SpatialFiltering {spdep}R Documentation

Semi-parametric spatial filtering

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

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

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 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 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

lm, eigen, nb2listw, listw2U

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))

[Package spdep version 0.4-34 Index]