festLASSO {eshrink}

Compute ‘Future Loss’ Ridge or LASSO Estimates

Description

Computes a ridge or LASSO estimate for a given regression problem, with penalty parameter chosen to minimize bias and variance.

Usage

festLASSO(
  X,
  y,
  loss = c("fMSE", "fMBV", "both"),
  ind = 1,
  lseq,
  B = 500,
  penalize,
  rescale.lambda = TRUE,
  scale = FALSE,
  returnMSE = FALSE,
  postsamp,
  returnPS = FALSE,
  nPost = 1000,
  se.version = c("varExp", "full", "none"),
  ...
)

festRidge(
  X,
  y,
  loss = c("fMSE", "fMBV", "both"),
  ind = 1,
  lseq,
  penalize,
  scale = FALSE,
  returnMSE = FALSE,
  postsamp,
  returnPS = FALSE,
  nPost = 1000,
  se.version = c("varExp", "full", "none"),
  XtXlamIinv = NULL,
  ...
)

Arguments

X

Design matrix for the regression. Assumed to contain only numeric values, so any factors should be coded according to desired contrast (e.g., via model.matrix)

y

Outcome vector. Unless X contains an intercept column, this should typically be centered.

loss

Loss function for choosing the penalty parameter. See details.

ind

Vector of integers or logicals indicating which coefficients the loss is to be computed on.

lseq

Sequence of penalty values to consider.

B

Number of future datasets to simulate for each point in posterior sample.

penalize

See estRidge

rescale.lambda

If TRUE, then lambda is rescaled to account for the default re-scaling done by glmnet. Can also be a scalar scaling factor.

scale

Logical indicating whether the design matrix X be scaled. See details.

returnMSE

Logical indicating whether mse object should be returned.

postsamp

List containing posterior sample (from samplePosterior). If missing, then a posterior sample is drawn. Currently checks on the provided postsamp are limited, so use with caution. Designed to facilitate simulations or other scenarios where it may be pre-computed.

returnPS

logical indicating whether or not the full posterior sample should be included in output.

nPost

Size of posterior sample to compute

se.version

String indicating which version of standard errors to use. See vcovfestRidge.

...

Other arguments passed to samplePosterior

XtXlamIinv

explicit value of (X'X + diag(penalty))^-1. Useful for simulations to save computation.

Details

The value of the ridge or LASSO penalty is selected by minimizing the posterior expectation of the loss function, which is chosen by the argument loss. Possible options are fMBV, which uses the loss function fMBV = max(Bias(\beta)^2, Var(\beta)) and fMSE, which uses the loss function fMSE = Bias(\beta)^2 + Var(\beta).

To balance the influence of covariates, it is recommended that the design matrix be standardized. This can be done by the user or via the argument scale. If scale=TRUE, then coefficient and standard error estimates are back-transformed.

Use the XtXlamIinv argument with caution. No checks are done on the provided value. Note that lseq is re-ordered to be decreasing, and provided values of XtXlamIinv must account for this.

See Also

mseRidge,vcovfestRidge, simLASSO, check_CIbound