SpatialFiltering: Semi-parametric spatial filtering
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
View source: R/SpatialFiltering.R
Description
The function selects eigenvectors in a semi-parametric spatial filtering approach to removing spatial dependence from linear models. Selection is by brute force by finding the single eigenvector reducing the standard variate of Moran's I for regression residuals most, and continuing until no candidate eigenvector reduces the value by more than tol. It returns a summary table from the selection process and a matrix of selected eigenvectors for the specified model.
Usage
1
2
3
Arguments
formula
a symbolic description of the model to be fit, assuming a spatial error representation; when lagformula is given, it should include only the response and the intercept term
lagformula
An extra one-sided formula to be used when a spatial lag representation is desired; the intercept is excluded within the function if present because it is part of the formula argument, but excluding it explicitly in the lagformula argument in the presence of factors generates a collinear model matrix
data
an optional data frame containing the variables in the model
nb
an object of class nb
glist
list of general weights corresponding to neighbours
style
style can take values W, B, C, U, and S
zero.policy
default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors
tol
tolerance value for convergence of spatial filtering
zerovalue
eigenvectors with eigenvalues of an absolute value smaller than zerovalue will be excluded in eigenvector search
ExactEV
Set ExactEV=TRUE to use exact expectations and variances rather than the expectation and variance of Moran's I from the previous iteration, default FALSE
symmetric
Should the spatial weights matrix be forced to symmetry, default TRUE
alpha
if not NULL, used instead of the tol= argument as a stopping rule to choose all eigenvectors up to and including the one with a probability value exceeding alpha.
alternative
a character string specifying the alternative hypothesis, must be one of greater, less or two.sided (default).
verbose
default NULL, use global option value; if TRUE report eigenvectors selected
Value
An SFResult object, with:
selection
a matrix summarising the selection of eigenvectors for inclusion, with columns:
- Step
Step counter of the selection procedure
- SelEvec
number of selected eigenvector (sorted descending)
- Eval
its associated eigenvalue
- MinMi
value Moran's I for residual autocorrelation
- ZMinMi
standardized value of Moran's I assuming a normal approximation
- pr(ZI)
probability value of the permutation-based standardized deviate for the given value of the alternative argument
- R2
R\^2 of the model including exogenous variables and eigenvectors
- gamma
regression coefficient of selected eigenvector in fit
The first row is the value at the start of the search
dataset
a matrix of the selected eigenvectors in order of selection
Author(s)
Yongwan Chun, Michael Tiefelsdorf, Roger Bivand
References
Tiefelsdorf M, Griffith DA. (2007) Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach. Environment and Planning A, 39 (5) 1193 - 1221. http://www.spatialfiltering.com
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
example(columbus)
lmbase <- lm(CRIME ~ INC + HOVAL, data=columbus)
sarcol <- SpatialFiltering(CRIME ~ INC + HOVAL, data=columbus,
nb=col.gal.nb, style="W", ExactEV=TRUE)
sarcol
