Permutation test for PLSC latent variables — perm

Uses row-wise permutation of the Y block to assess the significance of each latent variable (LV) in a fitted plsc model. The test statistic is the singular value of the cross-covariance matrix for each LV.

Usage

# S3 method for class 'plsc'
perm_test(
  x,
  X,
  Y,
  nperm = 1000,
  comps = ncomp(x),
  stepwise = TRUE,
  shuffle_fun = NULL,
  parallel = FALSE,
  alternative = c("greater", "less", "two.sided"),
  alpha = 0.05,
  ...
)

Arguments

x: A fitted plsc model object.
X: Original X block used to fit x.
Y: Original Y block used to fit x.
nperm: Number of permutations to perform (default 1000).
comps: Number of components (LVs) to test. Defaults to ncomp(x).
stepwise: Logical; if TRUE (default), test the leading singular value after sequential deflation by observed component directions, stopping at the first non-significant component. If FALSE, compare every ordered singular value with its counterpart in a common row-permutation bank.
shuffle_fun: Optional function to permute Y; defaults to shuffling rows.
parallel: Logical; if TRUE, use parallel processing via future.apply.
alternative: Character string for the alternative hypothesis: "greater" (default), "less", or "two.sided".
alpha: Significance level used to report n_significant; not used directly in p-value calculation.
...: Additional arguments (currently unused).

Details

Non-stepwise tests compare the ordered spectrum with complete independence between blocks; later components do not test the composite null that cross-covariance has rank less than that component number. Stepwise tests estimate deflation directions from the observed paired data and hold them fixed during permutation. Their later-component rank interpretation is approximate and requires application-specific calibration. The reported n_significant counts consecutive unadjusted rejections from the first component; it is not a generally calibrated rank estimator. Rows must be exchangeable under the chosen shuffle scheme. Supply shuffle_fun for restrictions such as permutations within groups.