/
gwr.R
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gwr.R
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# Copyright 2001-2013 Roger Bivand and Danlin Yu
#
gwr <- function(formula, data = list(), coords, bandwidth,
gweight=gwr.Gauss, adapt=NULL, hatmatrix=FALSE, fit.points,
longlat=NULL, se.fit=FALSE, weights, cl=NULL, predictions=FALSE,
fittedGWRobject=NULL, se.fit.CCT=TRUE) {
timings <- list()
.ptime_start <- proc.time()
this.call <- match.call()
p4s <- as.character(NA)
Polys <- NULL
if (is(data, "SpatialPolygonsDataFrame"))
Polys <- as(data, "SpatialPolygons")
if (is(data, "Spatial")) {
if (!missing(coords))
warning("data is Spatial* object, ignoring coords argument")
coords <- coordinates(data)
p4s <- proj4string(data)
if (is.null(longlat) || !is.logical(longlat)) {
if (!is.na(is.projected(data)) && !is.projected(data)) {
longlat <- TRUE
} else {
longlat <- FALSE
}
}
data <- as(data, "data.frame")
}
if (is.null(longlat) || !is.logical(longlat)) longlat <- FALSE
if (missing(coords))
stop("Observation coordinates have to be given")
if (is.null(colnames(coords)))
colnames(coords) <- c("coord.x", "coord.y")
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "weights"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
mt <- attr(mf, "terms")
dp.n <- length(model.extract(mf, "response"))
weights <- as.vector(model.extract(mf, "weights"))
# set up default weights
if (!is.null(weights) && !is.numeric(weights))
stop("'weights' must be a numeric vector")
if (is.null(weights)) weights <- rep(as.numeric(1), dp.n)
if (any(is.na(weights))) stop("NAs in weights")
if (any(weights < 0)) stop("negative weights")
y <- model.extract(mf, "response")
x <- model.matrix(mt, mf)
lm <- lm.wfit(x, y, w=weights)
lm$x <- x
lm$y <- y
gTSS <- c(cov.wt(matrix(y, ncol=1), wt=weights, method="ML")$cov*dp.n)
if (hatmatrix) se.fit <- TRUE
if (hatmatrix) predictions <- TRUE
if (missing(fit.points)) {
fp.given <- FALSE
fittedGWRobject <- NULL
predictions <- TRUE
fit.points <- coords
colnames(fit.points) <- colnames(coords)
predx <- x
} else fp.given <- TRUE
griddedObj <- FALSE
if (is(fit.points, "Spatial")) {
if (predictions) {
t1 <- try(slot(fit.points, "data"), silent=TRUE)
if (inherits(t1, "try-error"))
stop("No data slot in fit.points")
predx <- try(model.matrix(delete.response(mt), fit.points))
if (inherits(predx, "try-error"))
stop("missing RHS variable in fit.points")
if (ncol(predx) != ncol(x))
stop("new data matrix columns mismatch")
}
Polys <- NULL
if (is(fit.points, "SpatialPolygonsDataFrame")) {
Polys <- as(fit.points, "SpatialPolygons")
fit.points <- coordinates(fit.points)
} else {
griddedObj <- gridded(fit.points)
fit.points <- coordinates(fit.points)
}
} else {
if (predictions && fp.given)
stop("predictions not available for matrix fit points")
}
n <- NROW(fit.points)
rownames(fit.points) <- NULL
if (is.null(colnames(fit.points))) colnames(fit.points) <- c("x", "y")
if (predictions) {
if (nrow(predx) != nrow(fit.points))
stop("new data matrix rows mismatch")
fit.points <- cbind(fit.points, predx)
}
# if (is.null(fit.points)) fit.points <- coords
# cluster issue with fit.points 120505 Maximilian Spross
fit_are_data <- isTRUE(all.equal(fit.points, coords,
check.attributes=FALSE))
input_predictions <- predictions
if (fit_are_data && !predictions) {
predictions <- TRUE
input_predictions <- FALSE
predx <- x
fit.points <- cbind(fit.points, predx)
}
m <- NCOL(x)
if (NROW(x) != NROW(coords))
stop("Input data and coordinates have different dimensions")
if (missing(bandwidth) && is.null(adapt))
stop("Bandwidth must be given for non-adaptive weights")
if (!is.null(adapt)) {
stopifnot(is.numeric(adapt))
stopifnot((adapt >= 0))
stopifnot((adapt <= 1))
} else {
stopifnot(length(bandwidth) == 1)
}
if (missing(bandwidth)) bandwidth <- NULL
lhat <- NA
yhat <- NULL
if (!is.null(fittedGWRobject)) {
yhat <- fittedGWRobject$SDF$pred