lmsar <- lm(CRIME ~ INC + HOVAL + fitted(sarcol), data=columbus)
lmsar
anova(lmbase, lmsar)
lm.morantest(lmsar, nb2listw(col.gal.nb))
lagcol <- SpatialFiltering(CRIME ~ 1, ~ INC + HOVAL - 1, data=columbus,
nb=col.gal.nb, style="W")
lagcol
lmlag <- lm(CRIME ~ INC + HOVAL + fitted(lagcol), data=columbus)
lmlag
anova(lmbase, lmlag)
lm.morantest(lmlag, nb2listw(col.gal.nb))
Example output
Loading required package: sp
Loading required package: spData
To access larger datasets in this package, install the spDataLarge
package with: `install.packages('spDataLarge',
repos='https://nowosad.github.io/drat/', type='source')`
Loading required package: sf
Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1
colmbs> columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE)
colmbs> col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
Registered S3 methods overwritten by 'spatialreg':
method from
residuals.stsls spdep
deviance.stsls spdep
coef.stsls spdep
print.stsls spdep
summary.stsls spdep
print.summary.stsls spdep
residuals.gmsar spdep
deviance.gmsar spdep
coef.gmsar spdep
fitted.gmsar spdep
print.gmsar spdep
summary.gmsar spdep
print.summary.gmsar spdep
print.lagmess spdep
summary.lagmess spdep
print.summary.lagmess spdep
residuals.lagmess spdep
deviance.lagmess spdep
coef.lagmess spdep
fitted.lagmess spdep
logLik.lagmess spdep
fitted.SFResult spdep
print.SFResult spdep
fitted.ME_res spdep
print.ME_res spdep
print.lagImpact spdep
plot.lagImpact spdep
summary.lagImpact spdep
HPDinterval.lagImpact spdep
print.summary.lagImpact spdep
print.sarlm spdep
summary.sarlm spdep
residuals.sarlm spdep
deviance.sarlm spdep
coef.sarlm spdep
vcov.sarlm spdep
fitted.sarlm spdep
logLik.sarlm spdep
anova.sarlm spdep
predict.sarlm spdep
print.summary.sarlm spdep
print.sarlm.pred spdep
as.data.frame.sarlm.pred spdep
residuals.spautolm spdep
deviance.spautolm spdep
coef.spautolm spdep
fitted.spautolm spdep
print.spautolm spdep
summary.spautolm spdep
logLik.spautolm spdep
print.summary.spautolm spdep
print.WXImpact spdep
summary.WXImpact spdep
print.summary.WXImpact spdep
predict.SLX spdep
Warning message:
Function SpatialFiltering moved to the spatialreg package
Step SelEvec Eval MinMi ZMinMi Pr(ZI) R2
0 0 0 0.0000000 0.212374153 2.68100025 0.007340246 0.5524040
1 1 5 0.7148326 0.121528166 1.89037770 0.058707464 0.6209393
2 2 3 0.8408661 0.065848648 1.54064108 0.123404165 0.6481722
3 3 1 1.0206316 -0.005424824 1.08514557 0.277857187 0.6726114
4 4 10 0.3658588 -0.039356232 0.80357070 0.421644951 0.7000258
5 5 14 0.1831325 -0.072949543 0.47790213 0.632719864 0.7393770
6 6 11 0.3144120 -0.108332631 0.18566599 0.852706701 0.7611907
7 7 2 0.9157325 -0.153675621 -0.03464097 0.972366030 0.7713163
gamma
0 0.00000
1 30.34786
2 19.13010
3 -18.12234
4 19.19379
5 22.99586
6 17.12127
7 11.66487
Call:
lm(formula = CRIME ~ INC + HOVAL + fitted(sarcol), data = columbus)
Coefficients:
(Intercept) INC HOVAL
68.6190 -1.5973 -0.2739
fitted(sarcol)vec5 fitted(sarcol)vec3 fitted(sarcol)vec1
30.3479 19.1301 -18.1223
fitted(sarcol)vec10 fitted(sarcol)vec14 fitted(sarcol)vec11
19.1938 22.9959 17.1213
fitted(sarcol)vec2
11.6649
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(sarcol)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 39 3073.1 7 2941.8 5.3334 0.0002445 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ INC + HOVAL + fitted(sarcol), data =
columbus)
weights: nb2listw(col.gal.nb)
Moran I statistic standard deviate = -0.034641, p-value = 0.5138
