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# Copyright 2001-18 by Roger Bivand
#
moran <- function(x, listw, n, S0, zero.policy=NULL, NAOK=FALSE) {
if (is.null(zero.policy))
zero.policy <- get("zeroPolicy", envir = .spdepOptions)
stopifnot(is.logical(zero.policy))
n1 <- length(listw$neighbours)
x <- c(x)
if (n1 != length(x)) stop("objects of different length")
xx <- mean(x, na.rm=NAOK)
z <- x - xx
zz <- sum(z^2, na.rm=NAOK)
K <- (length(x)*sum(z^4, na.rm=NAOK))/(zz^2)
lz <- lag.listw(listw, z, zero.policy=zero.policy, NAOK=NAOK)
# I <- (n / S0) * ((t(z) %*% lz) / zz)
I <- (n / S0) * ((sum(z*lz, na.rm=NAOK)) / zz)
res <- list(I=I, K=K)
res
}
moran.test <- function(x, listw, randomisation=TRUE, zero.policy=NULL,
alternative="greater", rank = FALSE, na.action=na.fail, spChk=NULL,
adjust.n=TRUE, drop.EI2=FALSE) {
alternative <- match.arg(alternative, c("greater", "less", "two.sided"))
if (!inherits(listw, "listw")) stop(paste(deparse(substitute(listw)),
"is not a listw object"))
if (!is.numeric(x)) stop(paste(deparse(substitute(x)),
"is not a numeric vector"))
if (is.null(zero.policy))
zero.policy <- get("zeroPolicy", envir = .spdepOptions)
stopifnot(is.logical(zero.policy))
if (is.null(spChk)) spChk <- get.spChkOption()
if (spChk && !chkIDs(x, listw))
stop("Check of data and weights ID integrity failed")
# if (any(is.na(x))) stop("NA in X")
xname <- deparse(substitute(x))
wname <- deparse(substitute(listw))
NAOK <- deparse(substitute(na.action)) == "na.pass"
x <- na.action(x)
na.act <- attr(x, "na.action")
if (!is.null(na.act)) {
subset <- !(1:length(listw$neighbours) %in% na.act)
listw <- subset(listw, subset, zero.policy=zero.policy)
}
n <- length(listw$neighbours)
if (n != length(x)) stop("objects of different length")
wc <- spweights.constants(listw, zero.policy=zero.policy,
adjust.n=adjust.n)
S02 <- wc$S0*wc$S0
res <- moran(x, listw, wc$n, wc$S0, zero.policy=zero.policy,
NAOK=NAOK)
I <- res$I
K <- res$K
if (rank) K <- (3*(3*wc$n^2 -7))/(5*(wc$n^2 - 1))
EI <- (-1) / wc$n1
if(randomisation) {
VI <- wc$n*(wc$S1*(wc$nn - 3*wc$n + 3) - wc$n*wc$S2 + 3*S02)
tmp <- K*(wc$S1*(wc$nn - wc$n) - 2*wc$n*wc$S2 + 6*S02)
if (tmp > VI) warning("Kurtosis overflow,\ndistribution of variable does not meet test assumptions")
VI <- (VI - tmp) / (wc$n1*wc$n2*wc$n3*S02)
if (!drop.EI2) VI <- (VI - EI^2)
if (VI < 0) warning("Negative variance,\ndistribution of variable does not meet test assumptions")
} else {
VI <- (wc$nn*wc$S1 - wc$n*wc$S2 + 3*S02) / (S02*(wc$nn - 1))
if (!drop.EI2) VI <- (VI - EI^2)
if (VI < 0) warning("Negative variance,\ndistribution of variable does not meet test assumptions")
}
ZI <- (I - EI) / sqrt(VI)
statistic <- ZI
names(statistic) <- "Moran I statistic standard deviate"
if (alternative == "two.sided")
PrI <- 2 * pnorm(abs(ZI), lower.tail=FALSE)
else if (alternative == "greater")
PrI <- pnorm(ZI, lower.tail=FALSE)
else PrI <- pnorm(ZI)
if (!is.finite(PrI) || PrI < 0 || PrI > 1)
warning("Out-of-range p-value: reconsider test arguments")
vec <- c(I, EI, VI)
names(vec) <- c("Moran I statistic", "Expectation", "Variance")
method <- paste("Moran I test under", ifelse(randomisation,
"randomisation", "normality"))
data.name <- paste(xname, ifelse(rank,
"using rank correction",""), "\nweights:",
wname, ifelse(is.null(na.act), "", paste("\nomitted:",
paste(na.act, collapse=", "))),
ifelse(adjust.n && isTRUE(any(sum(card(listw$neighbours) == 0L))),
"n reduced by no-neighbour observations\n", ""),
