r.regression.multi(1grass) GRASS GIS User's Manual r.regression.multi(1grass)
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 [residu-
als=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 pro-
cessed 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 pos-
itive) 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 determi-
nation (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 identi-
cal to the one obtained from R-stats’s stepAIC() function (in case of
backwards stepping, identical to the Start value). The AIC value cor-
rected for the number of explaining variables and the BIC (Bayesian In-
formation 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 ex-
cluding 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 inclu-
sion of this variable significantly increases the explaining power of
the model, relative to the global model excluding this explaining vari-
able. 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 speci-
fied 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 vari-
ables, 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
SEE ALSO
d.correlate, r.regression.line, r.stats
AUTHOR
Markus Metz
SOURCE CODE
Available at: r.regression.multi source code (history)
Accessed: unknown
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© 2003-2022 GRASS Development Team, GRASS GIS 7.8.7 Reference Manual
GRASS 7.8.7 r.regression.multi(1grass)
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