r.regression.multigrass - Online in the Cloud

PROGRAM:

NAME

r.regression.multi - Calculates multiple linear regression from raster maps.

KEYWORDS

raster, statistics, regression

SYNOPSIS

r.regression.multi
r.regression.multi --help
r.regression.multi [-g] mapx=name[,name,...] mapy=name [residuals=name]
[estimates=name] [output=name] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

Flags:
-g
Print in shell script style

--overwrite
Allow output files to overwrite existing files

--help
Print usage summary

--verbose
Verbose module output

--quiet
Quiet module output

--ui
Force launching GUI dialog

Parameters:
mapx=name[,name,...] [required]
Map for x coefficient

mapy=name [required]
Map for y coefficient

residuals=name
Map to store residuals

estimates=name
Map to store estimates

output=name
ASCII file for storing regression coefficients (output to screen if file not
specified).

DESCRIPTION

r.regression.multi calculates a multiple linear regression from raster maps, according to
the formula
Y = b0 + sum(bi*Xi) + E
where
X = {X1, X2, ..., Xm}
m = number of explaining variables
Y = {y1, y2, ..., yn}
Xi = {xi1, xi2, ..., xin}
E = {e1, e2, ..., en}
n = number of observations (cases)
In R notation:
Y ~ sum(bi*Xi)
b0 is the intercept, X0 is set to 1

r.regression.multi is designed for large datasets that can not be processed in R. A p
value is therefore not provided, because even very small, meaningless effects will become
significant with a large number of cells. Instead it is recommended to judge by the
estimator b, the amount of variance explained (R squared for a given variable) and the
gain in AIC (AIC without a given variable minus AIC global must be positive) whether the
inclusion of a given explaining variable in the model is justified.

The global model
The b coefficients (b0 is offset), R squared or coefficient of determination (Rsq) and F
are identical to the ones obtained from R-stats’s lm() function and R-stats’s anova()
function. The AIC value is identical to the one obtained from R-stats’s stepAIC() function
(in case of backwards stepping, identical to the Start value). The AIC value corrected for
the number of explaining variables and the BIC (Bayesian Information Criterion) value
follow the logic of AIC.

The explaining variables
R squared for each explaining variable represents the additional amount of explained
variance when including this variable compared to when excluding this variable, that is,
this amount of variance is explained by the current explaining variable after taking into
consideration all the other explaining variables.

The F score for each explaining variable allows testing if the inclusion of this variable
significantly increases the explaining power of the model, relative to the global model
excluding this explaining variable. That means that the F value for a given explaining
variable is only identical to the F value of the R-function summary.aov if the given
explaining variable is the last variable in the R-formula. While R successively includes
one variable after another in the order specified by the formula and at each step
calculates the F value expressing the gain by including the current variable in addition
to the previous variables, r.regression.multi calculates the F-value expressing the gain
by including the current variable in addition to all other variables, not only the
previous variables.

The AIC value is identical to the one obtained from the R-function stepAIC() when
excluding this variable from the full model. The AIC value corrected for the number of
explaining variables and the BIC value (Bayesian Information Criterion) value follow the
logic of AIC. BIC is identical to the R-function stepAIC with k = log(n). AICc is not
available through the R-function stepAIC.

EXAMPLE

Multiple regression with soil K-factor and elevation, aspect, and slope (North Carolina
dataset). Output maps are the residuals and estimates:
g.region raster=soils_Kfactor -p
r.regression.multi mapx=elevation,aspect,slope mapy=soils_Kfactor
residuals=soils_Kfactor.resid estimates=soils_Kfactor.estim

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