# R/rg-mva.R In StatDA: Statistical Analysis for Environmental Data

```"rg.mva" <-
function(x, main = deparse(substitute(x)))
{
# Procedure to undertake non-robust multivariate data analyses; the object
# generated is identical to that of rg.robmva so that the saved list may be
# passed to other rotation and display functions.  Thus weights are set to
# 1, and other variables are set to appropriate defaults.  The estimation
# of Mahalanobis distances is only undertaken if x is non-singular, i.e.,
# the lowest eigenvalue is > 10e-4.
#
# Note this procedure uses svd() rather than the classic solve().
#
# PCA output may be plotted with rg.rqpca.plot() and rg.rqpca.screeplot(),
# and Mahalanobis distances may be plotted with rg.md.plot().
#
# Determine the length of the vectors
if(!is.matrix(x)) stop("Not a Matrix")
n <- length(x[, 1])
p <- length(x[1,  ])
matnames <- dimnames(x)
wts <- numeric(n)
wts[1:n] <- 1
nc <- n
cat("  n =", n, "\tnc =", n, "\tp =", p, "\t\tnc/p =", round(nc/p, 2), "\n")
if(nc <= 5 * p)
cat("  *** Proceed with Care, n is < 5p ***\n")
if(nc <= 3 * p)
cat("  *** Proceed With Great Care, n = ", n, ", which is < 3p ***\n")
# Compute means & SDs, and standardize the data set.  Note cov.wt() is used in order
# to have cov and r entries for the saved object
save <- cov.wt(x, wt = wts, cor = TRUE)
xmean <- save\$center
xsd <- sqrt(diag(save\$cov))
# Compute SNDs
temp <- sweep(x, 2, xmean, "-")
snd <- sweep(temp, 2, xsd, "/")
# The following procedure duplicates that in rg.rqpca() for iwght = "r"
# Standardize centred x for R-mode PCA and compute
xsd2 <- sqrt(n) * xsd
w <- sweep(temp, 2, xsd2, "/")
wt <- t(as.matrix(w))
a <- wt %*% as.matrix(w)
b <- svd(a)
cat("  Eigenvalues:", signif(b\$d, 4), "\n")
sumc <- sum(b\$d)
econtrib <- 100 * (b\$d/sumc)
rqscore <- w %*% b\$v
###	vcontrib <- colVars(rqscore)
vcontrib <- apply(rqscore,2,var)
sumv <- sum(vcontrib)
pvcontrib <- (100 * vcontrib)/sumv
cpvcontrib <- cumsum(pvcontrib)
b1 <- b\$v * 0
diag(b1) <- sqrt(b\$d)
rcr <- rload[,  ] * 0
rcr <- 100 * sweep(rload^2, 1, rcr1, "/")
# Test for non-singularity and compute Mahalanobis distances
if(b\$d[p] > 0.001) {
md <- mahalanobis(x, save\$center, save\$cov)
temp <- (nc - p)/(p * (nc + 1))
ppm <- 1 - pf(temp * md, p, nc - p)
epm <- 1 - pchisq(md, p)
}
else {
cat("  Lowest eigenvalue < 10^-4, Mahalanobis distances not computed\n")
md <- NULL
ppm <- NULL
epm <- NULL
}
invisible(list(main = main, input = deparse(substitute(x)), proc = "cov", n = n, nc = nc,
p = p, matnames = matnames, wts = wts, mean = xmean, cov = save\$cov, sd = xsd,
snd = snd, r = save\$cor, eigenvalues = b\$d, econtrib = econtrib, eigenvectors =
b\$v, rload = rload, rcr = rcr, rqscore = rqscore, vcontrib = vcontrib, pvcontrib
= pvcontrib, cpvcontrib = cpvcontrib, md = md, ppm = ppm, epm = epm, nr = NULL)
)
}
```

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StatDA documentation built on March 13, 2020, 2:42 a.m.