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# Copyright 2005-2008 by Roger Bivand and Pedro Peres-Neto (from Matlab)
#
ME <- function(formula, data, family = gaussian, weights, offset, listw,
alpha=0.05, nsim=99, verbose=NULL, stdev=FALSE) {
MoraneI.boot <- function(var, i, ...) {
var <- var[i]
I <- (n/S0)*(crossprod(sW %*% var, var))/cpvar
return(c(as(I, "matrix")))
}
MIR_a <- function(resids, sW, n, cpvar, S0, nsim, stdev=TRUE,
par_boot_args=list()) {
boot1 <- boot(resids, statistic=MoraneI.boot, R=nsim,
sim="permutation", sW=sW, n=n, S0=S0, cpvar=cpvar,
parallel=par_boot_args$parallel,
ncpus=par_boot_args$ncpus, cl=par_boot_args$cl)
mi <- boot1$t0
if (stdev) {
zi <- (boot1$t0 - mean(boot1$t))/sqrt(var(boot1$t))
pri <- pnorm(abs(zi), lower.tail=FALSE)
} else {
zi <- NA
pri <- (sum(boot1$t >= mi)+1)/(nsim+1)
}
res <- list(estimate=mi, statistic=zi, p.value=pri)
res
}
if (is.null(verbose)) verbose <- get("verbose", envir = .spdepOptions)
stopifnot(is.logical(verbose))
listw <- listw2U(listw) # make weights symmetric
sW <- as(listw, "CsparseMatrix")
Wmat <- listw2mat(listw) # convert to full matrix form
n <- ncol(Wmat)
S0 <- Szero(listw)
# argument handling copied from stats:::glm
# call <- match.call()
if (is.character(family))
family <- get(family, mode = "function", envir = parent.frame())
if (is.function(family)) family <- family()
if (is.null(family$family)) {
print(family)
stop("'family' not recognized")
}
if (missing(data)) data <- environment(formula)
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "weights", "offset"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
mt <- attr(mf, "terms")
Y <- model.extract(mf, "response") # extract X and Y
X <- model.matrix(mt, mf)
weights <- model.weights(mf)
if (!is.null(weights) && any(weights < 0))
stop("negative weights not allowed")
offset <- model.offset(mf)
if (!is.null(offset) && length(offset) != NROW(Y))
stop("number of offsets should equal number of observations")
glm_fit <- glm.fit(x=X, y=Y, weights=weights, offset=offset,
family=family)
glm_res <- glm_fit$y - glm_fit$fitted.values
cpvar <- crossprod(glm_res)
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")
}
}
par_boot_args <- list(parallel=parallel, ncpus=ncpus, cl=cl)
mRES <- MIR_a(glm_res, sW=sW, n=n, cpvar=cpvar, S0=S0, nsim=nsim,
stdev=stdev, par_boot_args=par_boot_args)
pIZ <- mRES$p.value
tres <- c(NA, mRES$statistic, pIZ)
if (pIZ > alpha) stop("base correlation larger than alpha")
Cent <- diag(n) - (matrix(1/n, n, n))
CWC <- Cent %*% Wmat %*% Cent
rm(Cent, Wmat)
CWC2 <- 0.5*(CWC+t(CWC))
rm(CWC)
eV <- eigen(CWC2)$vectors
rm(CWC2)
iZ <- numeric(n)
for (i in 1:n) {
iX <- cbind(X, eV[,i])
i_glm <- glm.fit(x=iX, y=Y, weights=weights, offset=offset,
family=family)
glm_res <- i_glm$y - i_glm$fitted.values
cpvar <- crossprod(glm_res)
# iZ[i] <- MIR_a(glm_res, sW=sW, n=n, cpvar=cpvar, S0=S0,
# nsim=nsim)$statistic
iZ[i] <- c(as((n/S0)*(crossprod(sW %*% glm_res, glm_res)) /
cpvar, "matrix"))
}
min_iZ <- which.min(abs(iZ))
X <- cbind(X, eV[, min_iZ])
glm_fit <- glm.fit(x=X, y=Y, weights=weights, offset=offset,
family=family)
glm_res <- glm_fit$y - glm_fit$fitted.values
cpvar <- crossprod(glm_res)
mRES <- MIR_a(glm_res, sW=sW, n=n, cpvar=cpvar, S0=S0, nsim=nsim,
stdev=stdev, par_boot_args=par_boot_args)
pIZ <- mRES$p.value
used <- rep(FALSE, n)
used[min_iZ] <- TRUE
min_v <- min_iZ
if (verbose) cat("eV[,", min_iZ, "], I: ", mRES$estimate, " ZI: ",
mRES$statistic, ", pr(ZI): ", pIZ, "\n", sep="")
tres <- rbind(tres, c(min_iZ, mRES$statistic, pIZ))
while (pIZ <= alpha) {
for (i in 1:n) {
if (!used[i]) {
iX <- cbind(X, eV[,i])
i_glm <- glm.fit(x=iX, y=Y, weights=weights,
offset=offset, family=family)
glm_res <- i_glm$y - i_glm$fitted.values
cpvar <- crossprod(glm_res)
# iZ[i] <- MIR_a(glm_res, sW=sW, n=n, cpvar=cpvar, S0=S0,
# nsim=nsim)$statistic
iZ[i] <- c(as((n/S0)*(crossprod(sW %*% glm_res,
glm_res))/cpvar, "matrix"))
} else iZ[i] <- NA
}
min_iZ <- which.min(abs(iZ))
X <- cbind(X, eV[, min_iZ])
glm_fit <- glm.fit(x=X, y=Y, weights=weights, offset=offset,
family=family)
glm_res <- glm_fit$y - glm_fit$fitted.values
cpvar <- crossprod(glm_res)
mRES <- MIR_a(glm_res, sW=sW, n=n, cpvar=cpvar, S0=S0,
nsim=nsim, stdev=stdev, par_boot_args=par_boot_args)
pIZ <- mRES$p.value
used[min_iZ] <- TRUE
min_v <- c(min_v, min_iZ)
if (verbose) cat("eV[,", min_iZ, "], I: ", mRES$estimate,
" ZI: ", mRES$statistic, ", pr(ZI): ", pIZ,
"\n", sep="")
tres <- rbind(tres, c(min_iZ, mRES$statistic, pIZ))
}
sv <- eV[,min_v, drop=FALSE]
colnames(sv) <- paste("vec", min_v, sep="")
colnames(tres) <- c("Eigenvector", "ZI", "pr(ZI)")
rownames(tres) <- 0:(nrow(tres)-1)
res <- list(selection=tres, vectors=sv)
class(res) <- "ME_res"
res
}
print.ME_res <- function(x, ...) {
print(x$selection)
}
fitted.ME_res <- function(object, ...) {
object$vectors
}
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