Partial Least Squares (PLS) Regression Interface

Performs Partial Least Squares (PLS) regression using either the NIPALS or SVD algorithm for component extraction. This is the main user-facing function for computing PLS models. Internally, it delegates to either NIPALS.pls() or SVD.pls().

Usage

pls.regression(x, y, n.components = NULL, calc.method = c("SVD", "NIPALS"))

Arguments

x: A numeric matrix or data frame of predictor variables (X), with dimensions n × p.
y: A numeric matrix or data frame of response variables (Y), with dimensions n × q.
n.components: Integer specifying the number of latent components (H) to extract. If NULL, defaults to the rank of x.
calc.method: Character string indicating the algorithm to use. Must be either "SVD" (default) or "NIPALS".

Value

A list (from either SVD.pls() or NIPALS.pls()) containing:

model.type: Character string ("PLS Regression").
T, U: Score matrices for X and Y.
W, C: Weight matrices for X and Y.
P_loadings, Q_loadings: Loading matrices.
B_vector: Component-wise regression weights.
coefficients: Final regression coefficient matrix (rescaled).
intercept: Intercept vector (typically zero due to centering).
X_explained, Y_explained: Variance explained by each component.
X_cum_explained, Y_cum_explained: Cumulative variance explained.

Details

This function provides a unified interface for Partial Least Squares regression. Based on the value of calc.method, it computes latent variables using either:

"SVD" — A direct method using the singular value decomposition of the cross-covariance matrix (\(X^\top Y\)).
"NIPALS" — An iterative method that alternately estimates predictor and response scores until convergence.

The outputs from both methods include scores, weights, loadings, regression coefficients, and explained variance.

References

Abdi, H., & Williams, L. J. (2013). Partial least squares methods: Partial least squares correlation and partial least square regression. Methods in Molecular Biology (Clifton, N.J.), 930, 549–579. doi:10.1007/978-1-62703-059-5_23

de Jong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18(3), 251–263. doi:10.1016/0169-7439(93)85002-X

Examples

if (FALSE) { # \dontrun{
X <- matrix(rnorm(100 * 10), 100, 10)
Y <- matrix(rnorm(100 * 2), 100, 2)

# Using SVD (default)
model1 <- pls.regression(X, Y, n.components = 3)

# Using NIPALS
model2 <- pls.regression(X, Y, n.components = 3, calc.method = "NIPALS")
} # }