Find the Nearest Proper Correlation Matrix
nearcor(R, eig.tol = 1e-06, conv.tol = 1e-07, posd.tol = 1e-08,
maxits = 100, verbose = FALSE)R |
a square symmetric approximate correlation matrix |
eig.tol |
defines relative positiveness of eigenvalues compared to largest, default=1.0e-6. |
conv.tol |
convergence tolerance for algorithm, default=1.0e-7 |
posd.tol |
tolerance for enforcing positive definiteness, default=1.0e-8 |
maxits |
maximum number of iterations |
verbose |
logical specifying if convergence monitoring should be verbose. |
This implements the algorithm of Higham (2002), then forces symmetry,
then forces positive definiteness using code from
posdefify. This implementation does not make
use of direct LAPACK access for tuning purposes as in the MATLAB code
of Lucas (2001). The algorithm of Knol DL and ten Berge (1989) (not
implemented here) is more general in (1) that it allows contraints to
fix some rows (and columns) of the matrix and (2) to force the
smallest eigenvalue to have a certain value.
A list, with components
cor |
resulting correlation matrix |
fnorm |
Froebenius norm of difference of input and output |
iterations |
number of iterations used |
converged |
logical |
Jens Oehlschlägel
See those in posdefify.
the slightly more flexible nearPD which also
returns a classed matrix (class dpoMatrix).
For new code, nearPD() is really preferred to nearcor(),
which hence is considered deprecated.
cat("pr is the example matrix used in Knol DL, ten Berge (1989)\n")
pr <- matrix(c(1, 0.477, 0.644, 0.478, 0.651, 0.826,
0.477, 1, 0.516, 0.233, 0.682, 0.75,
0.644, 0.516, 1, 0.599, 0.581, 0.742,
0.478, 0.233, 0.599, 1, 0.741, 0.8,
0.651, 0.682, 0.581, 0.741, 1, 0.798,
0.826, 0.75, 0.742, 0.8, 0.798, 1),
nrow = 6, ncol = 6)
ncr <- nearcor(pr)
nr <- ncr$cor
plot(pr[lower.tri(pr)],
nr[lower.tri(nr)]); abline(0,1, lty=2)
round(cbind(eigen(pr)$values, eigen(nr)$values), 8)
cat("The following will fail:\n")
try(factanal(cov=pr, factors=2))
cat("and this should work\n")
try(factanal(cov=nr, factors=2))
if(require("polycor")) {
n <- 400
x <- rnorm(n)
y <- rnorm(n)
x1 <- (x + rnorm(n))/2
x2 <- (x + rnorm(n))/2
x3 <- (x + rnorm(n))/2
x4 <- (x + rnorm(n))/2
y1 <- (y + rnorm(n))/2
y2 <- (y + rnorm(n))/2
y3 <- (y + rnorm(n))/2
y4 <- (y + rnorm(n))/2
dat <- data.frame(x1, x2, x3, x4, y1, y2, y3, y4)
x1 <- ordered(as.integer(x1 > 0))
x2 <- ordered(as.integer(x2 > 0))
x3 <- ordered(as.integer(x3 > 1))
x4 <- ordered(as.integer(x4 > -1))
y1 <- ordered(as.integer(y1 > 0))
y2 <- ordered(as.integer(y2 > 0))
y3 <- ordered(as.integer(y3 > 1))
y4 <- ordered(as.integer(y4 > -1))
odat <- data.frame(x1, x2, x3, x4, y1, y2, y3, y4)
xcor <- cor(dat)
pcor <- cor(data.matrix(odat)) # cor() no longer works for factors
hcor <- hetcor(odat, ML=TRUE, std.err=FALSE)$correlations
ncor <- nearcor(hcor)$cor
try(factanal(covmat=xcor, factors=2, n.obs=n))
try(factanal(covmat=pcor, factors=2, n.obs=n))
try(factanal(covmat=hcor, factors=2, n.obs=n))
try(factanal(covmat=ncor, factors=2, n.obs=n))
}Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.