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ML_models.R
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# Copyright 1998-2016 by Roger Bivand (non-W styles Rein Halbersma)
#
errorsarlm <- function(formula, data = list(), listw, na.action, weights=NULL,
Durbin, etype, method="eigen", quiet=NULL, zero.policy=NULL,
interval=NULL, tol.solve=.Machine$double.eps, trs=NULL, control=list()) {
timings <- list()
.ptime_start <- proc.time()
con <- list(tol.opt=.Machine$double.eps^0.5, returnHcov=TRUE,
pWOrder=250, fdHess=NULL, optimHess=FALSE,
optimHessMethod="optimHess", LAPACK=FALSE,
compiled_sse=FALSE, Imult=2, cheb_q=5, MC_p=16, MC_m=30,
super=NULL, spamPivot="MMD", in_coef=0.1, type="MC",
correct=TRUE, trunc=TRUE, SE_method="LU", nrho=200,
interpn=2000, small_asy=TRUE, small=1500, SElndet=NULL,
LU_order=FALSE, pre_eig=NULL, return_impacts=TRUE)
nmsC <- names(con)
con[(namc <- names(control))] <- control
if (length(noNms <- namc[!namc %in% nmsC]))
warning("unknown names in control: ", paste(noNms, collapse = ", "))
if (is.null(quiet)) quiet <- !get("verbose", envir = .spatialregOptions)
stopifnot(is.logical(quiet))
if (is.null(zero.policy))
zero.policy <- get("zeroPolicy", envir = .spatialregOptions)
stopifnot(is.logical(zero.policy))
if (!inherits(listw, "listw")) stop("No neighbourhood list")
stopifnot(is.logical(con$optimHess))
stopifnot(is.logical(con$LAPACK))
# stopifnot(is.logical(con$super))
stopifnot(is.logical(con$compiled_sse))
stopifnot(is.character(con$spamPivot))
stopifnot(is.logical(con$return_impacts))
if (!inherits(formula, "formula")) formula <- as.formula(formula)
# mt <- terms(formula, data = data)
# mf <- lm(formula, data, na.action=na.action, method="model.frame")
#
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "weights", "na.action"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
mt <- attr(mf, "terms")
if (attr(mt, "intercept") == 1 && !any(attr(mt, "factors") == 1) &&
(!missing(Durbin)) && (is.formula(Durbin) || isTRUE(Durbin))) {
warning("intercept-only model, Durbin invalid and set FALSE")
Durbin <- FALSE
}
have_factor_preds <- have_factor_preds_mf(mf)
#
na.act <- attr(mf, "na.action")
if (!is.null(na.act)) {
subset <- !(1:length(listw$neighbours) %in% na.act)
listw <- subset(listw, subset, zero.policy=zero.policy)
if (!is.null(con$pre_eig)) {
warning("NAs found, precomputed eigenvalues ignored")
con$pre_eig <- NULL
}
}
if (missing(etype)) etype <- "error"
if (etype == "Durbin") etype <- "emixed"
if (missing(Durbin)) Durbin <- ifelse(etype == "error", FALSE, TRUE)
# FIXME does this hold?
# if (listw$style != "W" && is.formula(Durbin)) {
# Durbin <- TRUE
# warning("formula Durbin requires row-standardised weights; set TRUE")
# }
if (is.logical(Durbin) && isTRUE(Durbin)) {
etype <- "emixed"
if (have_factor_preds) warn_factor_preds(have_factor_preds)
}
if (is.formula(Durbin)) etype <- "emixed"
if (is.logical(Durbin) && !isTRUE(Durbin)) etype <- "error"
switch(etype, error = if (!quiet)
cat("\nSpatial autoregressive error model\n"),
emixed = if (!quiet)
cat("\nSpatial mixed autoregressive error model\n"),
stop("\nUnknown model type\n"))
y <- model.response(mf, "numeric")
if (any(is.na(y))) stop("NAs in dependent variable")
x <- model.matrix(mt, mf)
if (any(is.na(x))) stop("NAs in independent variable")
n <- nrow(x)
if (n != length(listw$neighbours))
stop("Input data and neighbourhood list have different dimensions")
#
weights <- as.vector(model.extract(mf, "weights"))
if (!is.null(weights) && !is.numeric(weights))
stop("'weights' must be a numeric vector")
if (is.null(weights)) weights <- rep(as.numeric(1), n)
if (any(is.na(weights))) stop("NAs in weights")
if (any(weights < 0)) stop("negative weights")
#
m <- NCOL(x)
xxcolnames <- colnames(x)
stopifnot(is.logical(con$small_asy))
if (method != "eigen") {
if (con$small >= n && con$small_asy) do_asy <- TRUE
else do_asy <- FALSE
} else do_asy <- TRUE
if (is.null(con$fdHess)) {
con$fdHess <- method != "eigen" && !do_asy
fdHess <- NULL
}
stopifnot(is.logical(con$fdHess))
dvars <- c(NCOL(x), 0L)
if (is.formula(Durbin) || isTRUE(Durbin)) {
prefix <- "lag"
if (isTRUE(Durbin)) {