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
-0.153675621 -0.150918131 0.006336477
Warning message:
Function SpatialFiltering moved to the spatialreg package
Step SelEvec Eval MinMi ZMinMi Pr(ZI) R2
0 0 0 0.0000000 0.21237415 2.68100025 0.007340246 0.5524040
1 1 6 0.7161123 0.11782248 1.84511963 0.065020139 0.6038801
2 2 4 0.8682938 0.06242664 1.49482111 0.134961136 0.6531288
3 3 1 1.0310063 -0.02066604 0.88134183 0.378132834 0.6924845
4 4 5 0.7905397 -0.04619973 0.84746904 0.396733736 0.7136578
5 5 15 0.1753342 -0.07609524 0.55233191 0.580720971 0.7558543
6 6 9 0.5501433 -0.10190889 0.43919419 0.660520837 0.7626784
7 7 8 0.5721041 -0.12232942 0.41846803 0.675604953 0.7757314
8 8 3 0.9026222 -0.14991822 0.38315383 0.701605709 0.7908693
9 9 2 0.9649166 -0.21756342 -0.28556733 0.775209527 0.8078727
10 10 7 0.6219404 -0.22017920 -0.04856547 0.961265592 0.8082842
gamma
0 0.000000
1 19.848854
2 35.542595
3 -30.697851
4 -24.540372
5 25.227798
6 7.590082
7 -16.933168
8 -20.556931
9 -18.434534
10 -2.597572
Call:
lm(formula = CRIME ~ INC + HOVAL + fitted(lagcol), data = columbus)
Coefficients:
(Intercept) INC HOVAL
56.7977 -0.4857 -0.3821
fitted(lagcol)vec6 fitted(lagcol)vec4 fitted(lagcol)vec1
19.8489 35.5426 -30.6979
fitted(lagcol)vec5 fitted(lagcol)vec15 fitted(lagcol)vec9
-24.5404 25.2278 7.5901
fitted(lagcol)vec8 fitted(lagcol)vec3 fitted(lagcol)vec2
-16.9332 -20.5569 -18.4345
fitted(lagcol)vec7
-2.5976
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 36 2576.3 10 3438.6 4.8049 0.0002165 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ INC + HOVAL + fitted(lagcol), data =
columbus)
weights: nb2listw(col.gal.nb)
Moran I statistic standard deviate = -0.048565, p-value = 0.5194
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
-0.220179195 -0.217083975 0.004061888
spdep documentation built on Aug. 19, 2017, 3:01 a.m.
R Package Documentation
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Description Usage Arguments Value Author(s) References See Also Examples
View source: R/SpatialFiltering.R
Description
The function selects eigenvectors in a semi-parametric spatial filtering approach to removing spatial dependence from linear models. Selection is by brute force by finding the single eigenvector reducing the standard variate of Moran's I for regression residuals most, and continuing until no candidate eigenvector reduces the value by more than tol. It returns a summary table from the selection process and a matrix of selected eigenvectors for the specified model.
Usage
1 2 3 |
Arguments
formula |
a symbolic description of the model to be fit, assuming a spatial error representation; when lagformula is given, it should include only the response and the intercept term |
lagformula |
An extra one-sided formula to be used when a spatial lag representation is desired; the intercept is excluded within the function if present because it is part of the formula argument, but excluding it explicitly in the lagformula argument in the presence of factors generates a collinear model matrix |
data |
an optional data frame containing the variables in the model |
nb |
an object of class |
glist |
list of general weights corresponding to neighbours |
style |
|
zero.policy |
default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors |
tol |
tolerance value for convergence of spatial filtering |
zerovalue |
eigenvectors with eigenvalues of an absolute value smaller than zerovalue will be excluded in eigenvector search |
