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# Copyright 2001-7 by Roger Bivand
#
lm.LMtests <- function(model, listw, zero.policy=NULL, test="LMerr",
spChk=NULL, naSubset=TRUE) {
if (inherits(model, "lm")) na.act <- model$na.action
else na.act <- attr(model, "na.action")
listw_name <- deparse(substitute(listw))
if (!inherits(listw, "listw")) stop(paste(listw_name,
"is not a listw object"))
if (is.null(zero.policy))
zero.policy <- get("zeroPolicy", envir = .spdepOptions)
stopifnot(is.logical(zero.policy))
if (!is.null(na.act) && naSubset) {
subset <- !(1:length(listw$neighbours) %in% na.act)
listw <- subset(listw, subset, zero.policy=zero.policy)
}
if (length(test) == 1L && test[1] == "LMerr") {
res <- lm.LMErr(model=model, listw=listw,
zero.policy=zero.policy, spChk=spChk)
if (inherits(model, "lm")) res$data.name <- paste("\n",
paste(strwrap(paste("model: ",
gsub("[ ]+", " ", paste(deparse(model$call),
sep="", collapse="")))), collapse="\n"),
"\nweights: ", listw_name, "\n", sep="")
else res$data.name <- paste("\nresiduals: ",
deparse(substitute(model)), "\nweights: ",
listw_name, "\n", sep="")
tres <- vector(mode="list", length=1)
names(tres) <- test
tres[[1]] <- res
class(tres) <- "LMtestlist"
return(tres)
}
if(!inherits(model, "lm")) stop(paste(deparse(substitute(model)),
"not an lm object"))
N <- length(listw$neighbours)
u <- resid(model)
if (N != length(u)) stop("objects of different length")
if (is.null(spChk)) spChk <- get.spChkOption()
if (spChk && !chkIDs(u, listw))
stop("Check of data and weights ID integrity failed")
u <- as.vector(u)
if (is.null(attr(listw$weights, "W")) || !attr(listw$weights, "W"))
warning("Spatial weights matrix not row standardized")
all.tests <- c("LMerr", "LMlag", "RLMerr", "RLMlag", "SARMA")
if (test[1] == "all") test <- all.tests
if (!all(test %in% all.tests))
stop("Invalid test selected - must be either \"all\" or a vector of tests")
y <- model.response(model.frame(model))
X <- model.matrix(terms(model), model.frame(model))
yhat <- as.vector(fitted(model))
p <- model$rank
p1 <- 1:p
nacoefs <- which(is.na(coefficients(model)))
# fixed after looking at TOWN dummy in Boston data
if (length(nacoefs) > 0L) X <- X[,-nacoefs]
XtXinv <- chol2inv(model$qr$qr[p1, p1, drop = FALSE])
sigma2 <- (t(u) %*% u) / N
TrW <- tracew(listw)
Wu <- lag.listw(listw, u, zero.policy)
Wy <- lag.listw(listw, y, zero.policy)
Wyhat <- lag.listw(listw, yhat, zero.policy)
XtWyhat <- t(X) %*% Wyhat
dutWu <- (t(u) %*% Wu) / sigma2
resa <- (dutWu ^ 2) / TrW
J <- (1/(N*sigma2)) *
((t(Wyhat) %*% Wyhat) -
(t(XtWyhat) %*% XtXinv %*% XtWyhat) +
(TrW * sigma2))
dutWy <- (t(u) %*% Wy) / sigma2
nt <- length(test)
if (nt < 1) stop("non-positive number of tests")
tres <- vector(mode="list", length=nt)
names(tres) <- test
for (i in 1:nt) {
testi <- test[i]
zz <- switch(testi,
LMerr = vec <- c(resa, 1),
LMlag = vec <- c((dutWy ^ 2) / (N * J), 1),
RLMerr = vec <- c(((dutWu - (TrW*((N*J)^-1))*dutWy)^2) /
(TrW * (1 - TrW*((N*J)^-1))), 1),
RLMlag = vec <- c(((dutWy - dutWu)^2)/ ((N*J) - TrW), 1),
SARMA = vec <- c(((dutWy - dutWu)^2)/ ((N*J) - TrW) + resa, 2)
)
if (is.null(zz)) stop(paste(testi, ": no such test", sep=""))
statistic <- vec[1]
names(statistic) <- testi
parameter <- vec[2]
names(parameter) <- "df"
p.value <- 1 - pchisq(statistic, parameter)
if (!is.finite(p.value) || p.value < 0 || p.value > 1)
warning("Out-of-range p-value: reconsider test arguments")
