Regression in GRID

FE423 - February 27, 2000

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

Outline

Probability models - simulationLinear models - regressionLogistic RegressionAnswering questions with data

Questions

In forest management, we have questions like:

Does logging cause landsliding?

Does logging impact fish?

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.

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.

Probability Models in GRID

We can model this natural variability in GRID with random functions

RAND()

NORMAL()

The RAND() Function

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

Simulating Random Events

Example: We can use SMORPH hazard ranking to simulate landslide observations.

haz = con(slope < 40 and plan < .5, 1, ~...

prob = con(haz eq 0, .001, haz eq 1, .01, .1)LS_sim = con(rand() < prob, 1, 0)

Simulating Random Events

slope

Simulated landslideshazard

Planform curvature

The NORMAL() Function

The normal() function makes draws from standard normal distribution

Simulating Random Events

Example: fish countswe can model observations

fish = 40 + 10 * normal()

and include physical inputsfish = 20+stand_age+10*normal()

Regression Overview

Just like prediction, but in reverse. Start withfish = 20+age+10*normal()

but, let’s say we don’t know the parametersfish = a+b*age+e*normal()

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.

Plotting Relationships

Plotting in GRID is done through Stacks.

MAKESTACK <stack> LIST <grid ... grid>

STACKSCATTERGRAM <stack>

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

The SAMPLE Function

SAMPLE(<mask_grid>, {grid, ..., grid})SAMPLE(<* | point_file>, {grid, ..., grid}, {NEAREST | BILINEAR | CUBIC})Arguments<mask_grid> - 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.<*> - allows for the interactive graphical input of the input sample points. The grid

specified by {grid} should to be displayed for reference.<point_file> - the name of the ASCII text file containing coordinates of points to be

sampled.<NEAREST | BILINEAR | CUBIC> - 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.

The REGRESSION Command

REGRESSION <sample> {LINEAR | LOGISTIC} {DETAIL | BRIEF}Arguments<sample> - 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.

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 samp1coef # coef 0 1.250 1 -0.029 2 0.263point 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 -0.420RMS Error = 1.166Chi-Square = 16.307

Regression in GRID

fish = 20 + stream_age + 10 * normal()Grid: samp = sample(fish,stream_age)List grids ... 100%Grid: regression samp linear briefcoef # coef------ ---------------- 0 19.436 1 1.000------ ----------------RMS Error = 9.983Chi-Square = 3064046.998

Regression on Non-linear ModelsLinear regression on non-linear models doesn’t 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 briefcoef # coef 0 6.023 1 0.019 2 0.000 3 -0.105RMS Error = 1.453Chi-Square = 3335.795

Correct signIncorrect signCorrect sign

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() < prob,1,0)

prob = 1/(1+exp(-a0-a1*x1-a2*x2…))

Logistic Regression: Example

Grid: ls = con(curve < 0 and slope > 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 = 0.094Chi-Square = 366.098

Answering Questions

Map your data and lookPlot your data

make a stack make a stack scattergram adjust scale to fit one-to-one

Regression sample regression

Answering Questions

1. Are these landslides aspect dependent?

Can you prove that?