Regression in GRID

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Regression in GRID

• FE423 - February 27, 2000

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Labs

• Another reason for AML - re-sampling
• resample big grid to little grid
• do lab on little grid
• work out bugs on little grid
• write up aml
• check aml on little grid
• run aml on big grid while writing up lab
• Send me a note when you finish your lab

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Outline

• Probability models - simulation
• Linear models - regression
• Logistic Regression
• Answering questions with data

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Questions

• In forest management, we have questions like
• Does logging cause landsliding?
• Does logging impact fish?

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Spatial Data

• One tool for answering them is spatial data.
• Outcomes
• fish counts, landslides, sediment supply, etc.
• Management Activities
• harvest units, roads, etc.
• Other things that might impact
• slope, contributing area, etc.

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Natural Variability

• Unfortunately, natural processes are highly
  variable, so we rarely have a 1-to-1 causal
  relationship.
• Management impacts are usually small compared to
  the natural variation.
• In competitive ecosystems, a small impact can be
  the difference in survival.

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Probability Models in GRID

• We can model this natural variability in GRID
  with random functions
• RAND()
• NORMAL()

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The RAND() Function

• The RAND() function makes draws from the range
  (0,1)

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Simulating Random Events

• Example We can use SMORPH hazard ranking to
  simulate landslide observations.
• haz con(slope lt 40 and plan lt .5, 1,
• ...
• prob con(haz eq 0, .001, haz eq 1, .01, .1)
• LS_sim con(rand() lt prob, 1, 0)

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Simulating Random Events
Planform curvature
slope
Simulated landslides
hazard
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The NORMAL() Function

• The normal() function makes draws from standard
  normal distribution

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Simulating Random Events

• Example fish counts
• we can model observations
• fish 40 10 normal()
• and include physical inputs
• fish 20stand_age10normal()

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Regression Overview

• Just like prediction, but in reverse. Start with
• fish 20age10normal()
• but, lets say we dont know the parameters
• fish abageenormal()
• We should use coverages FISH and AGE to get the
  model parameters a, b, and e. b tells us how
  many more fish we will get if we keep older
  stands along the stream.

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Plotting Relationships

• Plotting in GRID is done through Stacks.
• MAKESTACK ltstackgt LIST ltgrid ... gridgt
• STACKSCATTERGRAM ltstackgt

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Regression in GRID

• In doing regression in GRID we
• make a SAMPLE file
• Grid samp1 sample(maskgrid, ing1, ing2)
• do REGRESSION on it
• Grid regression samp1

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The SAMPLE Function

• SAMPLE(ltmask_gridgt, grid, ..., grid)
• SAMPLE(lt point_filegt, grid, ..., grid,
  NEAREST BILINEAR CUBIC)
• Arguments
• ltmask_gridgt - the grid which defines the cells to
  sample. Cells in the mask grid with valid values
  will be sampled.
• grid, ..., grid - the name of one or more grids
  whose values will be sampled based upon the mask
  grid.
• ltgt - allows for the interactive graphical input
  of the input sample points. The grid specified by
  grid should to be displayed for reference.
• ltpoint_filegt - the name of the ASCII text file
  containing coordinates of points to be sampled.
• ltNEAREST BILINEAR CUBICgt - specifies the
  resampling algorithm to be used when sampling a
  grid. It is used only when point coordinates are
  entered as input. See Resampling grids for a
  description of the resampling methods.
• NEAREST - nearest neighbor assignment.
• BILINEAR - bilinear interpolation.
• CUBIC - cubic convolution.

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The REGRESSION Command

• REGRESSION ltsamplegt LINEAR LOGISTIC DETAIL
  BRIEF
• Arguments
• ltsamplegt - the name of the input file which can
  be created using the SAMPLE function.
• LINEAR LOGISTIC - keywords specifying the
  type of regression to be performed.
• LINEAR - linear regression with least square fit
  estimation is performed.
• LOGISTIC - logistic regression with maximum
  likelihood estimation is performed.
• DETAIL BRIEF - keywords specifying whether a
  full or abbreviated report will be displayed on a
  screen.
• DETAIL - displays a fully detailed report, the
  result of running the regression model.
• BRIEF - displays the values of coefficients, RMS
  Error and Chi-Square only.

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Regression in GRID

• Grid samp1 sample ( maskgrid, ing1, ing2 )
• Grid sys cat samp1
• 1 1.5 3.5 1 0.1
• 0 2.5 3.5 1 0.2
• 0 3.5 3.5 0 0.5
• 2 0.5 2.5 3 0.75
• 0 1.5 2.5 3 0.9
• 3 2.5 2.5 1 1
• 3 3.5 2.5 2 2
• 0 0.5 1.5 MISSING -0.1
• 0 1.5 1.5 0 -0.25
• 3 2.5 1.5 0 -1
• 2 3.5 1.5 2 0
• 1 0.5 0.5 3 0.707
• 1 1.5 0.5 2 0.866
• 0 3.5 0.5 0 MISSING

Grid regression samp1 coef coef
0 1.250 1 -0.029 2
0.263 point id z z error
1 1.000 -0.248 2
0.000 -1.274 3 0.000
-1.381 4 2.000 0.639
5 0.000 -1.400 6
3.000 1.516 8 0.000
-1.184 9 3.000 2.013
10 2.000 0.808 11
1.000 -0.350 12 1.000
-0.420 RMS Error 1.166 Chi-Square 16.307
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Regression in GRID

• fish 20 stream_age 10 normal()
• Grid samp sample(fish,stream_age)
• List grids ... 100
• Grid regression samp linear brief
• coef coef
• ------ ----------------
• 0 19.436
• 1 1.000
• ------ ----------------
• RMS Error 9.983
• Chi-Square 3064046.998

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Regression on Non-linear Models

• Linear regression on non-linear models doesnt
  always give the correct results, even on
  coefficient signs.
• Grid fish ln(age) ln(fa) - ln(gradient)
• Grid sumple sample(fish, age, fa, gradient)
• Grid regression sumple linear brief
• coef coef
• 0 6.023
• 1 0.019
• 2 0.000
• 3 -0.105
• RMS Error 1.453
• Chi-Square 3335.795

Correct sign Incorrect sign Correct sign
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Logistic Regression

• Regression on zeros and ones makes it hard to fit
  a line. We can however do regression on the
  probability.
• ls con(rand() lt prob,1,0)
• prob 1/(1exp(-a0-a1x1-a2x2))

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Logistic Regression Example

• Grid ls con(curve lt 0 and slope gt 40,1,0)
• Grid s_ls sample(ls, slope , curve ,aspect)
• Grid regression s_ls logistic brief
• coef coef
• 0 -25.321
• 1 0.507
• 2 -16.508
• 3 0.000
• RMS Error 0.094
• Chi-Square 366.098

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Answering Questions

• Map your data and look
• Plot your data
• make a stack
• make a stack scattergram
• adjust scale to fit one-to-one
• Regression
• sample
• regression

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Answering Questions

• 1. Are these landslides aspect dependent?
• Can you prove that?