Module 8: Discrete Choice Models with Changing Availability

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Module 8 Discrete Choice Models with Changing
Availability

• RSF Conference Workshop 11-13 January 2003

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Summary

• Discrete choice models explained
• Pigeon guillemot example

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Discrete Choice Models

• Motivation

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Discrete Choice Models

• Data consist of
• The set of units available at choice i and their
  characteristics
• The unit selected at choice i and its
  characteristics
• Define Cij xij unit j was available at choice
  i
• Define xi0characteristics of ith unit chosen

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Discrete Choice Models

• Assume that the RSF takes the form
• w(x) expß0 ß1x1 ... ßpxp.
• Then probability of choosing a unit with
  characteristics xi0 over all the others in the
  choice set is,

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Discrete Choice Models

• Full likelihood for ß multiplies terms

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Discrete Choice Models

• Methods are applicable when
• habitat changes over time , and/or
• animals are unable to move throughout their
  entire home range between observations.

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Illustration polar bears
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Pigeon Guillemot Example

• 3 pigeon guillemot sea-birds radio collared
• Researchers recorded data on 82 foraging bout
  locations in Prince William Sound

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Pigeon Guillemot Example
Nest Colony
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Pigeon Guillemot Example

• Used units grid cell of foraging bout
• Available units choice set a set of 232 cells
• In GIS, recorded over-water distance of every
  grid cell to last foraging bout.
• Would expect locations far away to have
  relatively little probability of selection

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Pigeon Guillemot Example

• Other variables
• Distance to last bout (DIST)
• Water depth (DEPTH)
• Schooling fish density (SFD)
• Distance to colony (COL_DIST)
• Benthic vs. herring feeders (Iben)

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Pigeon Guillemot Example

• Final discrete choice model
• w(x) exp-0.855(DIST) 0.456(DISTIben)
  0.007(DEPTH) 0.032(DEPTHIben) 0.262(SFD)
  0.497(SFDIben)
• Herring feeding birds
• w(x) exp-0.855(DIST)0.007(DEPTH)0.262(SFD)
• Benthic feeding birds
• w(x) exp-1.311(DIST)0.038(DEPTH)-0.235(SFD)

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RSF Surface, Herring Feeder
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RSF Surface, Benthic Feeder