GRTS for the Average Joe: A GRTS Sampler for Windows

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GRTS for the Average Joe A GRTS Sampler for
Windows

• Trent McDonald
• Monitoring Science Symposium
• Denver, CO
• 21-24 Sep 2004

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Outline

• Motivation for the GRTS sampler
• Description of the sampler, S-Draw
• Examples
• Performance
• Planned modifications

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Motivation

• Basic hypotheses
• Average Joe understands the utility of GRTS
  samples
• Average Joe does not totally understand the inner
  workings of GRTS sampling
• Average Joe could not draw a GRTS sample if his
  life depended on it.

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Motivation

• A GRTS sampler was needed because
• Average Joe should be able to draw GRTS samples
• I should be able to draw GRTS samples

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S-Draw

• Windows application
• Written in Fortran 95
• Amazing speed
• Cross-platform portability ok
• Cross-language calls easy (S-Plus, R, C)
• Used Lahey compiler
• Also S-DrawB

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S-Draw

• Draws samples of
• Discrete units (finite populations)
• Located in either 1-D or 2-D
• Examples
• 1-D River segments located by river mile
• 2-D Grid cells located in an area
• 2-D River segments located by coordinates of
  their midpoints

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S-Draw

• Coordinates of units are specified in a text file
  
• i.e., the sampling frame is a ASCII file
• Sampling frame can optionally contain weights and
  IDs

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S-Draw

• Frame Formats

K specified on the first line of the frame file
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S-Draw

• Example frame Eagle study

Columns following frame data ignored
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S-Draw

• Does the quadrant-recursive mapping of Stevens
  and Olsen (2004)

Randomize
2
4
n
0
1
3
2
3
1
4
2
4
4
3
1
2
1
3
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S-Draw

• Pixelsize size of smallest quadrant in
  recursive map
• S-Draw allows user to specify pixelsize

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S-Draw

• Line segment (0,n sampled using a systematic
  sample
• Random start between (0,1
• Step size 1.0

Random start 0.19
n
2
0
1
3
u1
u2
u4
u3
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S-Draw

• Reverse-hierarchical ordering of sample
  optionally applied
• Convert sample order to base-4 10010012004
• Reverse base-4 digits 012004002104
• Convert back to base-10 0021043610
• Sort sample on base-10 numbers

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S-Draw

• Users can pre-define the hierarchical sort keys
• Digits within each level of the hierarchy are
  randomly permuted, and sample is drawn as usual
• Allows use of a general recursive map
• Triangular-recursive
• IDs like state.county.watershed.segment

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S-Draw

• Triangular-recursive mapping

1
2
4
3
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Examples

• C\gts-drawb n 20 popsize 100
• Will produce 1-D GRTS sample of size 20 assuming
  units are located at coordinates 1, 2, , 100
• C\gts-drawb n 20 popsize 100 pixelsize 100
• Will produce a simple random sample of size 20
• C\gts-drawb n 20 popsize 100 nrand
• Will produce a fixed-size systematic sample

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Examples

• Golden eagle sample
• Dense grid of transect start points spaced 2km
  north-south, 100km east-west
• No-fly transect portions eliminated, new
  transect start created
• Frame
• 27,078 starting points over western US
• 2-D coordinates and IDs
• Desire sample of 416 transects
• 208 primary, 208 alternate

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Examples
Sample size
Coordinates and ID in frame
2-D
Frame file
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Examples
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Performance

• GRTS sample of size 500 from 100,000 took 4.2
  seconds on my laptop
• GRTS sample of size 500 from 1,000,000 took 44.3
  seconds
• Algorithms approximately O(N)
• Runs should take 4.45e-5(N) seconds
• N5,000,000 3.7 minutes

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Enhancements

• An S-Plus and R interface
• Ability to read .e00 file, and ArcGIS binary
  files
• Ability to take a true point sample