aic.islasso function

Optimization for the selection of the tuning parameter

This function performs a minimization of the AIC/BIC criterion for selecting the tuning parameter in ‘islasso’ .

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: a fitted model object of class "islasso".
• method: the criterion to optimize, AIC, BIC, AICc, GCV, GIC.
• interval: the lower and upper limits of $\lambda$ wherein the AIC/BIC criterion should be optimized. Can be missing, if object has been obtained via cross-validation (and therefore includes the range of lambdas)
• g: a value belonging to the interval [0, 1]. Classical BIC is returned by letting g = 0 (default value), whereas extended BIC corresponds to the case g = 0.5.
• y: if object is missing, the response vector of length n.
• X: if object is missing, the design matrix of dimension n * p.
• intercept: if object is missing, if TRUE the intercept is added to the model matrix.
• family: if object is missing, a description of the error distribution, family=gaussian, family=binomial and family=poisson are implemented with canonical link.
• alpha: The elasticnet mixing parameter, with $0\le\alpha\le 1$. The penalty is defined as

alpha=1

is the lasso penalty, and `alpha=0` the ridge penalty.

• offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases.
• weights: observation weights. Default is 1 for each observation.
• unpenalized: a vector used to specify the unpenalized estimators; unpenalized has to be a vector of logicals.
• control: a list of parameters for controlling the fitting process (see islasso.control for more details).
• trace: Should the iterative procedure be printed? TRUE is the default value.

Details

Minimization of the Akaike Information Criterion (AIC), or Bayesian Information Criterion (BIC) or several other criteria are sometimes employed to select the tuning parameter as an alternative to the cross validation. The model degrees of freedom (not necessarly integers as in the plain lasso) used in all methods are computed as trace of the hat matrix at convergence.

Returns

the optimal lambda value is returned

Author(s)

Maintainer: Gianluca Sottile gianluca.sottile@unipa.it

See Also

islasso.fit, summary.islasso, residuals.islasso, logLik.islasso, predict.islasso and deviance.islasso methods.

Examples

set.seed(1)
n <- 100
p <- 100
p1 <- 20  #number of nonzero coefficients
coef.veri <- sort(round(c(seq(.5, 3, l=p1/2), seq(-1, -2, l=p1/2)), 2))
sigma <- 1

coef <- c(coef.veri, rep(0, p-p1))

X <- matrix(rnorm(n*p), n, p)
mu <- drop(X%*%coef)
y <- mu + rnorm(n, 0, sigma)

o <- islasso(y ~ ., data = data.frame(y = y, X))

## Not run:

#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(.1, 30), method = "BIC") 

#overwrites the evaluation interval for lambda using eBIC criterion
lambda_ebic <- aic.islasso(o, interval = c(.1, 30), method = "BIC", g = .5) 
## End(Not run)