Check and optionally repair LD matrix quality

Diagnoses positive-definiteness of an LD correlation matrix and optionally repairs it. Downstream methods like PRS-CS require positive-definite LD (Cholesky decomposition), while others (lassosum, SDPR) handle non-PD matrices internally via their own regularization.

Usage

checkLd(
  R,
  method = c("check", "shrink", "eigenfix"),
  rTol = 1e-08,
  shrinkage = 0.01
)

Arguments

R: Symmetric correlation matrix.
method: One of "check", "shrink", or "eigenfix".
rTol: Eigenvalue tolerance. Eigenvalues with absolute value below rTol are treated as zero. Default: 1e-8.
shrinkage: Shrinkage parameter for method = "shrink". Default: 0.01.

Value

A list with components:

R: The (possibly repaired) LD matrix.
isPd: Logical: is the matrix positive definite?
isPsd: Logical: is the matrix positive semidefinite (within rTol)?
minEigenvalue: Smallest eigenvalue of the original matrix.
nNegative: Number of negative eigenvalues (below -rTol).
conditionNumber: Ratio of largest to smallest positive eigenvalue (Inf if any eigenvalue is zero).
methodApplied: Character: "none", "shrink", or "eigenfix".

Details

Three modes are available:

"check": Diagnostic only - returns eigenvalue statistics without modifying the matrix.
"shrink": Apply shrinkage toward identity: R_s = (1 - shrinkage) * R + shrinkage * I. Simple and fast; always produces a positive-definite matrix when shrinkage > 0.
"eigenfix": Set negative eigenvalues to zero and reconstruct the matrix. Matches the approach used in susieR's rss_lambda_constructor and is the closest positive semidefinite matrix in the Frobenius norm. Does not inflate the diagonal like shrinkage does.

Examples

# A well-conditioned matrix
R_good <- diag(5)
checkLd(R_good)$isPd  # TRUE
#> [1] TRUE

# A matrix with negative eigenvalues
R_bad <- matrix(0.9, 3, 3); diag(R_bad) <- 1; R_bad[1,3] <- R_bad[3,1] <- -0.5
checkLd(R_bad)$isPsd  # FALSE
#> [1] FALSE
R_fixed <- checkLd(R_bad, method = "eigenfix")$R
checkLd(R_fixed)$isPsd  # TRUE
#> [1] FALSE