Multi-output linear regression — regress • multivarious

Fit a multivariate regression model for a matrix of basis functions, X, and a response matrix Y. The goal is to find a projection matrix that can be used for mapping and reconstruction.

Usage

regress(
  X,
  Y,
  preproc = pass(),
  method = c("lm", "enet", "mridge", "pls"),
  intercept = FALSE,
  lambda = 0.001,
  alpha = 0,
  ncomp = ceiling(ncol(X)/2),
  ...
)

Arguments

X: the set of independent (basis) variables
Y: the response matrix
preproc: A preprocessing pipeline applied to X before fitting the model
method: the regression method: lm, enet, mridge, or pls
intercept: whether to include an intercept term
lambda: ridge shrinkage parameter (for methods mridge and enet)
alpha: the elastic net mixing parameter if method is enet
ncomp: number of PLS components if method is pls
...: extra arguments sent to the underlying fitting function

Value

a bi-projector of type regress. The sdev component of this object stores the standard deviations of the columns of the design matrix (X potentially including an intercept) used in the fit, not the standard deviations of latent components as might be typical in other bi_projector contexts (e.g., SVD).

Examples

# Generate synthetic data
set.seed(123) # for reproducibility
Y <- matrix(rnorm(10 * 100), 10, 100)
X <- matrix(rnorm(10 * 9), 10, 9)

# Fit regression models and reconstruct the fitted response matrix
r_lm <- regress(X, Y, intercept = FALSE, method = "lm")
recon_lm <- reconstruct(r_lm) # Reconstructs fitted Y

r_mridge <- regress(X, Y, intercept = TRUE, method = "mridge", lambda = 0.001)
recon_mridge <- reconstruct(r_mridge)

r_enet <- regress(X, Y, intercept = TRUE, method = "enet", lambda = 0.001, alpha = 0.5)
recon_enet <- reconstruct(r_enet)

r_pls <- regress(X, Y, intercept = TRUE, method = "pls", ncomp = 5)
#> Error in t.default(cf): argument is not a matrix
recon_pls <- reconstruct(r_pls)
#> Error: object 'r_pls' not found