}
GWR_args <- list(fp.given=fp.given, hatmatrix=hatmatrix,
longlat=longlat, bandwidth=bandwidth, adapt=adapt, se.fit=se.fit,
predictions=predictions, se.fit.CCT=se.fit.CCT,
fit_are_data=fit_are_data)
timings[["set_up"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
if (!is.null(cl) && length(cl) > 1 && fp.given && !hatmatrix) {
if (requireNamespace("parallel", quietly = TRUE)) {
l_fp <- lapply(parallel::splitIndices(nrow(fit.points), length(cl)),
function(i) fit.points[i,, drop=FALSE])
parallel::clusterEvalQ(cl, library(spgwr))
varlist <- list("GWR_args", "coords", "gweight", "y",
"x", "weights", "yhat")
env <- new.env()
assign("GWR_args", GWR_args, envir = env)
assign("coords", coords, envir = env)
assign("gweight", gweight, envir = env)
assign("y", y, envir = env)
assign("x", x, envir = env)
assign("weights", weights, envir = env)
assign("yhat", yhat, envir = env)
# clusterExport_l <- function(cl, list) {
# gets <- function(n, v) {
# assign(n, v, envir = .GlobalEnv)
# NULL
# }
# for (name in list) {
# clusterCall(cl, gets, name, get(name))
# }
# }
#
# clusterExport_l(cl, list("GWR_args", "coords", "gweight", "y",
# "x", "weights", "yhat"))
parallel::clusterExport(cl, varlist, env)
res <- parallel::parLapply(cl, l_fp, function(fp) .GWR_int(fit.points=fp,
coords=coords, gweight=gweight, y=y, x=x,
weights=weights, yhat=yhat, GWR_args=GWR_args))
parallel::clusterEvalQ(cl, rm(varlist))
rm(env)
df <- list()
df$df <- as.data.frame(do.call("rbind",
lapply(res, function(x) x$df)))
bw <- do.call("c", lapply(res, function(x) x$bw))
results <- NULL
} else {
stop("parallel not available")
}
} else { # cl
df <- .GWR_int(fit.points=fit.points, coords=coords,
gweight=gweight, y=y, x=x, weights=weights, yhat=yhat,
GWR_args=GWR_args)
if (!fp.given && hatmatrix) lhat <- df$lhat
bw <- df$bw
# df <- as.data.frame(df$df)
results <- NULL
} # cl
timings[["run_gwr"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
if (predictions && !input_predictions) predictions <- FALSE
if (!fp.given && hatmatrix) {
#This section calculates the effective degree of freedoms, edf;
#the normalized residual sum of square, sigma2; the model
#residual of squares, rss; and various version of AICs
#As long as the hat matrix is obtained, many statistics can be
#calculated, such as the effective degree of freedom, AIC, etc.
#Now calculate the effective degree of freedom of the residual
#Reference: GWR book, page 55
#obtain v1 and v2:
v1 <- sum(diag(lhat))
B2 <- t(lhat)%*%lhat
v2 <- sum(diag(B2))
#effective d.f. is n - 2*v1 + v2
edf <- dp.n - 2*v1 + v2
#Follow Leung et al. EPA 2000 page 15, the estimate of sigma square
#can be obtained through rss and delta1 (which is actually edf)
#Calculate rss:
B1 <- t(diag(dp.n)-lhat)%*%(diag(dp.n)-lhat)
rss <- c(t(y)%*%B1%*%y)
delta1 <- sum (diag (B1))
sigma2 <- rss/delta1 #line 77
#Now the problem is, there are several version of AIC's calculation
#formula, the GWR book's (page 61,96), Brunsdon's handouts,
#and the one from Hurvich, Simonoff and Tsai (1998, page 276)
#I will implement all of them, and called them
#AICb, from the book, AICh, from Brunsdon, and AICc, from Hurvich et al.
#AICb <- n*log(sigma2) + n*log(2*3.14) + (n * (n + v1) / (n - 2 - v1))
#AICh <- n*log(sigma2) + ((n + v1) / (n + 2 - v1))
#To calculate AICc, there are several interal parameters
#delta1 has already been calculated, detailed formula see
#Hurvich et al. 1998, page 275, 276
#B1 (above) and B2, delta2, nu1, nu2:
odelta2 <- sum(diag(B1)^2)
# Patrick Zimmerman 090617
delta2 <- sum(diag(B1 %*% B1))
nu1 <- sum(diag(B2))
#nu2 <- sum(diag(B2^)2)
#AICc is from the formula in Hurvich et al. 1998 page 276
#AICc1:
#AICc <- n*log(sigma2) + n * ((delta1/delta2)*(n + nu1))/((delta1^2/delta2)-2)
#One thing that I did not notice is that the sigma2 here I used is not
#the same sigma2 used in the GWR book (detailed reference in page 96).