names(p.value) <- ""
method <- "Lagrange multiplier diagnostics for spatial dependence"
data.name <- paste("\n", paste(strwrap(paste("model: ",
gsub("[ ]+", " ", paste(deparse(model$call),
sep="", collapse="")))), collapse="\n"),
"\nweights: ", listw_name, "\n", sep="")
tres[[i]] <- list(statistic=statistic, parameter=parameter,
p.value=p.value, method=method, data.name=data.name)
class(tres[[i]]) <- "htest"
}
class(tres) <- "LMtestlist"
tres
}
print.LMtestlist <- function(x, ...) {
for (i in seq(along=x)) print(x[[i]])
invisible(x)
}
summary.LMtestlist <- function(object, p.adjust.method="none", ...) {
res <- as.data.frame(t(sapply(object, "[", 1:3)))
res[,3] <- p.adjust(res[,3], method=p.adjust.method)
object$results <- res
class(object) <- "LMtestlist.summary"
object
}
print.LMtestlist.summary <- function(x, digits=max(3, getOption("digits") - 2), ...) {
cat(strwrap(x[[1]]$method, prefix = "\t"), sep = "\n")
cat("data: ", x[[1]]$data.name, "\n")
printCoefmat(x$results, has.Pvalue=TRUE, digits=digits, ...)
invisible(x)
}
tracew <- function (listw) {
dlmtr <- 0
n <- length(listw$neighbours)
if (n < 1) stop("non-positive n")
ndij <- card(listw$neighbours)
dlmtr <- 0
for (i in 1:n) {
dij <- listw$neighbours[[i]]
wdij <- listw$weights[[i]]
for (j in seq(length=ndij[i])) {
k <- dij[j]
# Luc Anselin 2006-11-11 problem with asymmetric listw
dk <- which(listw$neighbours[[k]] == i)
if (length(dk) > 0L && dk > 0L &&
dk <= length(listw$neighbours[[k]]))
wdk <- listw$weights[[k]][dk]
else wdk <- 0
dlmtr <- dlmtr + (wdij[j]*wdij[j]) + (wdij[j]*wdk)
}
}
dlmtr
}
lm.LMErr <- function(model, listw, zero.policy=FALSE, spChk=NULL) {
if (!inherits(listw, "listw")) stop("listw is not a listw object")
N <- length(listw$neighbours)
if (inherits(model, "lm")) u <- resid(model)
else if (is.numeric(model) && length(model) == N) {
u <- model
if (!isTRUE(all.equal(mean(u), 0.0)))
warning("mean of externally provided residuals not zero")
} else stop(paste(deparse(substitute(model)),
"not an lm object or a numeric vector of correct length"))
if (N != length(u)) stop("objects of different length")
if (is.null(spChk)) spChk <- get.spChkOption()
if (spChk && !chkIDs(u, listw))
stop("Check of data and weights ID integrity failed")
u <- as.vector(u)
if (is.null(attr(listw$weights, "W")) || !attr(listw$weights, "W"))
warning("Spatial weights matrix not row standardized")
TrW <- tracew(listw)
Wu <- lag.listw(listw, u, zero.policy)
sigma2 <- (t(u) %*% u) / N
dutWu <- (t(u) %*% Wu) / sigma2
resa <- (dutWu ^ 2) / TrW
statistic <- resa
names(statistic) <- "LMErr"
parameter <- 1
names(parameter) <- "df"
p.value <- 1 - pchisq(statistic, parameter)
if (!is.finite(p.value) || p.value < 0 || p.value > 1)
warning("Out-of-range p-value: reconsider test arguments")
names(p.value) <- ""
method <- "Lagrange multiplier diagnostics for spatial dependence"
if (inherits(model, "lm")) data.name <- paste("\n",
paste(strwrap(paste("model: ",
gsub("[ ]+", " ", paste(deparse(model$call),
sep="", collapse="")))), collapse="\n"),
"\nweights: ", deparse(substitute(listw)), "\n", sep="")
else data.name <- paste("\nresiduals: ", deparse(substitute(model)),
"\nweights: ", deparse(substitute(listw)), "\n", sep="")
res <- list(statistic=statistic, parameter=parameter,
p.value=p.value, method=method, data.name=data.name)
class(res) <- "htest"
res
}
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