ladlasso {perryExamples}

LAD-lasso with penalty parameter selection

Description

Fit LAD-lasso models and select the penalty parameter by estimating the respective prediction error via (repeated) K-fold cross-validation, (repeated) random splitting (also known as random subsampling or Monte Carlo cross-validation), or the bootstrap.

Usage

ladlasso(
  x,
  y,
  lambda,
  standardize = TRUE,
  intercept = TRUE,
  splits = foldControl(),
  cost = mape,
  selectBest = c("hastie", "min"),
  seFactor = 1,
  ncores = 1,
  cl = NULL,
  seed = NULL,
  ...
)

ladlasso.fit(x, y, lambda, standardize = TRUE, intercept = TRUE, ...)

Arguments

x

a numeric matrix containing the predictor variables.

y

a numeric vector containing the response variable.

lambda

for ladlasso, a numeric vector of non-negative values to be used as penalty parameter. For ladlasso.fit, a single non-negative value to be used as penalty parameter.

standardize

a logical indicating whether the predictor variables should be standardized to have unit MAD (the default is TRUE).

intercept

a logical indicating whether a constant term should be included in the model (the default is TRUE).

splits

an object giving data splits to be used for prediction error estimation (see perryTuning).

cost

a cost function measuring prediction loss (see perryTuning for some requirements). The default is to use the mean absolute prediction error (see cost).

selectBest, seFactor

arguments specifying a criterion for selecting the best model (see perryTuning). The default is to use a one-standard-error rule.

ncores, cl

arguments for parallel computing (see perryTuning).

seed

optional initial seed for the random number generator (see .Random.seed and perryTuning).

...

for ladlasso, additional arguments to be passed to the prediction loss function cost. For ladlasso.fit, additional arguments to be passed to rq.fit.lasso.

Value

For ladlasso, an object of class "perryTuning", see perryTuning). It contains information on the prediction error criterion, and includes the final model with the optimal tuning paramter as component finalModel.

For ladlasso.fit, an object of class ladlasso with the following components:

lambda

numeric; the value of the penalty parameter.

coefficients

a numeric vector containing the coefficient estimates.

fitted.values

a numeric vector containing the fitted values.

residuals

a numeric vector containing the residuals.

standardize

a logical indicating whether the predictor variables were standardized to have unit MAD.

intercept

a logical indicating whether the model includes a constant term.

muX

a numeric vector containing the medians of the predictors.

sigmaX

a numeric vector containing the MADs of the predictors.

muY

numeric; the median of the response.

call

the matched function call.

Author(s)

Andreas Alfons

References

Wang, H., Li, G. and Jiang, G. (2007) Robust regression shrinkage and consistent variable selection through the LAD-lasso. Journal of Business & Economic Statistics, 25(3), 347–355.

See Also

perryTuning, rq.fit.lasso

Examples

## load data
data("Bundesliga")
Bundesliga <- Bundesliga[, -(1:2)]
f <- log(MarketValue) ~ Age + I(Age^2) + .
mf <- model.frame(f, data=Bundesliga)
x <- model.matrix(terms(mf), mf)[, -1]
y <- model.response(mf)

## set up repeated random splits
splits <- splitControl(m = 40, R = 10)

## select optimal penalty parameter
lambda <- seq(40, 0, length.out = 20)
fit <- ladlasso(x, y, lambda = lambda, splits = splits, seed = 2014)
fit

## plot prediction error results
plot(fit, method = "line")