Nothing
"pfa" <-
function (x, factors, data = NULL, covmat = NULL, n.obs = NA,
subset, na.action, start = NULL, scores = c("none", "regression",
"Bartlett"), rotation = "varimax", maxiter=5,control = NULL, ...)
{
#
# Function for Principal Factor Analysis (PFA), P. Filzmoser, 30 March 2004
#
# Input data x should be (robustly) scaled!!!
# covmat (if provided) should be a (robust) covariance OR correlation matrix!!!
#
sortLoadings <- function(Lambda) {
cn <- colnames(Lambda)
Phi <- attr(Lambda, "covariance")
ssq <- apply(Lambda, 2, function(x) -sum(x^2))
Lambda <- Lambda[, order(ssq), drop = FALSE]
colnames(Lambda) <- cn
neg <- colSums(Lambda) < 0
Lambda[, neg] <- -Lambda[, neg]
if (!is.null(Phi)) {
unit <- ifelse(neg, -1, 1)
attr(Lambda, "covariance") <- unit %*% Phi[order(ssq),
order(ssq)] %*% unit
}
Lambda
}
cl <- match.call()
na.act <- NULL
if (is.list(covmat)) {
if (any(is.na(match(c("cov", "n.obs"), names(covmat)))))
stop("covmat is not a valid covariance list")
cv <- covmat$cov
n.obs <- covmat$n.obs
have.x <- FALSE
}
else if (is.matrix(covmat)) {
cv <- covmat
have.x <- FALSE
}
else if (is.null(covmat)) {
if (missing(x))
stop("neither x nor covmat supplied")
have.x <- TRUE
if (inherits(x, "formula")) {
mt <- terms(x, data = data)
if (attr(mt, "response") > 0)
stop("response not allowed in formula")
attr(mt, "intercept") <- 0
mf <- match.call(expand.dots = FALSE)
names(mf)[names(mf) == "x"] <- "formula"
mf$factors <- mf$covmat <- mf$scores <- mf$start <- mf$rotation <- mf$control <- mf$... <- NULL
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
na.act <- attr(mf, "na.action")
z <- model.matrix(mt, mf)
}
else {
z <- as.matrix(x)
if (!missing(subset))
z <- z[subset, , drop = FALSE]
}
covmat <- cov.wt(z)
cv <- covmat$cov
n.obs <- covmat$n.obs
}
else stop("covmat is of unknown type")
scores <- match.arg(scores)
if (scores != "none" && !have.x)
z <- x
# stop("requested scores without an x matrix")
sds <- sqrt(diag(cv))
cv <- cv/(sds %o% sds)
p <- ncol(cv)
dof <- 0.5 * ((p - factors)^2 - p - factors)
# if (dof < 0)
# stop(paste(factors, "factors is too many for", p, "variables"))
cn <- list(nstart = 1, trace = FALSE, lower = 0.005)
cn[names(control)] <- control
more <- list(...)[c("nstart", "trace", "lower", "opt", "rotate")]
if (length(more))
cn[names(more)] <- more
if (is.null(start)) {
start <- (1 - 0.5 * factors/p)/diag(solve(cv))
# if ((ns <- cn$nstart) > 1)
# start <- cbind(start, matrix(runif(ns - 1), p, ns -
# 1, byrow = TRUE))
}
start <- as.matrix(start)
if (nrow(start) != p)
stop(paste("start must have", p, "rows"))
nc <- ncol(start)
if (nc < 1)
stop("no starting values supplied")
# best <- Inf
# for (i in 1:nc) {
# nfit <- factanal.fit.mle(cv, factors, start[, i], max(cn$lower,
# 0), cn$opt)
# if (cn$trace)
# cat("start", i, "value:", format(nfit$criteria[1]),
# "uniqs:", format(as.vector(round(nfit$uniquenesses,
# 4))), "\n")
# if (nfit$converged && nfit$criteria[1] < best) {
# fit <- nfit
# best <- fit$criteria[1]
# }
# }
# if (best == Inf)
# stop("Unable to optimize from these starting value(s)")
# PFA:
fit <- factanal.fit.principal(cv, factors, p=p, start=start[, 1],iter.max=maxiter)