WX <- create_WX(x, listw, zero.policy=zero.policy,
prefix=prefix)
} else {
data1 <- data
if (!is.null(na.act) && (inherits(na.act, "omit") ||
inherits(na.act, "exclude"))) {
data1 <- data1[-c(na.act),]
}
dmf <- lm(Durbin, data1, na.action=na.fail,
method="model.frame")
formula_durbin_factors <- have_factor_preds_mf(dmf)
if (formula_durbin_factors)
warn_factor_preds(formula_durbin_factors)
# dmf <- lm(Durbin, data, na.action=na.action,
# method="model.frame")
fx <- try(model.matrix(Durbin, dmf), silent=TRUE)
if (inherits(fx, "try-error"))
stop("Durbin variable mis-match")
WX <- create_WX(fx, listw, zero.policy=zero.policy,
prefix=prefix)
inds <- match(substring(colnames(WX), 5,
nchar(colnames(WX))), colnames(x))
if (anyNA(inds)) stop("WX variables not in X: ",
paste(substring(colnames(WX), 5,
nchar(colnames(WX)))[is.na(inds)], collapse=" "))
icept <- grep("(Intercept)", colnames(x))
iicept <- length(icept) > 0L
if (iicept) {
xn <- colnames(x)[-1]
} else {
xn <- colnames(x)
}
wxn <- substring(colnames(WX), nchar(prefix)+2,
nchar(colnames(WX)))
zero_fill <- NULL
if (length((which(!(xn %in% wxn)))) > 0L)
zero_fill <- length(xn) + (which(!(xn %in% wxn)))
}
dvars <- c(NCOL(x), NCOL(WX))
if (is.formula(Durbin)) {
attr(dvars, "f") <- Durbin
attr(dvars, "inds") <- inds
attr(dvars, "zero_fill") <- zero_fill
attr(dvars, "formula_durbin_factors") <- formula_durbin_factors
}
x <- cbind(x, WX)
m <- NCOL(x)
rm(WX)
}
# added aliased after trying boston with TOWN dummy
lm.base <- lm(y ~ x - 1, weights=weights)
aliased <- is.na(coefficients(lm.base))
cn <- names(aliased)
names(aliased) <- substr(cn, 2, nchar(cn))
if (any(aliased)) {
if (is.formula(Durbin)) {
stop("Aliased variables found: ",
paste(names(aliased)[aliased], collapse=" "))
} else {
warning("Aliased variables found: ",
paste(names(aliased)[aliased], collapse=" "))
nacoef <- which(aliased)
x <- x[,-nacoef]
m <- NCOL(x)
xxcolnames <- colnames(x)
}
}
#
sw <- sqrt(weights)
#
LL_null_lm <- NULL
if ("(Intercept)" %in% colnames(x)) LL_null_lm <- logLik(lm(y ~ 1,
weights=weights))
m <- NCOL(x)
xcolnames <- colnames(x)
K <- ifelse(xcolnames[1] == "(Intercept)", 2, 1)
wy <- lag.listw(listw, y, zero.policy=zero.policy)
if (any(is.na(wy)))
stop("NAs in lagged dependent variable")
# added no intercept Guillaume Blanchet 091103
if (m > 1 || (m == 1 && K == 1)) {
WX <- matrix(nrow=n,ncol=(m-(K-1)))
for (k in K:m) {
wx <- lag.listw(listw, x[,k], zero.policy=zero.policy)
if (any(is.na(wx)))
stop("NAs in lagged independent variable")
WX[,(k-(K-1))] <- wx
}
}
if (K == 2) {
# modified to meet other styles, email from Rein Halbersma
wx1 <- as.double(rep(1, n))
wx <- lag.listw(listw, wx1, zero.policy=zero.policy)
if (m > 1) WX <- cbind(wx, WX)
else WX <- matrix(wx, nrow=n, ncol=1)
}
colnames(WX) <- xcolnames
rm(wx)
can.sim <- FALSE
if (listw$style %in% c("W", "S"))
can.sim <- can.be.simmed(listw)
sum_lw <- sum(log(weights))
# env <- new.env(parent=globalenv())
env <- new.env()
assign("y", y, envir=env)
assign("x", x, envir=env)
assign("wy", wy, envir=env)
assign("WX", WX, envir=env)
assign("n", n, envir=env)
assign("p", m, envir=env)
assign("verbose", !quiet, envir=env)
assign("family", "SAR", envir=env)
assign("compiled_sse", con$compiled_sse, envir=env)
assign("first_time", TRUE, envir=env)
assign("LAPACK", con$LAPACK, envir=env)
assign("can.sim", can.sim, envir=env)
assign("listw", listw, envir=env)
assign("similar", FALSE, envir=env)
assign("f_calls", 0L, envir=env)
assign("hf_calls", 0L, envir=env)
assign("sum_lw", sum_lw, envir=env)
assign("sw", sw, envir=env)
timings[["set_up"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
if (!quiet) cat(paste("\nJacobian calculated using "))
interval <- jacobianSetup(method, env, con, pre_eig=con$pre_eig,
trs=trs, interval=interval)
assign("interval", interval, envir=env)
nm <- paste(method, "set_up", sep="_")
timings[[nm]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
if (con$compiled_sse) {
ptr <- .Call("opt_error_init", PACKAGE="spatialreg")
assign("ptr", ptr, envir=env)
}
opt <- optimize(sar.error.f, interval=interval,
maximum=TRUE, tol=con$tol.opt, env=env)
lambda <- opt$maximum
