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Check and optionally repair LD matrix quality

Source: R/LD.R
check_ld.Rd

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

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

Arguments

R

Symmetric correlation matrix.

method

One of "check", "shrink", or "eigenfix".

r_tol

Eigenvalue tolerance. Eigenvalues with absolute value below r_tol 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.

is_pd

Logical: is the matrix positive definite?

is_psd

Logical: is the matrix positive semidefinite (within r_tol)?

min_eigenvalue

Smallest eigenvalue of the original matrix.

n_negative

Number of negative eigenvalues (below -r_tol).

condition_number

Ratio of largest to smallest positive eigenvalue (Inf if any eigenvalue is zero).

method_applied

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)
check_ld(R_good)$is_pd  # 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
check_ld(R_bad)$is_psd  # FALSE
#> [1] FALSE
R_fixed <- check_ld(R_bad, method = "eigenfix")$R
check_ld(R_fixed)$is_psd  # TRUE
#> [1] FALSE