Estimate regression coefficients by using ridge regression.
lm_multiv_ridge(Y, X, lambda = 0, do_scale = FALSE)A list object with the components: 1) Psi - A list of estimated \(\mathbf{\Psi}\) matrices, 2) lambda - A vector of \(\lambda\) values, 3) GCV - A vector of GCV values
An N x K matrix of dependent variables.
An N x M matrix of regressors.
Numeric vector of lambda values
If true, X is centered and scaled, and Y is centered.
Consider the multivariate regression: $$\mathbf{Y} = \mathbf{X \Psi} + \mathbf{e}.$$ \(\mathbf{\Psi}\) is a M-by-K matrix of regression coefficients. The ridge regression estimate for the coefficients is $$\mathbf{\Psi} = (\mathbf{X'X} + \lambda \mathbf{I})^{-1} \mathbf{X'Y}.$$
G. H. Golub, M. Heath, G. Wahba (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215-223. doi: 10.2307/1268518