if (isTRUE(all.equal(lambda, interval[1])) ||
isTRUE(all.equal(lambda, interval[2])))
warning("lambda on interval bound - results should not be used")
names(lambda) <- "lambda"
LL <- opt$objective
if (con$compiled_sse) {
.Call("opt_error_free", get("ptr", envir=env), PACKAGE="spatialreg")
}
nm <- paste(method, "opt", sep="_")
timings[[nm]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
lm.target <- lm(I(y - lambda*wy) ~ I(x - lambda*WX) - 1,
weights=weights)
r <- as.vector(residuals(lm.target))
fit <- as.vector(y - r)
p <- lm.target$rank
SSE <- deviance(lm.target)
s2 <- SSE/n
rest.se <- (summary(lm.target)$coefficients[,2])*sqrt((n-p)/n)
coef.lambda <- coefficients(lm.target)
names(coef.lambda) <- xcolnames
sum_lm_target <- summary.lm(lm.target, correlation = FALSE)
emixedImps <- NULL
if (any(sum_lm_target$aliased)) warning("aliased variables found")
if (con$return_impacts && etype == "emixed") {
if (isTRUE(Durbin)) {
m.1 <- m > 1
if (m.1 && K == 2) {
m2 <- (m-1)/2
} else {
m2 <- m/2
}
cm <- matrix(0, ncol=m, nrow=m2)
if (K == 2) {
if (m.1) {
rownames(cm) <- xxcolnames[2:(m2+1)]
} else {
rownames(cm) <- xxcolnames[1:m2]
}
LI <- ifelse(!(listw$style == "W"), 1, 0) #TR: lagged intercept
for (i in 1:m2) cm[i, c(i+1, i+(m2+1 + LI)) ] <- 1 #TR: Add to index
# drop bug fix 2016-09-21 Philipp Hunziker
dirImps <- sum_lm_target$coefficients[2:(m2+1), 1:2, drop=FALSE]
rownames(dirImps) <- rownames(cm)
indirImps <- sum_lm_target$coefficients[((m2 + 2):m + LI), 1:2, drop=FALSE] #TR: Add to index
rownames(indirImps) <- rownames(cm)
} else {
rownames(cm) <- xxcolnames[1:m2]
for (i in 1:m2) cm[i, c(i, i+m2)] <- 1
dirImps <- sum_lm_target$coefficients[1:m2, 1:2, drop=FALSE]
rownames(dirImps) <- rownames(cm)
indirImps <- sum_lm_target$coefficients[(m2+1):m, 1:2, drop=FALSE]
rownames(indirImps) <- rownames(cm)
}
suppressWarnings(lc <- summary(multcomp::glht(lm.target, linfct=cm)))
totImps <- cbind("Estimate"=lc$test$coefficients, "Std. Error"=lc$test$sigma)
} else if (is.formula(Durbin)) {
#FIXME
LI <- ifelse(listw$style != "W"
&& attr(terms(Durbin), "intercept") == 1, 1, 0)
m <- sum(dvars)
KIL <- max((LI - (K - 1)), 0)
m2 <- dvars[2] - KIL
cm <- matrix(0, ncol=m, nrow=m2)
for (i in 1:m2) {
cm[i, c(inds[i], i+dvars[1] + KIL)] <- 1
}
if (LI == 1 && K == 1) {
rownames(cm) <- wxn[!grepl("Intercept", wxn)]
} else {
rownames(cm) <- wxn
}
dirImps <- sum_lm_target$coefficients[K:dvars[1], 1:2,
drop=FALSE]
rownames(dirImps) <- xn
indirImps <- sum_lm_target$coefficients[(dvars[1] + 1 + KIL):m, 1:2,
drop=FALSE]
if (!is.null(zero_fill)) {
if (length(zero_fill) > 0L) {
lres <- vector(mode="list", length=2L)
for (j in 1:2) {
jindirImps <- rep(as.numeric(NA), (dvars[1] + (1-K)))
for (i in seq(along=inds)) {
jindirImps[(inds[i]+(1-K))] <- indirImps[i, j]
}
lres[[j]] <- jindirImps
}
indirImps <- do.call("cbind", lres)
}
}
rownames(indirImps) <- xn
suppressWarnings(lc <- summary(multcomp::glht(lm.target, linfct=cm)))
totImps <- cbind("Estimate"=lc$test$coefficients, "Std. Error"=lc$test$sigma)
if (!is.null(zero_fill)) {
if (length(zero_fill) > 0L) {
lres <- vector(mode="list", length=2L)
for (j in 1:2) {
jtotImps <- dirImps[, j]
for (i in seq(along=inds)) {
jtotImps[(inds[i]+(1-K))] <- totImps[i, j]
}
lres[[j]] <- jtotImps
}
totImps <- do.call("cbind", lres)
}
}
rownames(totImps) <- xn
} else stop("undefined emixed state")
emixedImps <- list(dirImps=dirImps, indirImps=indirImps,
totImps=totImps)
}
Vs <- sum_lm_target$cov.unscaled
tarX <- model.matrix(lm.target)
tary <- model.response(model.frame(lm.target))
lm.model <- lm(y ~ x - 1, weights=weights)
logLik_lm.model <- logLik(lm.model)
AIC_lm.model <- AIC(lm.model)
ase <- FALSE
lambda.se <- NULL
LMtest <- NULL
asyvar1 <- FALSE
force_assign_eigen <- FALSE
Hcov <- NULL
pWinternal <- NULL
timings[["coefs"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
assign("first_time", TRUE, envir=env)
if (method == "eigen" || do_asy) {
tr <- function(A) sum(diag(A))
W <- listw2mat(listw)
A <- solve(diag(n) - lambda*W)
if (con$returnHcov) {
pp <- lm.model$rank
p1 <- 1L:pp
R <- chol2inv(lm.model$qr$qr[p1, p1, drop = FALSE])
B <- tcrossprod(R, (sw*x)) %*% A
