1r.regression.multi(1) GRASS GIS User's Manual r.regression.multi(1)
2
6 r.regression.multi - Calculates multiple linear regression from raster
7 maps.
8
10 raster, statistics, regression
11
13 r.regression.multi
14 r.regression.multi --help
15 r.regression.multi [-g] mapx=name[,name,...] mapy=name [residu‐
16 als=name] [estimates=name] [output=name] [--overwrite] [--help]
17 [--verbose] [--quiet] [--ui]
18 Flags:
20 -g
21 Print in shell script style
22 --overwrite
24 Allow output files to overwrite existing files
25 --help
27 Print usage summary
28 --verbose
30 Verbose module output
31 --quiet
33 Quiet module output
34 --ui
36 Force launching GUI dialog
37 Parameters:
39 mapx=name[,name,...]Â [required]
40 Map for x coefficient
41 mapy=name [required]
43 Map for y coefficient
44 residuals=name
46 Map to store residuals
47 estimates=name
49 Map to store estimates
50 output=name
52 ASCII file for storing regression coefficients (output to screen if
53 file not specified).
54
56 r.regression.multi calculates a multiple linear regression from raster
57 maps, according to the formula
58 Y = b0 + sum(bi*Xi) + E
59 where
60 X = {X1, X2, ..., Xm}
61 m = number of explaining variables
62 Y = {y1, y2, ..., yn}
63 Xi = {xi1, xi2, ..., xin}
64 E = {e1, e2, ..., en}
65 n = number of observations (cases)
66 In R notation:
67 Y ~ sum(bi*Xi)
68 b0 is the intercept, X0 is set to 1
69 r.regression.multi is designed for large datasets that can not be pro‐
71 cessed in R. A p value is therefore not provided, because even very
72 small, meaningless effects will become significant with a large number
73 of cells. Instead it is recommended to judge by the estimator b, the
74 amount of variance explained (R squared for a given variable) and the
75 gain in AIC (AIC without a given variable minus AIC global must be pos‐
76 itive) whether the inclusion of a given explaining variable in the
77 model is justified.
78 The global model
80 The b coefficients (b0 is offset), R squared or coefficient of determi‐
81 nation (Rsq) and F are identical to the ones obtained from R-stats’s
82 lm() function and R-stats’s anova() function. The AIC value is identi‐
83 cal to the one obtained from R-stats’s stepAIC() function (in case of
84 backwards stepping, identical to the Start value). The AIC value cor‐
85 rected for the number of explaining variables and the BIC (Bayesian In‐
86 formation Criterion) value follow the logic of AIC.
87 The explaining variables
89 R squared for each explaining variable represents the additional amount
90 of explained variance when including this variable compared to when ex‐
91 cluding this variable, that is, this amount of variance is explained by
92 the current explaining variable after taking into consideration all the
93 other explaining variables.
94 The F score for each explaining variable allows testing if the inclu‐
96 sion of this variable significantly increases the explaining power of
97 the model, relative to the global model excluding this explaining vari‐
98 able. That means that the F value for a given explaining variable is
99 only identical to the F value of the R-function summary.aov if the
100 given explaining variable is the last variable in the R-formula. While
101 R successively includes one variable after another in the order speci‐
102 fied by the formula and at each step calculates the F value expressing
103 the gain by including the current variable in addition to the previous
104 variables, r.regression.multi calculates the F-value expressing the
105 gain by including the current variable in addition to all other vari‐
106 ables, not only the previous variables.
107 The AIC value is identical to the one obtained from the R-function
109 stepAIC() when excluding this variable from the full model. The AIC
110 value corrected for the number of explaining variables and the BIC
111 value (Bayesian Information Criterion) value follow the logic of AIC.
112 BIC is identical to the R-function stepAIC with k = log(n). AICc is not
113 available through the R-function stepAIC.
114
116 Multiple regression with soil K-factor and elevation, aspect, and slope
117 (North Carolina dataset). Output maps are the residuals and estimates:
118 g.region raster=soils_Kfactor -p
119 r.regression.multi mapx=elevation,aspect,slope mapy=soils_Kfactor \
120 residuals=soils_Kfactor.resid estimates=soils_Kfactor.estim
121
123 d.correlate, r.regression.line, r.stats
124
126 Markus Metz
127
129 Available at: r.regression.multi source code (history)
130 Accessed: Saturday Jan 21 20:38:57 2023
132 Main index | Raster index | Topics index | Keywords index | Graphical
134 index | Full index
135 © 2003-2023 GRASS Development Team, GRASS GIS 8.2.1 Reference Manual
137GRASS 8.2.1 r.regression.multi(1)