# SpatialFiltering

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##### Semi-parametric spatial filtering

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.

Keywords
spatial
##### Usage
SpatialFiltering(formula, lagformula, data = list(), nb, glist = NULL, style = "C", zero.policy = NULL, tol = 0.1, zerovalue = 1e-04, ExactEV = FALSE, symmetric = TRUE, alpha=NULL, alternative="two.sided", verbose=NULL)
##### 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:

##### 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

lm, eigen, nb2listw, listw2U

##### Aliases
• SpatialFiltering
• print.SFResult
• fitted.SFResult
##### Examples
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))

Documentation reproduced from package spdep, version 0.6-9, License: GPL (>= 2)

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