# A <- solve(diag(n) - lambda*t(W))
C <- A %*% (sw*x) %*% R
Hcov <- B %*% C
attr(Hcov, "method") <- method
timings[["eigen_hcov"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
}
WA <- W %*% A
asyvar <- matrix(0, nrow=2+p, ncol=2+p)
asyvar[1,1] <- n / (2*(s2^2))
# asyvar[1,1] <- n / (2*(s2))
asyvar[2,1] <- asyvar[1,2] <- tr(WA) / s2
# asyvar[2,1] <- asyvar[1,2] <- tr(WA)
asyvar[2,2] <- tr(WA %*% WA) + tr(crossprod(WA))
# bug found 100224 German Muchnik Izon
# asyvar[3:(p+2),3:(p+2)] <- s2*(t(x - lambda*WX) %*%
xl <- sw * (x - lambda*WX)
# asyvar[3:(p+2),3:(p+2)] <- crossprod(xl)
asyvar[3:(p+2),3:(p+2)] <- crossprod(xl)/s2
asyvar1 <- try(solve(asyvar, tol=tol.solve), silent=TRUE)
if (inherits(asyvar1, "try-error")) {
timings[["eigen_se"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
con$fdHess <- TRUE
force_assign_eigen <- TRUE
warning(paste("inversion of asymptotic covariance",
"matrix failed for tol.solve =", tol.solve,
"\n", strsplit(attr(asyvar1, "condition")$message,
":")[[1]][2], "- using numerical Hessian."))
} else {
rownames(asyvar1) <- colnames(asyvar1) <-
c("sigma", "lambda", xcolnames)
lambda.se <- sqrt(asyvar1[2,2])
# lambda.se <- sqrt(s2*asyvar1[2,2])
timings[["eigen_se"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
ase <- TRUE
}
} else {
if (con$returnHcov) {
pp <- lm.model$rank
p1 <- 1L:pp
R <- chol2inv(lm.model$qr$qr[p1, p1, drop = FALSE])
B <- tcrossprod(R, (sw*x))
W <- as(get("listw", envir=env), "CsparseMatrix")
B0 <- powerWeights(W=W, rho=lambda, order=con$pWOrder,
X=B, tol=tol.solve)
if (!is.null(attr(B0, "internal")) &&
!attr(B0, "internal")$conv)
pWinternal <- c(pWinternal, attr(B0, "internal"))
B1 <- as(B0, "matrix")
C <- (sw*x) %*% R
C0 <- powerWeights(W=t(W), rho=lambda, order=con$pWOrder,
X=C, tol=tol.solve)
if (!is.null(attr(C0, "internal")) &&
!attr(C0, "internal")$conv)
pWinternal <- c(pWinternal, attr(C0, "internal"))
C1 <- as(C0, "matrix")
Hcov <- B1 %*% C1
attr(Hcov, "method") <- method
timings[["sparse_hcov"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
}
}
if (con$fdHess) {
coefs <- c(lambda, coef.lambda)
if (con$compiled_sse) {
ptr <- .Call("hess_error_init", PACKAGE="spatialreg")
assign("ptr", ptr, envir=env)
}
fdHess <- getVmate(coefs, env, s2, trs, tol.solve=tol.solve,
optim=con$optimHess, optimM=con$optimHessMethod)
if (con$compiled_sse) {
.Call("hess_error_free", get("ptr", envir=env),
PACKAGE="spatialreg")
}
if (is.null(trs)) {
rownames(fdHess) <- colnames(fdHess) <-
c("lambda", colnames(x))
if (method != "eigen" || force_assign_eigen) {
lambda.se <- sqrt(fdHess[1, 1])
}
} else {
rownames(fdHess) <- colnames(fdHess) <-
c("sigma2", "lambda", colnames(x))
if (method != "eigen" || force_assign_eigen) {
lambda.se <- sqrt(fdHess[2, 2])
}
}
nm <- paste(method, "fdHess", sep="_")
timings[[nm]] <- proc.time() - .ptime_start
} else fdHess <- FALSE
call <- match.call()
if (method=="SE_classic") {
iC <- get("intern_classic", envir=env)
} else iC <- NULL
names(r) <- names(y)
names(fit) <- names(y)
ret <- structure(list(type="error", etype=etype, lambda=lambda,
coefficients=coef.lambda, rest.se=rest.se,
LL=LL, s2=s2, SSE=SSE, parameters=(m+2), #lm.model=lm.model,
logLik_lm.model=logLik_lm.model, AIC_lm.model=AIC_lm.model,
coef_lm.model=coef(lm.model),
tarX=tarX, tary=tary, y=y, X=x,
method=method, call=call, residuals=r, #lm.target=lm.target,
opt=opt, fitted.values=fit, ase=ase, #formula=formula,
se.fit=NULL, resvar=asyvar1, similar=get("similar", envir=env),
lambda.se=lambda.se, LMtest=LMtest, zero.policy=zero.policy,
aliased=aliased, LLNullLlm=LL_null_lm, Hcov=Hcov, Vs=Vs,
interval=interval, fdHess=fdHess,
optimHess=con$optimHess, insert=!is.null(trs), trs=trs,
timings=do.call("rbind", timings)[, c(1, 3)],
f_calls=get("f_calls", envir=env),
hf_calls=get("hf_calls", envir=env), intern_classic=iC,
pWinternal=pWinternal, weights=weights, emixedImps=emixedImps,
dvars=dvars), class=c("Sarlm"))
attr(ret, "have_factor_preds") <- have_factor_preds
rm(env)
GC <- gc()
if (zero.policy) {
zero.regs <- attr(listw$neighbours,
"region.id")[which(card(listw$neighbours) == 0)]
if (length(zero.regs) > 0L)
attr(ret, "zero.regs") <- zero.regs
}
