The module makes each output cell value a function of the values assigned to the corresponding cells in the input raster map series.
Y(t) = b1 * X1(t) + b2 * X2(t) + ... + bn * Xn(t)
The module uses two models: ordinary least squares and robust linear models.
The number of predictor variables (X maps) must be the same in each (time) series (see examples below). If the different predictors have different or irregular time intervals, NULL raster maps can be inserted into time series to make time intervals equal.
The list of raster inputs (including NULLs) is passed to the regression function. The function computes the parameters over the non-NULL values, producing a NULL result only if there aren't enough non-NULL values for computing.
For example the csv file for regression between NDVI and (elevation, precipitation)
NDVI = b1*Elevation + b2*Precipitation
y,elevation,precipipation ndvi_1,elev_1,precip_1 ndvi_2,elev_2,precip_2 ... ndvi_n,elev_n,precip_n
The second paramether is result_prefix. It is used for construction of the coefficient names. For example if result_prefix="coef.", the names of the regression coefficients will be "coef.elevation" and "coef.precipitation".
r.mregression.series samples=settings result_prefix="coef."
If the regression model includes the intercept
NDVI = b0 + b1*Elevation + b2*Precipitation
r.mapcalc "ones = 1.0"
y,offset,elevation,precipipation ndvi_1,ones,elev_1,precip_1 ndvi_2,ones,elev_2,precip_2 ... ndvi_n,ones,elev_n,precip_n
r.mregression.series samples=settings result_prefix="coef."
Create X variables (random numbers):
r.mapcalc -s "x11 = rand(0, 20)" r.mapcalc -s "x21 = rand(0, 20)" r.mapcalc -s "x31 = rand(0, 20)" r.mapcalc -s "x41 = rand(0, 20)" r.mapcalc -s "x51 = rand(0, 20)"
r.mapcalc -s "x12 = rand(0, 20)" r.mapcalc -s "x22 = rand(0, 20)" r.mapcalc -s "x32 = rand(0, 20)" r.mapcalc -s "x42 = rand(0, 20)" r.mapcalc -s "x52 = rand(0, 20)"
Create constant raster for the intercept:
r.mapcalc "ones = 1.0"
Suppose Y is a linear function of x1 and x2 variables plus a random error. (For testing purposes we assume that Y = 12 + 5*x1 + 3*x2). Create 5 Y rasters:
r.mapcalc -s "y1 = 12 + 5* x11 + 3*x12 + rand(0, 4)" r.mapcalc -s "y2 = 12 + 5* x21 + 3*x22 + rand(0, 4)" r.mapcalc -s "y3 = 12 + 5* x31 + 3*x32 + rand(0, 4)" r.mapcalc -s "y4 = 12 + 5* x41 + 3*x42 + rand(0, 4)" r.mapcalc -s "y5 = 12 + 5* x51 + 3*x52 + rand(0, 4)"
So we have five test rasters Y and X. Forget for a moment that we know the function and try to find the coeffitients.
Create samples csv file:
echo "y,bias,x1,x2 y1,ones,x11,x12 y2,ones,x21,x22 y3,ones,x31,x32 y4,ones,x41,x42 y5,ones,x51,x52" > settings.csv
Run the command
r.mregression.series samples=settings.csv result_prefix="coef."
Three raster maps will be created: "coef.bias", "coef.x1", "coef.x2". This rasters contains the fitted coefitients.
Available at: r.mregression.series source code (history)
Latest change: Monday Jan 30 19:52:26 2023 in commit: cac8d9d848299297977d1315b7e90cc3f7698730
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