autocov_dist: Distance-weighted autocovariate

Description

Calculates the autocovariate to be used in autonormal, autopoisson or autologistic regression. Three distance-weighting schemes are available.

Usage

autocov_dist(z, xy, nbs = 1, type = "inverse", zero.policy = NULL, style = "B", longlat=NULL)

Arguments

the response variable

a matrix of coordinates or a SpatialPoints object

nbs

neighbourhood radius; default is 1

type

the weighting scheme: "one" gives equal weight to all data points in the neighbourhood; "inverse" (the default) weights by inverse distance; "inverse.squared" weights by the square of "inverse"

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

style

default “B” (changed from “W” 2015-01-27); style can take values “W”, “B”, “C”, “U”, and “S”

longlat

TRUE if point coordinates are longitude-latitude decimal, in which case distances are measured in kilometers; if xy is a SpatialPoints object, the value is taken from the object itself

Value

A numeric vector of autocovariate values

References

Augustin N.H., Mugglestone M.A. and Buckland S.T. (1996) An autologistic model for the spatial distribution of wildlife. Journal of Applied Ecology, 33, 339-347; Gumpertz M.L., Graham J.M. and Ristaino J.B. (1997) Autologistic model of spatial pattern of Phytophthora epidemic in bell pepper: effects of soil variables on disease presence. Journal of Agricultural, Biological and Environmental Statistics, 2, 131-156; Bardos, D.C., Guillera-Arroita, G. and Wintle, B.A. (2015) Valid auto-models for spatially autocorrelated occupancy and abundance data. arXiv, 1501.06529.

Examples

Run this code

example(columbus)
xy <- cbind(columbus$X, columbus$Y)
ac1a <- autocov_dist(columbus$CRIME, xy, nbs=10, style="B",
 type="one")
acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style="B",
 type="inverse")
acinv2a <- autocov_dist(columbus$CRIME, xy, nbs=10, style="B",
 type="inverse.squared")

plot(ac1a ~ columbus$CRIME, pch=16, asp=1)
points(acinva ~ columbus$CRIME, pch=16, col="red")
points(acinv2a ~ columbus$CRIME, pch=16, col="blue")
abline(0,1)

nb <- dnearneigh(xy, 0, 10)
lw <- nb2listw(nb, style="B")
ac1b <- lag(lw, columbus$CRIME)
all.equal(ac1b, ac1a)

nbd <- nbdists(nb, xy)
gl <- lapply(nbd, function(x) 1/x)
lw <- nb2listw(nb, glist=gl)
acinvb <- lag(lw, columbus$CRIME)
all.equal(acinvb, acinva)

gl2 <- lapply(nbd, function(x) 1/(x^2))
lw <- nb2listw(nb, glist=gl2)
acinv2b <- lag(lw, columbus$CRIME)
all.equal(acinv2b, acinv2a)

glm(CRIME ~ HOVAL + ac1b, data=columbus, family="gaussian")
spautolm(columbus$CRIME ~ HOVAL, data=columbus,
 listw=nb2listw(nb, style="W"))

xy <- SpatialPoints(xy)
acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style="W",
 type="inverse")
nb <- dnearneigh(xy, 0, 10)
nbd <- nbdists(nb, xy)
gl <- lapply(nbd, function(x) 1/x)
lw <- nb2listw(nb, glist=gl)
acinvb <- lag(lw, columbus$CRIME)
all.equal(acinvb, acinva)