if (!is.null(na.act))
ret$na.action <- na.act
if (is.formula(Durbin)) attr(ret, "Durbin") <- deparse(Durbin)
ret
}
sar_error_sse <- function(lambda, env) {
if (get("compiled_sse", envir=env)) {
ft <- get("first_time", envir=env)
SSE <- .Call("R_ml_sse_env", env, lambda, PACKAGE="spatialreg")
if (ft) assign("first_time", FALSE, envir=env)
} else {
yl <- get("y", envir=env) - lambda * get("wy", envir=env)
yl <- get("sw", envir=env) * yl
xl <- get("x", envir=env) - lambda * get("WX", envir=env)
xl <- get("sw", envir=env) * xl
xl.q <- qr.Q(qr(xl, LAPACK=get("LAPACK", envir=env)))
xl.q.yl <- crossprod(xl.q, yl)
# xl.q.yl <- qr.qty(qr(xl, LAPACK=get("LAPACK", envir=env)), yl)
SSE <- crossprod(yl) - crossprod(xl.q.yl)
}
SSE
}
sar.error.f <- function(lambda, env) {
SSE <- sar_error_sse(lambda, env)
n <- get("n", envir=env)
s2 <- SSE/n
ldet <- do_ldet(lambda, env)
ret <- (ldet + (1/2)*get("sum_lw", envir=env) - ((n/2)*log(2*pi)) -
(n/2)*log(s2) - (1/(2*(s2)))*SSE)
if (get("verbose", envir=env)) cat("lambda:", lambda, " function:", ret, " Jacobian:", ldet, " SSE:", SSE, "\n")
assign("f_calls", get("f_calls", envir=env)+1L, envir=env)
ret
}
lagsarlm <- function(formula, data = list(), listw,
na.action, Durbin, type, method="eigen", quiet=NULL,
zero.policy=NULL, interval=NULL, tol.solve=.Machine$double.eps,
trs=NULL, control=list()) {
timings <- list()
.ptime_start <- proc.time()
con <- list(tol.opt=.Machine$double.eps^0.5,
fdHess=NULL, optimHess=FALSE, optimHessMethod="optimHess",
compiled_sse=FALSE, Imult=2,
cheb_q=5, MC_p=16L, MC_m=30L, super=NULL, spamPivot="MMD",
in_coef=0.1, type="MC", correct=TRUE, trunc=TRUE,
SE_method="LU", nrho=200, interpn=2000, small_asy=TRUE,
small=1500, SElndet=NULL, LU_order=FALSE, pre_eig=NULL,
OrdVsign=1)
nmsC <- names(con)
con[(namc <- names(control))] <- control
if (length(noNms <- namc[!namc %in% nmsC]))
warning("unknown names in control: ", paste(noNms, collapse = ", "))
if (is.null(quiet)) quiet <- !get("verbose", envir = .spatialregOptions)
stopifnot(is.logical(quiet))
if (is.null(zero.policy))
zero.policy <- get.ZeroPolicyOption()
stopifnot(is.logical(zero.policy))
if (!inherits(formula, "formula")) formula <- as.formula(formula)
mt <- terms(formula, data = data)
mf <- lm(formula, data, na.action=na.action,
method="model.frame")
have_factor_preds <- have_factor_preds_mf(mf)
na.act <- attr(mf, "na.action")
if (!inherits(listw, "listw")) stop("No neighbourhood list")
can.sim <- FALSE
if (listw$style %in% c("W", "S"))
can.sim <- can.be.simmed(listw)
if (!is.null(na.act)) {
subset <- !(1:length(listw$neighbours) %in% na.act)
listw <- subset(listw, subset, zero.policy=zero.policy)
if (!is.null(con$pre_eig)) {
warning("NAs found, precomputed eigenvalues ignored")
con$pre_eig <- NULL
}
}
if (missing(type)) type <- "lag"
if (type == "Durbin") type <- "mixed"
if (missing(Durbin)) Durbin <- ifelse(type == "lag", FALSE, TRUE)
if (listw$style != "W" && is.formula(Durbin)) {
Durbin <- TRUE
warning("formula Durbin requires row-standardised weights; set TRUE")
}
if (is.logical(Durbin) && isTRUE(Durbin)) {
type <- "mixed"
if (have_factor_preds) warn_factor_preds(have_factor_preds)
}
if (is.formula(Durbin)) type <- "mixed"
if (is.logical(Durbin) && !isTRUE(Durbin)) type <- "lag"
switch(type, lag = if (!quiet) cat("\nSpatial lag model\n"),
mixed = if (!quiet) cat("\nSpatial mixed autoregressive model\n"),
stop("\nUnknown model type\n"))
y <- model.extract(mf, "response")
x <- model.matrix(mt, mf)
if (NROW(x) != length(listw$neighbours))
stop("Input data and weights have different dimensions")
n <- NROW(x)
m <- NCOL(x)
stopifnot(is.logical(con$small_asy))
if (method != "eigen") {
if (con$small >= n && con$small_asy) do_asy <- TRUE
else do_asy <- FALSE
} else do_asy <- TRUE
if (is.null(con$fdHess)) {
con$fdHess <- method != "eigen" && !do_asy
fdHess <- NULL
}
stopifnot(is.logical(con$fdHess))
stopifnot(is.numeric(con$OrdVsign))
stopifnot(length(con$OrdVsign) == 1)
stopifnot(abs(con$OrdVsign) == 1)
xcolnames <- colnames(x)
K <- ifelse(xcolnames[1] == "(Intercept)", 2, 1)
wy <- lag.listw(listw, y, zero.policy=zero.policy)
if (any(is.na(wy))) stop("NAs in lagged dependent variable")
