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

SEE ALSO

        d.correlate, r.regression.line, r.stats

AUTHOR

       Markus Metz

SOURCE CODE

       Available at: r.regression.multi source code (history)

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       © 2003-2019 GRASS Development Team, GRASS GIS 7.8.2 Reference Manual