#The sigma2 I used is from Leung et al (2000, p 15), calculated in line 77
#The sigma2 in the GWR book is a maximum likelihood estimate
#It should be: sigma2 <- rss/n instead of sigma2 <- rss/delta1
#For this reason, a corrected AICb.b, AICh.b, AICc.b are therefore provided
#followed by creating the sigma sqare used in the book, termed here sigma2.b
#All the above unncessary calculation is then commented out.
sigma2.b <- rss / dp.n
AICb.b <- 2*dp.n*log(sqrt(sigma2.b)) + dp.n*log(2*pi) +
(dp.n * ((n + v1) / (dp.n - 2 - v1)))
# NOTE 2* and sqrt() inserted for legibility
AICh.b <- 2*dp.n*log(sqrt(sigma2.b)) + dp.n*log(2*pi) + dp.n + v1
# added omitted n*log(2*pi) term in AICc.b
# bug resolved by Christian Salas 090418
AICc.b <- 2*dp.n*log(sqrt(sigma2.b)) + dp.n*log(2*pi) + dp.n *
((delta1/delta2)*(dp.n + nu1))/((delta1^2/delta2)-2)
results <- list(v1=v1, v2=v2, delta1=delta1, delta2=delta2,
sigma2=sigma2, sigma2.b=sigma2.b, AICb=AICb.b,
AICh=AICh.b, AICc=AICc.b, edf=edf, rss=rss, nu1=nu1,
odelta2=odelta2, n=dp.n)
timings[["postprocess_hatmatrix"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
}
# df <- data.frame(sum.w=sum.w, gwr.b, gwr.R2, gwr.se, gwr.e)
# cluster issue with fit.points 120505 Maximilian Spross
if ((!fp.given || fit_are_data) && is.null(fittedGWRobject)) {
localR2 <- numeric(n)
if (is.null(adapt)) {
bw <- bandwidth
bandwidthR2 <- rep(bandwidth, n)
} else {
bandwidthR2 <- gw.adapt(dp=coords, fp=fit.points[,1:2,
drop=FALSE], quant=adapt, longlat=longlat)
# Maciej Kryza 130906 drop issue
bw <- bandwidthR2
}
if (any(bandwidth < 0)) stop("Invalid bandwidth")
for (i in 1:n) {
dxs <- spDistsN1(coords, fit.points[i,1:2],
longlat=GWR_args$longlat)
if (any(!is.finite(dxs)))
dxs[which(!is.finite(dxs))] <- .Machine$double.xmax/2
# if (!is.finite(dxs[i])) dxs[i] <- 0
w.i <- gweight(dxs^2, bandwidthR2[i])
w.i <- w.i * weights
if (any(w.i < 0 | is.na(w.i)))
stop(paste("Invalid weights for i:", i))
RSS <- sum(w.i * (y - df$df[,"pred"])^2)
yss <- sum(w.i * (y - weighted.mean(y, w.i))^2)
localR2[i] <- 1 - (RSS/yss)
}
df$df <- cbind(df$df, localR2)
timings[["postprocess_localR2"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
}
if (se.fit) {
EDFS <- NULL
normSigmaS <- NULL
EDF <- NULL
normSigma <- NULL
if (fp.given && !is.null(fittedGWRobject)) {
if (fittedGWRobject$hatmatrix) {
EDF <- fittedGWRobject$results$edf
normSigma <- sqrt(fittedGWRobject$results$rss/EDF)
EDFS <- fittedGWRobject$results$n -
fittedGWRobject$results$v1
normSigmaS <- sqrt(fittedGWRobject$results$rss/EDFS)
}
}
if (!fp.given && hatmatrix) {
EDFS <- results$n - results$v1
normSigmaS <- sqrt(results$rss/EDFS)
EDF <- results$edf
normSigma <- sqrt(results$rss/EDF)
}
ses <- grep("_se", colnames(df$df))
senms <- colnames(df$df)[ses]
betase <- df$df[, ses, drop=FALSE]
df$df[, ses] <- NA
if (predictions) {
pred.se <- df$df[, "pred.se", drop=FALSE]
df$df[, "pred.se"] <- NA
}
if (!is.null(EDF)) {
betaseEDF <- normSigma * sqrt(betase)
colnames(betaseEDF) <- paste(senms, "EDF", sep="_")
df$df[, ses] <- normSigmaS * sqrt(betase)
df$df <- cbind(df$df, betaseEDF)
