Revision 56d752cf6d1a8e2775e1acc46482c206cfd5b269 authored by Adrian Baddeley on 14 March 2012, 07:09:51 UTC, committed by cran-robot on 14 March 2012, 07:09:51 UTC
1 parent a4d492a
Gcom.R
#
# Gcom.R
#
# Model compensator of G
#
# $Revision: 1.2 $ $Date: 2011/06/26 03:39:11 $
#
################################################################################
#
Gcom <- function(object, r=NULL, breaks=NULL, ...,
correction=c("border", "Hanisch"),
conditional=!is.poisson(object),
restrict=FALSE,
trend=~1, interaction=Poisson(),
rbord=reach(interaction),
ppmcorrection="border",
truecoef=NULL, hi.res=NULL) {
if(inherits(object, "ppm"))
fit <- object
else if(inherits(object, "ppp") || inherits(object, "quad"))
fit <- ppm(object, trend=trend, interaction=interaction, rbord=rbord,
correction=ppmcorrection, ...)
else
stop("object should be a fitted point process model or a point pattern")
if(missing(conditional) || is.null(conditional))
conditional <- !is.poisson(fit)
rfixed <- !is.null(r) || !is.null(breaks)
# selection of edge corrections
correction.given <- !missing(correction) && !is.null(correction)
correction <- pickoption("correction", correction,
c(none="none",
border="border",
Hanisch="Hanisch",
hanisch="Hanisch",
best="Hanisch"),
multi=TRUE)
# Extract data and quadrature points
Q <- quad.ppm(fit, drop=FALSE)
X <- data.ppm(fit)
Win <- X$window
# edge correction algorithm
algo <- if(!conditional) "classical" else
if(restrict) "restricted" else "reweighted"
# conditioning on border region?
if(!conditional) {
Wfree <- Win
} else {
rbord <- fit$rbord
Wfree <- erosion(Win, rbord)
if(restrict) {
retain <- inside.owin(union.quad(Q), , Wfree)
Q <- Q[Wfree]
X <- X[Wfree]
Win <- Wfree
}
}
# Extract quadrature info
U <- union.quad(Q)
Z <- is.data(Q) # indicator data/dummy
E <- equalsfun.quad(Q)
WQ <- w.quad(Q) # quadrature weights
# basic statistics
npoints <- X$n
area <- area.owin(Win)
lambda <- npoints/area
# quadrature points used
USED <- if(algo == "reweighted") (bdist.points(U) > rbord) else rep(TRUE, U$n)
# adjustments to account for restricted domain
if(conditional) {
npoints.used <- sum(Z & USED)
area.used <- sum(WQ[USED])
lambda.used <- npoints.used/area.used
} else {
npoints.used <- npoints
area.used <- area
lambda.used <- lambda
}
# determine breakpoints for r values
rmaxdefault <- rmax.rule("G", if(restrict) Wfree else Win, lambda)
breaks <- handle.r.b.args(r, breaks, Wfree, rmaxdefault=rmaxdefault)
rvals <- breaks$r
rmax <- breaks$max
# residuals
resid <- residuals(fit, type="raw",drop=FALSE,
coefs=truecoef, quad=hi.res)
rescts <- with(resid, "continuous")
if(restrict) {
# keep only data inside Wfree
rescts <- rescts[retain]
}
# absolute weight for continuous integrals
wc <- -rescts
# nearest neighbours (quadrature point to data point)
nn <- nncross(U, X, seq(U$n), seq(X$n))
dIJ <- nn$dist
I <- seq(U$n)
J <- nn$which
DD <- Z <- (I <= X$n) # TRUE for data points
wcIJ <- -rescts
# determine whether a quadrature point will be used in integral
okI <- USED[I]
# initialise fv object
r <- breaks$r
df <- data.frame(r=r, pois=1 - exp(-pi * lambda * r^2))
G <- fv(df, "r", substitute(G(r), NULL), "pois", . ~ r,
alim=c(0, rmax),
labl=c("r","%s[pois](r)"),
desc=c("distance argument r", "theoretical Poisson %s"),
fname="G")
# distance to boundary
b <- bI <- bdist.points(U)
dotnames <- character(0)
# Border method
if("border" %in% correction) {
# reduced sample for G(r) of data only
RSX <- Kount(dIJ[DD & okI], bI[DD & okI], b[Z & USED], breaks)
Gb <- RSX$numerator/RSX$denom.count
G <- bind.fv(G, data.frame(border=Gb), "hat(%s)[bord](r)",
"border-corrected nonparametric estimate of %s",
"border")
# reduced sample for adjustment integral
RSD <- Kwtsum(dIJ[okI], bI[okI], wcIJ[okI], b[Z & USED],
rep(1, npoints.used), breaks)
Gbcom <- RSD$numerator/(1 + RSD$denominator)
G <- bind.fv(G, data.frame(bcom=Gbcom), "bold(C)~hat(%s)[bord](r)",
"model compensator of border-corrected %s",
"bcom")
dotnames <- c("border", "bcom", "pois")
}
# Hanisch correction for data
if("Hanisch" %in% correction) {
nnd <- dIJ[DD & okI]
bdry <- bI[DD & okI]
# weights
ea <- eroded.areas(Win, rvals)
if(algo == "reweighted") {
# replace weight(r) by weight(max(rbord,r))
ea[rvals < rbord] <- eroded.areas(Win, rbord)
}
# compute
x <- nnd[nnd <= bdry]
h <- whist(x[x <= rmax], breaks=breaks$val)
H <- (1/lambda) * cumsum(h/ea)
# glue on
G <- bind.fv(G, data.frame(han=H), "hat(%s)[han](r)",
"Hanisch correction estimate of %s",
"han")
# Hanisch correction for adjustment integral
nnd <- dIJ[okI]
bdry <- bI[okI]
wt <- wcIJ[okI]
x <- nnd[nnd <= bdry]
wt <- wt[nnd <= bdry]
h <- whist(x[x <= rmax], breaks=breaks$val, weights=wt[x <= rmax])
lambdaplus <- (npoints + 1)/area
Hint <- (1/lambdaplus) * cumsum(h/ea)
# glue on
G <- bind.fv(G, data.frame(hcom=Hint), "bold(C)~hat(%s)[han](r)",
"model compensator of Hanisch-corrected %s",
"hcom")
# pseudovariance for Hanisch residual
Hvar <- (1/lambdaplus^2) * cumsum(h/ea^2)
G <- bind.fv(G, data.frame(hvar=Hvar), "bold(C)^2~hat(%s)[han](r)",
"Poincare variance for Hanisch corrected %s",
"hcom")
# default plot does not show all components
dotnames <- c("han", "hcom", dotnames)
}
# compute sensible 'alim'
endpoint <- function(y, r, f) { min(r[y >= f * max(y)]) }
amax <- endpoint(G$pois, G$r, 0.99)
if(length(dotnames) > 0)
amax <- max(amax,
unlist(lapply(as.data.frame(G)[,dotnames,drop=FALSE],
endpoint,
r=r, f=0.9)))
attr(G, "alim") <- c(0, amax)
#
fvnames(G, ".") <- dotnames
unitname(G) <- unitname(X)
# secret tag used by 'Gres'
attr(G, "maker") <- "Gcom"
return(G)
}
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