multivarious (version 0.3.1)

regress: Multi-output linear regression

Description

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),
  ...
)

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).

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

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)
recon_pls <- reconstruct(r_pls)