Compute elastic net M-estimates along a grid of penalization levels with optional penalty loadings for adaptive elastic net.
regmest(
x,
y,
alpha,
nlambda = 50,
lambda,
lambda_min_ratio,
scale,
starting_points,
penalty_loadings,
intercept = TRUE,
cc = 4.7,
eps = 1e-06,
explore_solutions = 10,
explore_tol = 0.1,
max_solutions = 10,
comparison_tol = sqrt(eps),
sparse = FALSE,
ncores = 1,
standardize = TRUE,
algorithm_opts = mm_algorithm_options(),
add_zero_based = TRUE,
mscale_bdp = 0.25,
mscale_opts = mscale_algorithm_options()
)n by p matrix of numeric predictors.
vector of response values of length n.
For binary classification, y should be a factor with 2 levels.
elastic net penalty mixing parameter with \(0 \le \alpha \le 1\).
alpha = 1 is the LASSO penalty, and alpha = 0 the Ridge penalty.
number of penalization levels.
optional user-supplied sequence of penalization levels.
If given and not NULL, nlambda and lambda_min_ratio are ignored.
Smallest value of the penalization level as a fraction of the
largest level (i.e., the smallest value for which all coefficients are zero).
The default depends on the sample size relative to the number of variables and alpha.
If more observations than variables are available, the default is 1e-3 * alpha,
otherwise 1e-2 * alpha.
fixed scale of the residuals.
a list of staring points, created by starting_point().
The starting points are shared among all penalization levels.
a vector of positive penalty loadings (a.k.a. weights)
for different penalization of each coefficient. Only allowed for alpha > 0.
include an intercept in the model.
cutoff constant for Tukey's bisquare \(\rho\) function.
numerical tolerance.
number of solutions to compute up to the desired precision eps.
numerical tolerance for exploring possible solutions.
Should be (much) looser than eps to be useful.
only retain up to max_solutions unique solutions per penalization level.
numeric tolerance to determine if two solutions are equal.
The comparison is first done on the absolute difference in the value of the objective
function at the solution.
If this is less than comparison_tol, two solutions are deemed equal if the
squared difference of the intercepts is less than comparison_tol and the squared
\(L_2\) norm of the difference vector is less than comparison_tol.
use sparse coefficient vectors.
number of CPU cores to use in parallel. By default, only one CPU core is used. Not supported on all platforms, in which case a warning is given.
logical flag to standardize the x variables prior to fitting the
M-estimates. Coefficients are always returned on the original scale.
This can fail for variables with a large proportion of a single value
(e.g., zero-inflated data). In this case, either compute with
standardize = FALSE or standardize the data manually.
options for the MM algorithm to compute estimates.
See mm_algorithm_options() for details.
also consider the 0-based regularization path in addition to the given starting points.
options for the M-scale estimate used to standardize
the predictors (if standardize = TRUE).
a list-like object with the following items
alphathe sequence of alpha parameters.
lambdaa list of sequences of penalization levels, one per alpha parameter.
scalethe used scale of the residuals.
estimatesa list of estimates. Each estimate contains the following information:
interceptintercept estimate.
betabeta (slope) estimate.
lambdapenalization level at which the estimate is computed.
alphaalpha hyper-parameter at which the estimate is computed.
objf_valuevalue of the objective function at the solution.
statuscodeif > 0 the algorithm experienced issues when
computing the estimate.
statusoptional status message from the algorithm.
callthe original call.
regmest_cv() for selecting hyper-parameters via cross-validation.
coef.pense_fit() for extracting coefficient estimates.
plot.pense_fit() for plotting the regularization path.
Other functions to compute robust estimates:
pense()