dvars <- c(NCOL(x), 0L)
#FIXME
if (is.formula(Durbin) || isTRUE(Durbin)) {
prefix <- "lag"
if (isTRUE(Durbin)) {
WX <- create_WX(x, listw, zero.policy=zero.policy,
prefix=prefix)
} else {
data1 <- data
if (!is.null(na.act) && (inherits(na.act, "omit") ||
inherits(na.act, "exclude"))) {
data1 <- data1[-c(na.act),]
}
dmf <- lm(Durbin, data1, na.action=na.fail,
method="model.frame")
formula_durbin_factors <- have_factor_preds_mf(dmf)
if (formula_durbin_factors)
warn_factor_preds(formula_durbin_factors)
fx <- try(model.matrix(Durbin, dmf), silent=TRUE)
if (inherits(fx, "try-error"))
stop("Durbin variable mis-match")
WX <- create_WX(fx, listw, zero.policy=zero.policy,
prefix=prefix)
inds <- match(substring(colnames(WX), 5,
nchar(colnames(WX))), colnames(x))
if (anyNA(inds)) stop("WX variables not in X: ",
paste(substring(colnames(WX), 5,
nchar(colnames(WX)))[is.na(inds)], collapse=" "))
icept <- grep("(Intercept)", colnames(x))
iicept <- length(icept) > 0L
if (iicept) {
xn <- colnames(x)[-1]
} else {
xn <- colnames(x)
}
wxn <- substring(colnames(WX), nchar(prefix)+2,
nchar(colnames(WX)))
zero_fill <- NULL
if (length((which(!(xn %in% wxn)))) > 0L)
zero_fill <- length(xn) + (which(!(xn %in% wxn)))
}
dvars <- c(NCOL(x), NCOL(WX))
if (is.formula(Durbin)) {
attr(dvars, "f") <- Durbin
attr(dvars, "inds") <- inds
attr(dvars, "zero_fill") <- zero_fill
attr(dvars, "formula_durbin_factors") <- formula_durbin_factors
}
x <- cbind(x, WX)
m <- NCOL(x)
rm(WX)
}
# added aliased after trying boston with TOWN dummy
lm.base <- lm(y ~ x - 1)
aliased <- is.na(coefficients(lm.base))
cn <- names(aliased)
names(aliased) <- substr(cn, 2, nchar(cn))
#FIXME
if (any(aliased)) {
if (is.formula(Durbin)) {
stop("Aliased variables found: ",
paste(names(aliased)[aliased], collapse=" "))
} else {
warning("Aliased variables found: ",
paste(names(aliased)[aliased], collapse=" "))
nacoef <- which(aliased)
x <- x[,-nacoef]
}
}
LL_null_lm <- logLik(lm(y ~ 1))
m <- NCOL(x)
similar <- FALSE
lm.null <- lm(y ~ x - 1)
logLik_lm.model <- logLik(lm.null)
AIC_lm.model <- AIC(lm.null)
lm.w <- lm.fit(x, wy)
e.null <- lm.null$residuals
e.w <- lm.w$residuals
e.a <- t(e.null) %*% e.null
e.b <- t(e.w) %*% e.null
e.c <- t(e.w) %*% e.w
# env <- new.env(parent=globalenv())
env <- new.env()
assign("y", y, envir=env)
assign("wy", wy, envir=env)
assign("x", x, envir=env)
assign("n", n, envir=env)
assign("m", m, envir=env)
assign("K", K, envir=env)
assign("e.a", e.a, envir=env)
assign("e.b", e.b, envir=env)
assign("e.c", e.c, envir=env)
assign("family", "SAR", envir=env)
assign("verbose", !quiet, envir=env)
assign("compiled_sse", con$compiled_sse, envir=env)
assign("can.sim", can.sim, envir=env)
assign("listw", listw, envir=env)
assign("similar", FALSE, envir=env)
assign("f_calls", 0L, envir=env)
assign("hf_calls", 0L, envir=env)
timings[["set_up"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
if (!quiet) cat("Jacobian calculated using ")
interval <- jacobianSetup(method, env, con, pre_eig=con$pre_eig,
trs=trs, interval=interval)
assign("interval", interval, envir=env)
nm <- paste(method, "set_up", sep="_")
timings[[nm]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
opt <- optimize(sar.lag.mixed.f, interval=interval,
maximum=TRUE, tol=con$tol.opt, env=env)
rho <- opt$maximum
if (isTRUE(all.equal(rho, interval[1])) ||
isTRUE(all.equal(rho, interval[2])))
warning("rho on interval bound - results should not be used")
names(rho) <- "rho"
LL <- opt$objective
optres <- opt
nm <- paste(method, "opt", sep="_")
timings[[nm]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
lm.lag <- lm((y - rho*wy) ~ x - 1)
r <- residuals(lm.lag)
fit <- y - r
names(r) <- names(fit)
coef.rho <- coefficients(lm.lag)
tarX <- model.matrix(lm.lag)
tary <- model.response(model.frame(lm.lag))
names(coef.rho) <- colnames(x)
SSE <- deviance(lm.lag)
s2 <- SSE/n
timings[["coefs"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
assign("first_time", TRUE, envir=env)
LMtest <- NULL
varb <- FALSE
ase <- FALSE
force_assign_eigen <- FALSE
if (method == "eigen" || do_asy) {
rest.se <- NULL
rho.se <- NULL
tr <- function(A) sum(diag(A))
