nearcor: Find the Nearest Proper Correlation Matrix

In sfsmisc: Utilities from 'Seminar fuer Statistik' ETH Zurich

Find the Nearest Proper Correlation Matrix

Description

This function “smoothes” an improper correlation matrix as it can result from cor with use="pairwise.complete.obs" or hetcor.

It is deprecated now, in favor of nearPD() from package Matrix.

Usage

nearcor(R, eig.tol = 1e-6, conv.tol = 1e-07, posd.tol = 1e-8,
        maxits = 100, verbose = FALSE)

Arguments

R	a square symmetric approximate correlation matrix
eig.tol	defines relative positiveness of eigenvalues compared to largest, default=1e-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.

Details

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.

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

Author(s)

Jens Oehlschlägel

References

See those in posdefify.

See Also

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.

hetcor, eigen; posdefify for a simpler algorithm.

Examples

 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))
  }

sfsmisc documentation built on Sept. 11, 2024, 6:53 p.m.