R因子分析＆＃34; factanal＆＃34;对于大量的预测变量，导致系统在计算上是单数的？
大家好，
我试图对包含大约150个变量的数据集运行因子分析，但只有大约80个观察值。 我试过＆＃34; factanal＆＃34; R和R中的函数报告错误：
Error in solve.default(cv) :
system is computationally singular: reciprocal condition number = 3.0804e-20
有关替代方法/包的任何建议吗？
虚拟数据集的演示将是：
# This will work (dataset with 80 obs and 15 predictors)
set.seed(1234)
fake_df = as.data.frame(matrix(rnorm(80*15), nrow = 80))
factanal(fake_df, factors = 2, rotation = "varimax")
# This will not (dataset with 80 obs and 150 predictors)
set.seed(1234)
fake_df = as.data.frame(matrix(rnorm(80*150), nrow = 80))
factanal(fake_df, factors = 2, rotation = "varimax")
到目前为止，我已经取代了＆＃34; factanal＆＃34;我在下面创建的具有数值求解函数的源代码，但它没有解决问题：
solve_G = function(M){
library(matrixcalc)
if(!is.singular.matrix(M)){
return(solve(M))
} else{
s = svd(M)
U = s$u
V = s$v
D_Inv = diag(1/s$d)
Num_Inv = V %*% D_Inv %*% t(U)
cat("Singular Matrix! SVD Used.\n")
return(Num_Inv)
}
}
在您更换＆＃34;解决＆＃34;使用＆＃34; solve_G＆＃34;，发生了一个新错误：
Error in factanal.fit.mle(cv, factors, start[, i], max(cn$lower, 0), cn$opt) :
could not find function "factanal.fit.mle"
P.S。这是新的＆＃34; factanal＆＃34;名为my_factanal的函数： 运行以下行时发生错误：
nfit <- factanal.fit.mle(cv, factors, start[, i], max(cn$lower, 0), cn$opt)
要运行此操作，将x设置为80 * 150数值数据帧，设置因子= 2，设置分数=＆＃34;回归＆＃34;，旋转=＆＃34; varimax＆＃34;：
my_factanal = function (x, factors, data = NULL, covmat = NULL, n.obs = NA,
subset, na.action, start = NULL, scores = c("none", "regression",
"Bartlett"), rotation = "varimax", control = NULL, ...)
{
sortLoadings <- function(Lambda) {
cn <- colnames(Lambda)
Phi <- attr(Lambda, "covariance")
ssq <- apply(Lambda, 2L, function(x) -sum(x^2))
Lambda <- Lambda[, order(ssq), drop = FALSE]
colnames(Lambda) <- cn
neg <- colSums(Lambda) < 0
Lambda[, neg] <- -Lambda[, neg]
if (!is.null(Phi)) {
unit <- ifelse(neg, -1, 1)
attr(Lambda, "covariance") <- unit %*% Phi[order(ssq),
order(ssq)] %*% unit
}
Lambda
}
cl <- match.call()
na.act <- NULL
if (is.list(covmat)) {
if (any(is.na(match(c("cov", "n.obs"), names(covmat)))))
stop("'covmat' is not a valid covariance list")
cv <- covmat$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[[1L]] <- quote(stats::model.frame)
mf <- eval.parent(mf)
na.act <- attr(mf, "na.action")
if (.check_vars_numeric(mf))
stop("factor analysis applies only to numerical variables")
z <- model.matrix(mt, mf)
}
else {
z <- as.matrix(x)
if (!is.numeric(z))
stop("factor analysis applies only to numerical variables")
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)
stop("requested scores without an 'x' matrix")
p <- ncol(cv)
if (p < 3)
stop("factor analysis requires at least three variables")
dof <- 0.5 * ((p - factors)^2 - p - factors)
if (dof < 0)
stop(sprintf(ngettext(factors, "%d factor is too many for %d variables",
"%d factors are too many for %d variables"), factors,
p), domain = NA)
sds <- sqrt(diag(cv))
cv <- cv/(sds %o% sds)
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_G(cv))
if ((ns <- cn$nstart) > 1)
start <- cbind(start, matrix(runif(ns - 1), p, ns -
1, byrow = TRUE))
}
start <- as.matrix(start)
if (nrow(start) != p)
stop(sprintf(ngettext(p, "'start' must have %d row",
"'start' must have %d rows"), p), domain = NA)
nc <- ncol(start)
if (nc < 1)
stop("no starting values supplied")
best <- Inf
for (i in 1L:nc) {
nfit <- factanal.fit.mle(cv, factors, start[, i], max(cn$lower, 0), cn$opt)
if (cn$trace)
cat("start", i, "value:", format(nfit$criteria[1L]),
"uniqs:", format(as.vector(round(nfit$uniquenesses,
4))), "\\n")
if (nfit$converged && nfit$criteria[1L] < best) {
fit <- nfit
best <- fit$criteria[1L]
}
}
if (best == Inf)
stop(ngettext(nc, "unable to optimize from this starting value",
"unable to optimize from these starting values"),
domain = NA)
load <- fit$loadings
if (rotation != "none") {
rot <- do.call(rotation, c(list(load), cn$rotate))
load <- if (is.list(rot)) {
load <- rot$loadings
fit$rotmat <- if (inherits(rot, "GPArotation"))
t(solve_G(rot$Th))
else rot$rotmat
rot$loadings
}
else rot
}
fit$loadings <- sortLoadings(load)
class(fit$loadings) <- "loadings"
fit$na.action <- na.act
if (have.x && scores != "none") {
Lambda <- fit$loadings
zz <- scale(z, TRUE, TRUE)
switch(scores, regression = {
sc <- 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
}