Adaptive Elastic-Net

Usage

aenet(
  x,
  y,
  family = c("gaussian", "binomial", "poisson", "cox"),
  init = c("enet", "ridge"),
  alphas = seq(0.05, 0.95, 0.05),
  tune = c("cv", "ebic", "bic", "aic"),
  nfolds = 5L,
  rule = c("lambda.min", "lambda.1se"),
  ebic.gamma = 1,
  scale = 1,
  lower.limits = -Inf,
  upper.limits = Inf,
  penalty.factor.init = rep(1, ncol(x)),
  seed = 1001,
  parallel = FALSE,
  verbose = FALSE
)

Arguments

x: Data matrix.
y: Response vector if family is "gaussian", "binomial", or "poisson". If family is "cox", a response matrix created by Surv.
family: Model family, can be "gaussian", "binomial", "poisson", or "cox".
init: Type of the penalty used in the initial estimation step. Can be "enet" or "ridge".
alphas: Vector of candidate alphas to use in cv.glmnet.
tune: Parameter tuning method for each estimation step. Possible options are "cv", "ebic", "bic", and "aic". Default is "cv".
nfolds: Fold numbers of cross-validation when tune = "cv".
rule: Lambda selection criterion when tune = "cv", can be "lambda.min" or "lambda.1se". See cv.glmnet for details.
ebic.gamma: Parameter for Extended BIC penalizing size of the model space when tune = "ebic", default is 1. For details, see Chen and Chen (2008).
scale: Scaling factor for adaptive weights: weights = coefficients^(-scale).
lower.limits: Lower limits for coefficients. Default is -Inf. For details, see glmnet.
upper.limits: Upper limits for coefficients. Default is Inf. For details, see glmnet.
penalty.factor.init: The multiplicative factor for the penalty applied to each coefficient in the initial estimation step. This is useful for incorporating prior information about variable weights, for example, emphasizing specific clinical variables. To make certain variables more likely to be selected, assign a smaller value. Default is rep(1, ncol(x)).
seed: Random seed for cross-validation fold division.
parallel: Logical. Enable parallel parameter tuning or not, default is FALSE. To enable parallel tuning, load the doParallel package and run registerDoParallel() with the number of CPU cores before calling this function.
verbose: Should we print out the estimation progress?

Value

List of model coefficients, glmnet model object, and the optimal parameter set.

References

Zou, Hui, and Hao Helen Zhang. (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics 37(4), 1733–1751.

Author

Nan Xiao <https://nanx.me>

Examples

dat <- msaenet.sim.gaussian(
  n = 150, p = 500, rho = 0.6,
  coef = rep(1, 5), snr = 2, p.train = 0.7,
  seed = 1001
)

aenet.fit <- aenet(
  dat$x.tr, dat$y.tr,
  alphas = seq(0.2, 0.8, 0.2), seed = 1002
)

print(aenet.fit)
#> Call: aenet(x = dat$x.tr, y = dat$y.tr, alphas = seq(0.2, 0.8, 0.2), 
#>     seed = 1002) 
#>   Df      %Dev       Lambda
#> 1 12 0.7962207 9.644864e+14
msaenet.nzv(aenet.fit)
#>  [1]   2   3   4   5  33  35  49 114 269 363 379 441
msaenet.fp(aenet.fit, 1:5)
#> [1] 8
msaenet.tp(aenet.fit, 1:5)
#> [1] 4
aenet.pred <- predict(aenet.fit, dat$x.te)
msaenet.rmse(dat$y.te, aenet.pred)
#> [1] 2.640474
plot(aenet.fit)