ExactEV |
Set ExactEV=TRUE to use exact expectations and variances rather than the expectation and variance of Moran's I from the previous iteration, default FALSE |
symmetric |
Should the spatial weights matrix be forced to symmetry, default TRUE |
alpha |
if not NULL, used instead of the tol= argument as a stopping rule to choose all eigenvectors up to and including the one with a probability value exceeding alpha. |
alternative |
a character string specifying the alternative hypothesis, must be one of greater, less or two.sided (default). |
verbose |
default NULL, use global option value; if TRUE report eigenvectors selected |
Value
An SFResult object, with:
selection |
a matrix summarising the selection of eigenvectors for inclusion, with columns:
The first row is the value at the start of the search |
dataset |
a matrix of the selected eigenvectors in order of selection |
Author(s)
Yongwan Chun, Michael Tiefelsdorf, Roger Bivand
References
Tiefelsdorf M, Griffith DA. (2007) Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach. Environment and Planning A, 39 (5) 1193 - 1221. http://www.spatialfiltering.com
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | example(columbus)
lmbase <- lm(CRIME ~ INC + HOVAL, data=columbus)
sarcol <- SpatialFiltering(CRIME ~ INC + HOVAL, data=columbus,
nb=col.gal.nb, style="W", ExactEV=TRUE)
sarcol
lmsar <- lm(CRIME ~ INC + HOVAL + fitted(sarcol), data=columbus)
lmsar
anova(lmbase, lmsar)
lm.morantest(lmsar, nb2listw(col.gal.nb))
lagcol <- SpatialFiltering(CRIME ~ 1, ~ INC + HOVAL - 1, data=columbus,
nb=col.gal.nb, style="W")
lagcol
lmlag <- lm(CRIME ~ INC + HOVAL + fitted(lagcol), data=columbus)
lmlag
anova(lmbase, lmlag)
lm.morantest(lmlag, nb2listw(col.gal.nb))
|
Example output
Loading required package: sp
Loading required package: spData
To access larger datasets in this package, install the spDataLarge
package with: `install.packages('spDataLarge',
repos='https://nowosad.github.io/drat/', type='source')`
Loading required package: sf
Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1
colmbs> columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE)
colmbs> col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
Registered S3 methods overwritten by 'spatialreg':
method from
residuals.stsls spdep
deviance.stsls spdep
coef.stsls spdep
print.stsls spdep
summary.stsls spdep
print.summary.stsls spdep
residuals.gmsar spdep
deviance.gmsar spdep
coef.gmsar spdep
fitted.gmsar spdep
print.gmsar spdep
summary.gmsar spdep
print.summary.gmsar spdep
print.lagmess spdep
summary.lagmess spdep
print.summary.lagmess spdep
residuals.lagmess spdep
deviance.lagmess spdep
coef.lagmess spdep
fitted.lagmess spdep
logLik.lagmess spdep
fitted.SFResult spdep
print.SFResult spdep
fitted.ME_res spdep
print.ME_res spdep
print.lagImpact spdep
plot.lagImpact spdep
summary.lagImpact spdep
HPDinterval.lagImpact spdep
print.summary.lagImpact spdep
print.sarlm spdep
summary.sarlm spdep
residuals.sarlm spdep
deviance.sarlm spdep
coef.sarlm spdep
vcov.sarlm spdep
fitted.sarlm spdep
logLik.sarlm spdep
anova.sarlm spdep
predict.sarlm spdep
print.summary.sarlm spdep
print.sarlm.pred spdep
as.data.frame.sarlm.pred spdep
residuals.spautolm spdep
deviance.spautolm spdep
coef.spautolm spdep
fitted.spautolm spdep
print.spautolm spdep
summary.spautolm spdep
logLik.spautolm spdep
print.summary.spautolm spdep
print.WXImpact spdep
summary.WXImpact spdep
