Principal Sensitivity Components

Compute Principal Sensitivity Components for Elastic Net Regression

prinsens(
  x,
  y,
  alpha,
  lambda,
  intercept = TRUE,
  penalty_loadings,
  en_algorithm_opts,
  eps = 1e-06,
  sparse = FALSE,
  ncores = 1L,
  method = deprecated()
)

Arguments

x

n by p matrix of numeric predictors.

y

vector of response values of length n.

alpha

elastic net penalty mixing parameter with \(0 \le \alpha \le 1\). alpha = 1 is the LASSO penalty, and alpha = 0 the Ridge penalty. Can be a vector of several values, but alpha = 0 cannot be mixed with other values.

lambda

optional user-supplied sequence of penalization levels. If given and not NULL, nlambda and lambda_min_ratio are ignored.

intercept

include an intercept in the model.

penalty_loadings

a vector of positive penalty loadings (a.k.a. weights) for different penalization of each coefficient. Only allowed for alpha > 0.

en_algorithm_opts

options for the LS-EN algorithm. See en_algorithm_options for details.

eps

numerical tolerance.

sparse

use sparse coefficient vectors.

ncores

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.

method

defunct. PSCs are always computed for EN estimates. For the PY procedure for unpenalized estimation use package pyinit.

Value

a list of principal sensitivity components, one per element in lambda. Each PSC is itself a list with items lambda, alpha, and pscs.

References

Cohen Freue, G.V.; Kepplinger, D.; Salibián-Barrera, M.; Smucler, E. Robust elastic net estimators for variable selection and identification of proteomic biomarkers. Ann. Appl. Stat. 13 (2019), no. 4, 2065–2090 doi:10.1214/19-AOAS1269

Pena, D., and Yohai, V.J. A Fast Procedure for Outlier Diagnostics in Large Regression Problems. J. Amer. Statist. Assoc. 94 (1999). no. 446, 434–445. doi:10.2307/2670164

See also

Other functions for initial estimates: enpy_initial_estimates(), starting_point()