# beware of complex eigenvalues!
if (do_asy && method != "eigen") eigen_setup(env)
eig <- get("eig", envir=env)
O <- (eig/(1-rho*eig))^2
omega <- sum(O)
if (is.complex(omega)) omega <- Re(omega)
W <- listw2mat(listw)
A <- solve(diag(n) - rho*W)
AW <- A %*% W
zero <- rbind(rep(0,length(coef.rho)))
xtawxb <- s2*(t(x) %*% AW %*% x %*% coef.rho)
# V <- s2*(s2*tr(t(AW) %*% AW) +
# t(AW %*% x %*% coef.rho) %*%
# (AW %*% x %*% coef.rho)) + omega*s2^2
V <- s2*(s2*tr(crossprod(AW)) +
crossprod(AW %*% x %*% coef.rho)) +
sign(con$OrdVsign)*omega*s2^2
inf1 <- rbind(n/2, s2*tr(AW), t(zero))
inf2 <- rbind(s2*tr(AW), V, xtawxb)
# xtx <- s2*t(x) %*% x
xtx <- s2*crossprod(x)
inf3 <- rbind(zero, t(xtawxb), xtx)
inf <- cbind(inf1, inf2, inf3)
varb <- try(solve(inf, tol=tol.solve), silent=TRUE)
if (inherits(varb, "try-error")) {
timings[["eigen_se"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
con$fdHess <- TRUE
force_assign_eigen <- TRUE
warning(paste("inversion of asymptotic covariance",
"matrix failed for tol.solve =", tol.solve,
"\n", strsplit(attr(varb, "condition")$message,
":")[[1]][2], "- using numerical Hessian."))
} else {
varb <- (s2^2) * varb
rownames(varb) <- colnames(varb) <-
c("sigma", "rho", colnames(x))
rest.se <- sqrt(diag(varb))[-c(1:2)]
rho.se <- sqrt(varb[2,2])
TW <- (W %*% W) + crossprod(W)
T22 <- sum(diag(TW))
T21A <- sum(diag(TW %*% A))
LMtest <- ((t(r) %*% W %*% r)/s2)^2
LMtest <- LMtest/(T22 - ((T21A^2)*(rho.se^2)))
ase <- TRUE
timings[["eigen_se"]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
}
}
if (con$fdHess) {
coefs <- c(rho, coef.rho)
if (con$compiled_sse) {
ptr <- .Call("hess_lag_init", PACKAGE="spatialreg")
assign("ptr", ptr, envir=env)
}
fdHess <- getVmatl(coefs, env,
s2, trs, tol.solve=tol.solve, optim=con$optimHess,
optimM=con$optimHessMethod)
if (con$compiled_sse) {
.Call("hess_lag_free", get("ptr", envir=env),
PACKAGE="spatialreg")
}
if (is.null(trs)) {
rownames(fdHess) <- colnames(fdHess) <-
c("rho", colnames(x))
} else {
rownames(fdHess) <- colnames(fdHess) <-
c("sigma2", "rho", colnames(x))
}
if (is.null(trs)) {
if (method != "eigen" || force_assign_eigen) {
rest.se <- sqrt(diag(fdHess)[-1])
rho.se <- sqrt(fdHess[1,1])
}
} else {
if (method != "eigen" || force_assign_eigen) {
rest.se <- sqrt(diag(fdHess)[-c(1,2)])
rho.se <- sqrt(fdHess[2,2])
}
}
nm <- paste(method, "fdHess", sep="_")
timings[[nm]] <- proc.time() - .ptime_start
.ptime_start <- proc.time()
} else fdHess <- FALSE
call <- match.call()
if (method=="SE_classic") {
iC <- get("intern_classic", envir=env)
} else iC <- NULL
#FIXME
ret <- structure(list(type=type, dvars=dvars, rho=rho,
coefficients=coef.rho, rest.se=rest.se,
LL=LL, s2=s2, SSE=SSE, parameters=(m+2), #lm.model=lm.null,
logLik_lm.model=logLik_lm.model, AIC_lm.model=AIC_lm.model,
method=method, call=call, residuals=r, opt=optres,
tarX=tarX, tary=tary, y=y, X=x,
#lm.target=lm.lag,
fitted.values=fit,
se.fit=NULL, #formula=formula,
similar=similar,
ase=ase, rho.se=rho.se, LMtest=LMtest,
resvar=varb, zero.policy=zero.policy, aliased=aliased,
listw_style=listw$style, interval=interval, fdHess=fdHess,
optimHess=con$optimHess, insert=!is.null(trs), trs=trs,
LLNullLlm=LL_null_lm,
timings=do.call("rbind", timings)[, c(1, 3)],
f_calls=get("f_calls", envir=env),
hf_calls=get("hf_calls", envir=env), intern_classic=iC),
class=c("Sarlm"))
attr(ret, "have_factor_preds") <- have_factor_preds
rm(env)
GC <- gc()
if (zero.policy) {
zero.regs <- attr(listw$neighbours,
"region.id")[which(card(listw$neighbours) == 0)]
if (length(zero.regs) > 0L)
