lambdamax function

Function to Find the Maximal Value of the Penalty Parameter Lambda

Determines the value of the penalty parameter lambda when the first penalized parameter group enters the model.

lambdamax(x, ...)

## S3 method for class 'formula'
lambdamax(formula, nonpen = ~1, data, weights, subset,
          na.action, coef.init, penscale = sqrt, model = LogReg(),
          center = TRUE, standardize = TRUE, contrasts = NULL,
          nlminb.opt = list(), ...)

## Default S3 method:
lambdamax(x, y, index, weights = rep(1, length(y)),
          offset = rep(0, length(y)), coef.init = rep(0, ncol(x)),
          penscale = sqrt, model = LogReg(), center = TRUE,
          standardize = TRUE, nlminb.opt = list(), ...)

Arguments

• x: design matrix (including intercept)

• y: response vector

• formula: formula of the penalized variables. The response has to be on the left hand side of '~'.

• nonpen: formula of the nonpenalized variables. This will be added to the formula argument above and doesn't need to have the response on the left hand side.

• data: data.frame containing the variables in the model.

• index: vector which defines the grouping of the variables. Components sharing the same number build a group. Non-penalized coefficients are marked with NA.

• weights: vector of observation weights.

• subset: an optional vector specifying a subset of observations to be used in the fitting process.

• na.action: a function which indicates what should happen when the data contain 'NA's.

• offset: vector of offset values.

• coef.init: initial parameter vector. Penalized groups are discarded.

• penscale: rescaling function to adjust the value of the penalty parameter to the degrees of freedom of the parameter group. See the reference below.

• model: an object of class grpl.model implementing the negative log-likelihood, gradient, hessian etc. See grpl.model for more details.

• center: logical. If true, the columns of the design matrix will be centered (except a possible intercept column).

• standardize: logical. If true, the design matrix will be blockwise orthonormalized, such that for each block $X^TX = n 1$

  (after possible centering).

• contrasts: an (optional) list with the contrasts for the factors in the model.

• nlminb.opt: arguments to be supplied to nlminb.

• ...: additional arguments to be passed to the functions defined in model.

Details

Uses nlminb to optimize the non-penalized parameters.

Returns

An object of type numeric is returned.

References

Lukas Meier, Sara van de Geer and Peter B"uhlmann (2008), The Group Lasso for Logistic Regression, Journal of the Royal Statistical Society, 70 (1), 53 - 71

Examples

data(splice)
lambdamax(y ~ ., data = splice, model = LogReg(), center = TRUE,
          standardize = TRUE)