denotes matrix of explanatory variables at
  the 100m scale

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Option 1 Separate Models Approach
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Option 1 Separate Models Approach

• Disadvantages
• does not account for possible relationships
  between spatial extents
• multi-collinearity of explanatory variable
• 210 possible models for each spatial extent

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Options for Modeling Presence/Absence of Pine
Warbler

• (1) Separate Models for Each Spatial Extent
• (2) One Model for all Spatial Extents
• (3) Model using Functionals of Explanatory
  Variables
• (4) Bayesian Network (Graphical) Model

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Option 2 One Model for all Spatial Extents

• Mall log (p (1-p)-1) Zall ball
  
• where
• Y denotes n-length vector of binary response with
  Pr(Yi1) pi,
• Zall C1, C5, C10

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Option 2 One Model for all Spatial Extents
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Option 2 One Model for all Spatial Extents

• Advantages
• allows for interactions between scales
• Disadvantages
• serious multi-collinearity problems
• 230 possible models

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Options for Modeling Presence/Absence of Pine
Warbler

• (1) Separate Models for Each Spatial Extent
• (2) One Model for all Spatial Extents
• (3) Model using Functionals of Explanatory
  Variables
• (4) Bayesian Network (Graphical) Model

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Option 3 Model using Functionals of Explanatory
Variables

• Difference Model
• Mdiff log (p (1-p)-1) Zdiff
  bdiff where Zdiff C5 -
  C1 (element-wise)
• Proportional Model
• Mprop log (p (1-p)-1) Zprop bprop
• where Zprop C5 /C1 (element-wise)

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Option 3 Model using Functionals of Explanatory
Variables
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Option 3 Model using Functionals of Explanatory
Variables

• Advantages
• incorporates two spatial extents
• Disadvantages
• biologically meaningful?
• multi-collinearity
• model selection

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Options for Modeling Presence/Absence of Pine
Warbler

• (1) Separate Models for Each Spatial Extent
• (2) One Model for all Spatial Extents
• (3) Model using Functionals of Explanatory
  Variables
• (4) Bayesian Network (Graphical) Model

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Option 4 Graphical Model

• - think of explanatory variables and response
  holistically (i.e., as a single multivariate
  observation)

Logistic Regression Model
Bayesian Network (Graphical) Model
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Option 4 Graphical Model

• For comparison with MALL, we use the same
  explanatory variables

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Option 4 Graphical Model
Diagram of MALL
Diagram of Bayesian MALL
spruce-fir 1000m
N. hardwoods 100m
aspen-birch 100m
pine oak-pine 100m
Pine Warbler
Pine Warbler
Where Z variables in MALL
log (p (1-p)-1) Zball fixed Z
Z Multinomial(P,100) log(spruce-fir1000)
N(m,s2) log (p (1-p)-1) Z b b5
log(spruce-fir1000)
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Option 4 Graphical ModelComparison of MALL and
Bayesian MALL
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Option 4 Graphical Model
Bayesian MALL
Bayesian Network Model
Pine Warbler
Where Z variables in MALL Z
Multinomial(P,100) log(spruce-fir1000)
N(m,s2) log (p (1-p)-1) Z b b5
log(spruce-fir1000)
Zi Multinomial(Pi,100) Pi(Pi,1, Pi,2,
Pi,3, Pi,4, Pi,5) log(Pi,1/(1- Pi,1))f0 f1
log(spruce-fir1000) log(spruce-fir1000) N(m,s2)
log(p (1-p)-1) b0 b1 pine oak-pine100
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Option 4 Graphical ModelComparison of two
Bayesian Network Models
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Option 4 Graphical Model

• Advantages
• considers ecological system holistically
• can eliminate multi-collinearity
• biologically meaningful
• Disadvantages
• model selection
• implementation issues

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Acknowledgements

• Don Stevens, OSU
• Jerry Niemi, N.R.R.I Univ. of Minn., Duluth
• JoAnn Hanowski, N.R.R.I Univ. of Minn., Duluth