# cv.red <- cv - diag(1-start)
# eig <- eigen(cv.red)
# load <- eig$vectors[,1:factors]%*%diag(sqrt(eig$values[1:factors]))
# fit <- list(loadings=load,uniqueness=1-start,factors=factors,method="pfa",
# dof=dof,n.obs=n.obs)
load <- fit$loadings
if (rotation != "none") {
rot <- do.call(rotation, c(list(load), cn$rotate))
load <- if (is.list(rot))
rot$loadings
else rot
}
fit$loadings <- sortLoadings(load)
class(fit$loadings) <- "loadings"
fit$na.action <- na.act
# if (have.x && scores != "none") {
if (scores != "none") {
Lambda <- fit$loadings
# zz <- scale(z, TRUE, TRUE)
zz <- z
switch(scores, regression = {
sc <- as.matrix(zz) %*% solve(cv, Lambda)
if (!is.null(Phi <- attr(Lambda, "covariance")))
sc <- sc %*% Phi
}, Bartlett = {
d <- 1/fit$uniquenesses
tmp <- t(Lambda * d)
sc <- t(solve(tmp %*% Lambda, tmp %*% t(zz)))
})
rownames(sc) <- rownames(z)
colnames(sc) <- colnames(Lambda)
if (!is.null(na.act))
sc <- napredict(na.act, sc)
fit$scores <- sc
}
if (!is.na(n.obs) && dof > 0) {
fit$STATISTIC <- (n.obs - 1 - (2 * p + 5)/6 - (2 * factors)/3) *
fit$criteria["objective"]
fit$PVAL <- pchisq(fit$STATISTIC, dof, lower.tail = FALSE)
}
fit$n.obs <- n.obs
fit$call <- cl
fit
}
"factanal.fit.principal"<-
function(cmat, factors, p = ncol(cmat), start = NULL, iter.max=10 , unique.tol
= 0.0001)
{
dof <- 0.5 * ((p - factors)^2 - p - factors)
if(dof < 0)
warning("negative degrees of freedom")
if(any(abs(diag(cmat) - 1) > .Machine$single.eps))
stop("must have correlation matrix")
if(length(start)) {
if(length(start) != p)
stop("start is the wrong length")
if(any(start < 0 | start >= 1))
stop("all values in start must be between 0 and 1")
oldcomm <- 1 - start
}
else {
diag(cmat) <- NA
oldcomm <- apply(abs(cmat), 1, max, na.rm = TRUE)
}
diag(cmat) <- oldcomm
if(iter.max < 0)
stop("bad value for iter.max")
ones <- rep(1, factors)
if(iter.max == 0){
z <- eigen(cmat, symmetric = TRUE)
kvals <- z$values[1:factors]
if(any(kvals <= 0))
stop("impermissible estimate reached")
Lambda <- z$vectors[, 1:factors, drop = FALSE] * rep(kvals^0.5,
rep.int(p, factors))
newcomm <- oldcomm
#newcomm <- Lambda^2 %*% ones
#diag(cmat) <- newcomm
}
if(iter.max >0){
for(i in 1:iter.max) {
z <- eigen(cmat, symmetric = TRUE)
kvals <- z$values[1:factors]
if(any(kvals <= 0))
stop("impermissible estimate reached")
Lambda <- z$vectors[, 1:factors, drop = FALSE] * rep(kvals^0.5,
rep.int(p, factors))
newcomm <- Lambda^2 %*% ones
if(all(abs(newcomm - oldcomm) < unique.tol)) {
iter.max <- i
break
}
oldcomm <- newcomm
diag(cmat) <- newcomm
}
}
dn <- dimnames(cmat)[[1]]
dimnames(Lambda) <- list(dn, paste("Factor", 1:factors, sep = ""))
diag(cmat) <- 1
uniq <- 1 - drop(newcomm)
names(uniq) <- dn
ans <- list(loadings = Lambda, uniquenesses = uniq, correlation = cmat,
criteria = c(iterations = iter.max), factors = factors, dof =
dof, method = "principal")
class(ans) <- "factanal"
ans
}
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