if (predictions) {
pred.se_EDF <- normSigma * sqrt(pred.se)
df$df[, "pred.se"] <- normSigmaS * sqrt(pred.se)
df$df <- cbind(df$df, pred.se_EDF)
}
} else {
warning("standard errors set to NA, normalised RSS not available")
}
timings[["postprocess_SE"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
}
df <- as.data.frame(df$df)
if (predictions) fit.points <- fit.points[,1:2, drop=FALSE]
# Maciej Kryza 130906 drop issue
row.names(fit.points) <- row.names(df)
SDF <- SpatialPointsDataFrame(coords=fit.points,
data=df, proj4string=CRS(p4s))
if (griddedObj) {
gridded(SDF) <- TRUE
} else {
if (!is.null(Polys)) {
df <- data.frame(SDF@data)
rownames(df) <- sapply(slot(Polys, "polygons"),
function(i) slot(i, "ID"))
SDF <- SpatialPolygonsDataFrame(Sr=Polys, data=df)
}
}
timings[["final_postprocess"]] <- proc.time() - .ptime_start
z <- list(SDF=SDF, lhat=lhat, lm=lm, results=results,
bandwidth=bw, adapt=adapt, hatmatrix=hatmatrix,
gweight=deparse(substitute(gweight)), gTSS=gTSS,
this.call=this.call, fp.given=fp.given,
timings=do.call("rbind", timings)[, c(1, 3)])
class(z) <- "gwr"
invisible(z)
}
print.gwr <- function(x, ...) {
if(!inherits(x, "gwr")) stop("not a gwr object")
cat("Call:\n")
print(x$this.call)
cat("Kernel function:", x$gweight, "\n")
n <- length(x$lm$residuals)
if (is.null(x$adapt)) cat("Fixed bandwidth:", x$bandwidth, "\n")
else cat("Adaptive quantile: ", x$adapt, " (about ",
floor(x$adapt*n), " of ", n, " data points)\n", sep="")
if (x$fp.given) cat("Fit points: ", nrow(x$SDF), "\n", sep="")
m <- length(x$lm$coefficients)
cat("Summary of GWR coefficient estimates at ",
ifelse(x$fp.given, "fit", "data"), " points:\n", sep="")
df0 <- as(x$SDF, "data.frame")[,(1+(1:m)), drop=FALSE]
if (any(is.na(df0))) {
df0 <- na.omit(df0)
warning("NAs in coefficients dropped")
}
CM <- t(apply(df0, 2, summary))[,c(1:3,5,6)]
if (is.null(dim(CM))) CM <- t(as.matrix(CM))
if (!x$fp.given) {
CM <- cbind(CM, coefficients(x$lm))
colnames(CM) <- c(colnames(CM)[1:5], "Global")
}
printCoefmat(CM)
if (x$hatmatrix) {
cat("Number of data points:", n, "\n")
cat("Effective number of parameters (residual: 2traceS - traceS'S):", 2*x$results$v1 -
x$results$v2, "\n")
cat("Effective degrees of freedom (residual: 2traceS - traceS'S):", x$results$edf, "\n")
cat("Sigma (residual: 2traceS - traceS'S):",
sqrt(x$results$rss/x$results$edf), "\n")
cat("Effective number of parameters (model: traceS):",
x$results$v1, "\n")
cat("Effective degrees of freedom (model: traceS):",
(x$results$n - x$results$v1), "\n")
cat("Sigma (model: traceS):",
sqrt(x$results$rss/(x$results$n - x$results$v1)), "\n")
cat("Sigma (ML):", sqrt(x$results$sigma2.b), "\n")
cat("AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21):",
x$results$AICb, "\n")
cat("AIC (GWR p. 96, eq. 4.22):", x$results$AICh, "\n")
cat("Residual sum of squares:", x$results$rss, "\n")
cat("Quasi-global R2:", (1 - (x$results$rss/x$gTSS)), "\n")
}
invisible(x)
}
.GWR_int <- function(fit.points, coords, gweight, y, x, weights, yhat,
GWR_args) {
if (GWR_args$predictions) {
predx <- fit.points[, -c(1,2), drop=FALSE]
