nearcor function

Find the Nearest Proper Correlation Matrix

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 list("Matrix").

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.

Returns

A list, with components - cor: resulting correlation matrix

• fnorm: Froebenius norm of difference of input and output

• iterations: number of iterations used

• converged: logical

References

See those in posdefify.

Author(s)

Jens Oehlschlägel

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))
  }