spdep (version 0.6-15)

SpatialFiltering: 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 = 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:

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

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

# NOT RUN {
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))
# }