ifelse(drop.EI2, "EI^2 term dropped in VI", ""), "\n")
res <- list(statistic=statistic, p.value=PrI, estimate=vec,
alternative=alternative, method=method, data.name=data.name)
if (!is.null(na.act)) attr(res, "na.action") <- na.act
class(res) <- "htest"
res
}
moran.mc <- function(x, listw, nsim, zero.policy=NULL,
alternative="greater", na.action=na.fail, spChk=NULL,
return_boot=FALSE, adjust.n=TRUE) {
alternative <- match.arg(alternative, c("greater", "less"))
if(!inherits(listw, "listw")) stop(paste(deparse(substitute(listw)),
"is not a listw object"))
if(!is.numeric(x)) stop(paste(deparse(substitute(x)),
"is not a numeric vector"))
if (is.null(zero.policy))
zero.policy <- get("zeroPolicy", envir = .spdepOptions)
stopifnot(is.logical(zero.policy))
if(missing(nsim)) stop("nsim must be given")
if (is.null(spChk)) spChk <- get.spChkOption()
if (spChk && !chkIDs(x, listw))
stop("Check of data and weights ID integrity failed")
cards <- card(listw$neighbours)
if (!zero.policy && any(cards == 0))
stop("regions with no neighbours found")
# if (any(is.na(x))) stop("NA in X")
xname <- deparse(substitute(x))
wname <- deparse(substitute(listw))
if (deparse(substitute(na.action)) == "na.pass")
stop("na.pass not permitted")
x <- na.action(x)
na.act <- attr(x, "na.action")
if (!is.null(na.act)) {
subset <- !(1:length(listw$neighbours) %in% na.act)
listw <- subset(listw, subset, zero.policy=zero.policy)
}
n <- length(listw$neighbours)
if (n != length(x)) stop("objects of different length")
gamres <- suppressWarnings(nsim > gamma(n + 1))
if (gamres) stop("nsim too large for this number of observations")
if (nsim < 1) stop("nsim too small")
if (adjust.n) n <- n - sum(cards == 0L)
S0 <- Szero(listw)
if (return_boot) {
moran_boot <- function(var, i, ...) {
var <- var[i]
return(moran(x=var, ...)$I)
}
cores <- get.coresOption()
if (is.null(cores)) {
parallel <- "no"
} else {
parallel <- ifelse (get.mcOption(), "multicore", "snow")
}
ncpus <- ifelse(is.null(cores), 1L, cores)
cl <- NULL
if (parallel == "snow") {
cl <- get.ClusterOption()
if (is.null(cl)) {
parallel <- "no"
warning("no cluster in ClusterOption, parallel set to no")
}
}
res <- boot(x, statistic=moran_boot, R=nsim,
sim="permutation", listw=listw, n=n, S0=S0,
zero.policy=zero.policy, parallel=parallel, ncpus=ncpus, cl=cl)
return(res)
}
res <- numeric(length=nsim+1)
for (i in 1:nsim) res[i] <- moran(sample(x), listw, n, S0,
zero.policy)$I
res[nsim+1] <- moran(x, listw, n, S0, zero.policy)$I
rankres <- rank(res)
xrank <- rankres[length(res)]
diff <- nsim - xrank
diff <- ifelse(diff > 0, diff, 0)
if (alternative == "less")
pval <- punif((diff + 1)/(nsim + 1), lower.tail=FALSE)
else if (alternative == "greater")
pval <- punif((diff + 1)/(nsim + 1))
if (!is.finite(pval) || pval < 0 || pval > 1)
warning("Out-of-range p-value: reconsider test arguments")
statistic <- res[nsim+1]
names(statistic) <- "statistic"
parameter <- xrank
names(parameter) <- "observed rank"
method <- "Monte-Carlo simulation of Moran I"
data.name <- paste(xname, "\nweights:",
wname, ifelse(is.null(na.act), "", paste("\nomitted:",
paste(na.act, collapse=", "))), "\nnumber of simulations + 1:",
nsim+1, "\n")
lres <- list(statistic=statistic, parameter=parameter,
p.value=pval, alternative=alternative, method=method,
data.name=data.name, res=res)
if (!is.null(na.act)) attr(lres, "na.action") <- na.act
class(lres) <- c("htest", "mc.sim")
lres
}
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