adapt4pv (version 0.1.0)

adapt_ridge: fit an adaptive lasso with adaptive weights derived from ridge regression

Description

Fit first a ridge regression with cross-validation to determine adaptive weights, then run an adaptive lasso with this penalty weighting. BIC or cross-validation could either be used for the adaptive lasso for variable selection. Can deal with very large sparse data matrices. Intended for binary reponse only (option family = "binomial" is forced). Depends on the glmnet and relax.glmnet function from the package glmnet.

Usage

adapt_ridge(
  x,
  y,
  gamma = 1,
  criterion = "bic",
  maxp = 50,
  path = TRUE,
  nfolds = 5,
  foldid = NULL,
  betaPos = TRUE,
  ...
)

Arguments

x

Input matrix, of dimension nobs x nvars. Each row is an observation vector. Can be in sparse matrix format (inherit from class "sparseMatrix" as in package Matrix).

y

Binary response variable, numeric.

gamma

Tunning parameter to defined the penalty weights. See details below. Default is set to 1.

criterion

Character, indicates which criterion is used with the adaptive lasso for variable selection. Could be either "bic" or "cv". Default is "bic"

maxp

Used only if criterion = "bic", ignored if criterion = "cv". A limit on how many relaxed coefficients are allowed. Default is 50, in glmnet option default is 'n-3', where 'n' is the sample size.

path

Used only if criterion = "bic", ignored if criterion = "cv". Since glmnet does not do stepsize optimization, the Newton algorithm can get stuck and not converge, especially with relaxed fits. With path=TRUE, each relaxed fit on a particular set of variables is computed pathwise using the original sequence of lambda values (with a zero attached to the end). Default is path=TRUE.

nfolds

Used for the cross-validation in ridge regression and if criterion = "cv". Number of folds - default is 5. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3.

foldid

Used for the cross-validation in ridge regression and if criterion = "cv". An optional vector of values between 1 and nfolds identifying what fold each observation is in. If supplied, nfolds can be missing.

betaPos

Should the covariates selected by the procedure be positively associated with the outcome ? Default is TRUE.

…

Other arguments that can be passed to glmnet from package glmnet other than penalty.factor, alpha, family, maxp and path.

Value

An object with S3 class "adaptive".

aws

Numeric vector of penalty weights derived from ridge regression. Length equal to nvars.

criterion

Character, same as input. Could be either "bic" or "cv".

beta

Numeric vector of regression coefficients in the adaptive lasso. If criterion = "cv" the regression coefficients are PENALIZED, if criterion = "bic" the regression coefficients are UNPENALIZED. Length equal to nvars. Could be NA if adaptive weights are all equal to infinity.

selected_variables

Character vector, names of variable(s) selected with this adaptive approach. If betaPos = TRUE, this set is the covariates with a positive regression coefficient in beta. Else this set is the covariates with a non null regression coefficient in beta. If criterion = "bic", covariates are ordering according to magnitude of their regression coefficients absolute value in the adaptive lasso. If criterion = "bic", covariates are ordering according to the p-values (two-sided if betaPos = FALSE , one-sided if betaPos = TRUE) in the classical multiple logistic regression model that minimzes the BIC in the adaptive lasso.

Details

The adaptive weight for a given covariate i is defined by $$w_i = 1/|\beta^{L2}_i|^\gamma$$ where \(\beta^L2_i\) is the PENALIZED ridge regression coefficient associated to covariate i obtained with cross-validation.

Examples

# NOT RUN {
set.seed(15)
drugs <- matrix(rbinom(100*20, 1, 0.2), nrow = 100, ncol = 20)
colnames(drugs) <- paste0("drugs",1:ncol(drugs))
ae <- rbinom(100, 1, 0.3)
ar <- adapt_ridge(x = drugs, y = ae, criterion = "cv", nfolds = 3)

# }