print.summary.WXImpact spdep
predict.SLX spdep
Warning message:
Function SpatialFiltering moved to the spatialreg package
Step SelEvec Eval MinMi ZMinMi Pr(ZI) R2
0 0 0 0.0000000 0.212374153 2.68100025 0.007340246 0.5524040
1 1 5 0.7148326 0.121528166 1.89037770 0.058707464 0.6209393
2 2 3 0.8408661 0.065848648 1.54064108 0.123404165 0.6481722
3 3 1 1.0206316 -0.005424824 1.08514557 0.277857187 0.6726114
4 4 10 0.3658588 -0.039356232 0.80357070 0.421644951 0.7000258
5 5 14 0.1831325 -0.072949543 0.47790213 0.632719864 0.7393770
6 6 11 0.3144120 -0.108332631 0.18566599 0.852706701 0.7611907
7 7 2 0.9157325 -0.153675621 -0.03464097 0.972366030 0.7713163
gamma
0 0.00000
1 30.34786
2 19.13010
3 -18.12234
4 19.19379
5 22.99586
6 17.12127
7 11.66487
Call:
lm(formula = CRIME ~ INC + HOVAL + fitted(sarcol), data = columbus)
Coefficients:
(Intercept) INC HOVAL
68.6190 -1.5973 -0.2739
fitted(sarcol)vec5 fitted(sarcol)vec3 fitted(sarcol)vec1
30.3479 19.1301 -18.1223
fitted(sarcol)vec10 fitted(sarcol)vec14 fitted(sarcol)vec11
19.1938 22.9959 17.1213
fitted(sarcol)vec2
11.6649
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(sarcol)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 39 3073.1 7 2941.8 5.3334 0.0002445 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ INC + HOVAL + fitted(sarcol), data =
columbus)
weights: nb2listw(col.gal.nb)
Moran I statistic standard deviate = -0.034641, p-value = 0.5138
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
-0.153675621 -0.150918131 0.006336477
Warning message:
Function SpatialFiltering moved to the spatialreg package
Step SelEvec Eval MinMi ZMinMi Pr(ZI) R2
0 0 0 0.0000000 0.21237415 2.68100025 0.007340246 0.5524040
1 1 6 0.7161123 0.11782248 1.84511963 0.065020139 0.6038801
2 2 4 0.8682938 0.06242664 1.49482111 0.134961136 0.6531288
3 3 1 1.0310063 -0.02066604 0.88134183 0.378132834 0.6924845
4 4 5 0.7905397 -0.04619973 0.84746904 0.396733736 0.7136578
5 5 15 0.1753342 -0.07609524 0.55233191 0.580720971 0.7558543
6 6 9 0.5501433 -0.10190889 0.43919419 0.660520837 0.7626784
7 7 8 0.5721041 -0.12232942 0.41846803 0.675604953 0.7757314
8 8 3 0.9026222 -0.14991822 0.38315383 0.701605709 0.7908693
9 9 2 0.9649166 -0.21756342 -0.28556733 0.775209527 0.8078727
10 10 7 0.6219404 -0.22017920 -0.04856547 0.961265592 0.8082842
gamma
0 0.000000
1 19.848854
2 35.542595
3 -30.697851
4 -24.540372
5 25.227798
6 7.590082
7 -16.933168
8 -20.556931
9 -18.434534
10 -2.597572
Call:
lm(formula = CRIME ~ INC + HOVAL + fitted(lagcol), data = columbus)
Coefficients:
(Intercept) INC HOVAL
56.7977 -0.4857 -0.3821
fitted(lagcol)vec6 fitted(lagcol)vec4 fitted(lagcol)vec1
19.8489 35.5426 -30.6979
fitted(lagcol)vec5 fitted(lagcol)vec15 fitted(lagcol)vec9
-24.5404 25.2278 7.5901
fitted(lagcol)vec8 fitted(lagcol)vec3 fitted(lagcol)vec2
-16.9332 -20.5569 -18.4345
fitted(lagcol)vec7
-2.5976
Analysis of Variance Table
Model 1: CRIME ~ INC + HOVAL
Model 2: CRIME ~ INC + HOVAL + fitted(lagcol)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 6014.9
2 36 2576.3 10 3438.6 4.8049 0.0002165 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Global Moran I for regression residuals
data:
model: lm(formula = CRIME ~ INC + HOVAL + fitted(lagcol), data =
columbus)
weights: nb2listw(col.gal.nb)
Moran I statistic standard deviate = -0.048565, p-value = 0.5194
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
-0.220179195 -0.217083975 0.004061888
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