| get.Amat {lqa} | R Documentation |
Computation of the approximated penalty matrix.
Description
The function get.Amat computes and returns
\mathbf{A}_\lambda = \sum_{j=1}^J \frac{p_{\lambda,j}'(|\mathbf{a}_j^\top \boldsymbol{\beta}|)}{\sqrt{(\mathbf{a}_j^\top \boldsymbol{\beta})^2 + c}}\mathbf{a}_j\mathbf{a}_j^\top,
where c > 0 is a small real number. However, this function is primarily intended for internal use. It acts as a link between penalty
objects and methods which require the approximated penalty matrix \mathbf{A}_\lambda.
Usage
get.Amat (initial.beta = NULL, penalty = NULL, intercept = TRUE,
c1 = lqa.control()$c1, x = NULL, ...)
Arguments
initial.beta |
the current beta vector. |
penalty |
member of the |
intercept |
logical. If ‘TRUE’ an intercept is included in the model. |
c1 |
double: small positive real number used in the approximation of the linear combinations in the penalty. |
x |
optional argument containing the original regressor matrix. This will be used by some penalties, such as |
... |
further arguments. |
Details
See penalty or the accompanying ‘User’s Guide' for further details on \mathbf{A}_\lambda.
Value
This function returns a (p \times p)-dimensional matrix or if an intercept is included a ((p+1) \times (p+1))-dimensional matrix.
Author(s)
Jan Ulbricht
See Also
Examples
penalty <- lasso (lambda = 1.5)
beta <- c (1, -2, 3, -4)
get.Amat (initial.beta = beta, penalty = penalty, intercept = FALSE)