fit.points <- fit.points[, c(1,2), drop=FALSE]
# Maciej Kryza 130906 drop issue
}
n <- nrow(fit.points)
m <- NCOL(x)
x1 <- matrix(1, nrow=nrow(x), ncol=1)
sum.w <- numeric(n)
betas <- matrix(nrow=n, ncol=m)
colnames(betas) <- colnames(x)
if(!GWR_args$fp.given) {
gwr.e <- numeric(n)
} else {
gwr.e <- NULL
}
if (GWR_args$se.fit) {
betase <- matrix(nrow=n, ncol=m)
colnames(betase) <- paste(colnames(x), "se", sep="_")
} else {
betase <- NULL
}
if (GWR_args$predictions) {
pred <- numeric(n)
if (GWR_args$se.fit) {
pred.se <- numeric(n)
} else {
pred.se <- NULL
}
} else {
pred <- NULL
pred.se <- NULL
}
if (is.null(yhat)) {
localR2 <- NULL
} else {
localR2 <- numeric(n)
}
if (!GWR_args$fp.given && GWR_args$hatmatrix)
lhat <- matrix(nrow=n, ncol=n)
if (is.null(GWR_args$adapt)) {
bw <- GWR_args$bandwidth
bandwidth <- rep(GWR_args$bandwidth, n)
} else {
bandwidth <- gw.adapt(dp=coords, fp=fit.points,
quant=GWR_args$adapt, longlat=GWR_args$longlat)
bw <- bandwidth
}
if (any(bandwidth < 0)) stop("Invalid bandwidth")
for (i in 1:n) {
dxs <- spDistsN1(coords, fit.points[i,],
longlat=GWR_args$longlat)
if (any(!is.finite(dxs)))
dxs[which(!is.finite(dxs))] <- 0
# if (!is.finite(dxs[i])) dxs[i] <- 0
w.i <- gweight(dxs^2, bandwidth[i])
w.i <- w.i * weights
if (any(w.i < 0 | is.na(w.i)))
stop(paste("Invalid weights for i:", i))
lm.i <- lm.wfit(x, y, w.i)
sum.w[i] <- sum(w.i)
betas[i,] <- coefficients(lm.i)
ei <- residuals(lm.i)
# prediction fitted values at fit point
if (GWR_args$predictions) {
pred[i] <- sum(predx[i,] * betas[i,])
}
# use of diag(w.i) dropped to avoid forming n by n matrix
# bug report: Ilka Afonso Reis, July 2005
# local R-squared as explained by Tomoki Nakaya, 090624 (in GWR4)
# differs from local weighted regression R-squared
if (!is.null(yhat)) {
RSS <- sum(w.i * (y - yhat)^2)
yss <- sum(w.i * (y - weighted.mean(y, w.i))^2)
localR2[i] <- 1 - (RSS/yss)
}
if (GWR_args$se.fit) {
p <- lm.i$rank
if (p != m) {
warning(paste("OLS fit not full rank at fit point", i))
} else {
p1 <- 1:p
inv.Z <- chol2inv(lm.i$qr$qr[p1, p1, drop=FALSE])
# p. 55 CC definition
if (GWR_args$se.fit.CCT) {
C <- inv.Z %*% t(x) %*% diag(w.i)
CC <- C %*% t(C)
# only return coefficient covariance matrix diagonal raw values
# for post-processing
betase[i,] <- diag(CC)
} else {
betase[i,] <- diag(inv.Z)
}
# prediction "standard errors"
# only return raw values for post-processing
if (GWR_args$predictions && (p==m)) {
if (GWR_args$se.fit.CCT) {
pred.se[i] <- t(predx[i,]) %*% CC %*% predx[i,]
} else {
pred.se[i] <- t(predx[i,]) %*% inv.Z %*% predx[i,]
}
}
}
}
# assigning residual bug Torleif Markussen Lunde 090529
# cluster issue with fit.points 120505 Maximilian Spross
if (!GWR_args$fp.given || GWR_args$fit_are_data)
gwr.e[i] <- ei[i]
if (!GWR_args$fp.given && GWR_args$hatmatrix && (p==m))
lhat[i,] <- t(x[i,]) %*% inv.Z %*% t(x) %*% diag(w.i)
}
df <- cbind(sum.w, betas, betase, gwr.e, pred, pred.se, localR2)
if (!GWR_args$fp.given && GWR_args$hatmatrix)
return(list(df=df, lhat=lhat, bw=bw))
else return(list(df=df, bw=bw))
} # GWR_int