attr(ret, "zero.regs") <- zero.regs
}
if (!is.null(na.act))
ret$na.action <- na.act
if (is.formula(Durbin)) attr(ret, "Durbin") <- deparse(Durbin)
ret
}
sar.lag.mixed.f <- function(rho, env) {
e.a <- get("e.a", envir=env)
e.b <- get("e.b", envir=env)
e.c <- get("e.c", envir=env)
SSE <- e.a - 2*rho*e.b + rho*rho*e.c
n <- get("n", envir=env)
s2 <- SSE/n
ldet <- do_ldet(rho, env)
ret <- (ldet - ((n/2)*log(2*pi)) - (n/2)*log(s2)
- (1/(2*s2))*SSE)
if (get("verbose", envir=env)) cat("rho:\t", rho, "\tfunction value:\t", ret, "\n")
assign("f_calls", get("f_calls", envir=env)+1L, envir=env)
ret
}
# Copyright 2010-12 by Roger Bivand
sacsarlm <- function(formula, data = list(), listw, listw2=NULL, na.action,
Durbin, type, method="eigen", quiet=NULL, zero.policy=NULL,
tol.solve=.Machine$double.eps, llprof=NULL, interval1=NULL, interval2=NULL,
trs1=NULL, trs2=NULL, control=list()) {
timings <- list()
.ptime_start <- proc.time()
con <- list(fdHess=NULL, #LAPACK=FALSE,
Imult=2L, cheb_q=5L, MC_p=16L, MC_m=30L, spamPivot="MMD",
in_coef=0.1, super=NULL, opt_method="nlminb", opt_control=list(),
pars=NULL, npars=4L, pre_eig1=NULL, pre_eig2=NULL)
nmsC <- names(con)
con[(namc <- names(control))] <- control
if (length(noNms <- namc[!namc %in% nmsC]))
warning("unknown names in control: ", paste(noNms, collapse = ", "))
if (is.null(quiet)) quiet <- !get("verbose", envir = .spatialregOptions)
#FIXME
if (missing(type)) type <- "sac"
if (type == "Durbin") type <- "sacmixed"
if (missing(Durbin)) Durbin <- ifelse(type == "sac", FALSE, TRUE)
if (listw$style != "W" && is.formula(Durbin)) {
Durbin <- TRUE
warning("formula Durbin requires row-standardised weights; set TRUE")
}
if (is.logical(Durbin) && isTRUE(Durbin)) type <- "sacmixed"
if (is.formula(Durbin)) type <- "sacmixed"
if (is.logical(Durbin) && !isTRUE(Durbin)) type <- "sac"
switch(type, sac = if (!quiet) cat("\nSpatial ARAR model\n"),
sacmixed = if (!quiet) cat("\nSpatial ARAR mixed model (Manski)\n"),
stop("\nUnknown model type\n"))
stopifnot(is.logical(quiet))
if (is.null(zero.policy))
zero.policy <- get("zeroPolicy", envir = .spatialregOptions)
stopifnot(is.logical(zero.policy))
if (!inherits(formula, "formula")) formula <- as.formula(formula)
mt <- terms(formula, data = data)
mf <- lm(formula, data, na.action=na.action, method="model.frame")
have_factor_preds <- have_factor_preds_mf(mf)
na.act <- attr(mf, "na.action")
if (!inherits(listw, "listw")) stop("No neighbourhood list")
if (is.null(listw2)) listw2 <- listw
if (!is.null(con$pre_eig1) && is.null(con$pre_eig2))
con$pre_eig2 <- con$pre_eig1
else if (!inherits(listw2, "listw")) stop("No 2nd neighbourhood list")
if (is.null(con$fdHess)) con$fdHess <- method != "eigen"
if (!is.null(con$pars)) {
stopifnot(is.numeric(con$pars))
}
# stopifnot(is.integer(con$npars))
# stopifnot(is.logical(con$fdHess))
# stopifnot(is.logical(con$LAPACK))
# stopifnot(is.logical(con$super))
can.sim <- FALSE
if (listw$style %in% c("W", "S"))
can.sim <- can.be.simmed(listw)
if (!is.null(na.act)) {
subset <- !(1:length(listw$neighbours) %in% na.act)
listw <- subset(listw, subset, zero.policy=zero.policy)
if (!is.null(con$pre_eig1)) {
warning("NAs found, precomputed eigenvalues ignored")
con$pre_eig1 <- NULL
}
}
can.sim2 <- FALSE
if (listw2$style %in% c("W", "S"))
can.sim2 <- can.be.simmed(listw2)
if (!is.null(na.act)) {
subset <- !(1:length(listw2$neighbours) %in% na.act)
listw2 <- subset(listw2, subset, zero.policy=zero.policy)
if (!is.null(con$pre_eig2)) {
warning("NAs found, precomputed eigenvalues ignored")
con$pre_eig2 <- NULL
}
}