Partial Least Squares Correlation (PLSC)

Reference implementation of symmetric brain-behavior PLS (a.k.a. Behavior PLSC). It finds paired weight vectors for X and Y that maximize their cross-block covariance, obtained from the SVD of the cross-covariance (or correlation) matrix \(C_{XY} = X^\top Y / (n-1)\).

Usage

plsc(
  X,
  Y,
  ncomp = NULL,
  preproc_x = standardize(),
  preproc_y = standardize(),
  ...
)

Arguments

X: Numeric matrix of predictors (n x p_x).
Y: Numeric matrix of outcomes/behaviors (n x p_y). Must have the same number of rows as X.
ncomp: Number of latent variables to return. Defaults to min(nrow(X), ncol(X), ncol(Y)).
preproc_x: Preprocessor for the X block (default: standardize()). Use center() if you want covariance-based PLSC instead of correlation.
preproc_y: Preprocessor for the Y block (default: standardize()).
...: Extra arguments stored on the returned object.

Value

A cross_projector with class "plsc" containing

vx, vy: X and Y loading/weight matrices.
sx, sy: subject scores for X and Y blocks.
singvals: singular values of \(C_{XY}\) (strength of each LV).
explained_cov: proportion of cross-block covariance per LV.
preproc_x, preproc_y: fitted preprocessors for reuse.

Examples

set.seed(1)
X <- matrix(rnorm(80), 20, 4)
Y <- matrix(rnorm(60), 20, 3)
fit <- plsc(X, Y, ncomp = 3)
fit$singvals
#> [1] 0.53051217 0.34069860 0.06144928