Optimization for Lambda Selection

Minimizes information criteria to select the optimal tuning parameter lambda for islasso models. Supports AIC, BIC, AICc, GCV, and GIC.

Usage

aic.islasso(
  object,
  method = c("AIC", "BIC", "AICc", "GCV", "GIC"),
  interval,
  g = 0,
  y,
  X,
  intercept = FALSE,
  family = gaussian(),
  alpha = 1,
  offset,
  weights,
  unpenalized,
  control = is.control(),
  trace = TRUE
)

Arguments

object: Fitted model of class "islasso".
method: Criterion to minimize. Options are "AIC", "BIC", "AICc", "GCV", "GIC".
interval: Numeric vector (length 2) giving lower and upper bounds for lambda optimization. Optional if object includes prior cross-validation.
g: Numeric in [0,1]. Governs BIC generalization: g = 0 is classic BIC, g = 0.5 is extended BIC.
y: Response vector. Required only if object is missing.
X: Design matrix. Required only if object is missing.
intercept: Logical. Whether to include intercept in X. Used if object is missing.
family: Error distribution. Accepted: gaussian, binomial, poisson. Uses canonical link.
alpha: Elastic-net mixing parameter, 0 <= alpha <= 1. Lasso: alpha = 1; Ridge: alpha = 0.
offset: Optional numeric vector. Adds known linear predictor component.
weights: Optional weights for observations. Defaults to 1.
unpenalized: Logical vector indicating variables to exclude from penalization.
control: List of control parameters. See is.control.
trace: Logical. If TRUE, prints progress of optimization. Default is TRUE.

Value

Optimal lambda value as numeric.

Details

Instead of using cross-validation, this function selects the best lambda by minimizing criteria like AIC or BIC. Degrees of freedom are computed as the trace of the hat matrix (not necessarily an integer).

Author

Gianluca Sottile gianluca.sottile@unipa.it

Examples

set.seed(1)
n <- 100; p <- 100
beta <- c(rep(2, 20), rep(0, p - 20))
sim1 <- simulXy(n = n, p = p, beta = beta, seed = 1, family = gaussian())
o <- islasso(y ~ ., data = sim1$data, family = gaussian())

if (FALSE) { # \dontrun{
# Use the evaluation interval of the fit
lambda_aic <- aic.islasso(o, method = "AIC")

# Overwrites the evaluation interval for lambda
lambda_bic <- aic.islasso(o, interval = c(0.1, 30), method = "BIC")

# Overwrites the evaluation interval for lambda using eBIC criterion
lambda_ebic <- aic.islasso(o, interval = c(0.1, 30), method = "BIC", g = 0.5)
} # }