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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=NULL, data=list(), na.action=na.fail,
 nb=NULL, 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

na.action

a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the spatial weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.

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.

See Also

Examples

require("sf", quietly=TRUE)
columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE)
#require("spdep", quietly=TRUE)
col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1])
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)
(x <- summary(lmsar))
coef(x)
anova(lmbase, lmsar)
spdep::lm.morantest(lmsar, spdep::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)
spdep::lm.morantest(lmlag, spdep::nb2listw(col.gal.nb))
NA.columbus <- columbus
NA.columbus$CRIME[20:25] <- NA
COL.SF.NA <- SpatialFiltering(CRIME ~ INC + HOVAL, data=NA.columbus,
 nb=col.gal.nb, style="W", na.action=na.exclude)
COL.SF.NA$na.action
summary(lm(CRIME ~ INC + HOVAL + fitted(COL.SF.NA), data=NA.columbus,
 na.action=na.exclude))

spatialreg

Spatial Regression Analysis

v1.1-8
GPL-2
Authors
Roger Bivand [cre, aut] (<https://orcid.org/0000-0003-2392-6140>), Gianfranco Piras [aut], Luc Anselin [ctb], Andrew Bernat [ctb], Eric Blankmeyer [ctb], Yongwan Chun [ctb], Virgilio Gómez-Rubio [ctb], Daniel Griffith [ctb], Martin Gubri [ctb], Rein Halbersma [ctb], James LeSage [ctb], Angela Li [ctb], Jielai Ma [ctb], Abhirup Mallik [ctb, trl], Giovanni Millo [ctb], Kelley Pace [ctb], Pedro Peres-Neto [ctb], Tobias Rüttenauer [ctb], Mauricio Sarrias [ctb], JuanTomas Sayago [ctb], Michael Tiefelsdorf [ctb]
Initial release
2021-05-03

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