sfsmisc (version 1.0-15)

nearcor: Find the Nearest Proper Correlation Matrix

Description

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

Usage

nearcor(R, eig.tol = 1e-06, conv.tol = 1e-07, posd.tol = 1e-08,
        maxits = 100, verbose = FALSE)

Arguments

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.

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

encoding

latin1

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.

References

See those in posdefify.

See Also

the slightly more flexible nearPD which also returns a classed matrix (class dpoMatrix); hetcor, eigen; posdefify for a simpler algorithm.

Examples

cat("pr is the example matrix used in Knol DL, ten Berge (1989)
")
 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$cor
 stopifnot(all.equal(nr[lower.tri(nr)],
            c(0.487968018215891, 0.642651880010905, 0.490638670907082, 0.64409905308119,
              0.808711184549399, 0.514114729435273, 0.250668810831206, 0.672351311297071,
              0.725832055882792, 0.596827778712155, 0.582191779051908, 0.744963163381413,
              0.729882058012398, 0.772150225146827, 0.813191720191943)))
 plot(pr[lower.tri(pr)],
      nr[lower.tri(nr)]); abline(0,1, lty=2)
 round(cbind(eigen(pr)$values, eigen(nr)$values), 8)

 cat("The following will fail:
")
 try(factanal(cov=pr, factors=2))
 cat("and this should work
")
 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))
  }