Penalized generalized linear models {penalized}R Documentation

Penalized regression

Description

Fitting generalized linear models with L1 (lasso) and/or L2 (ridge) penalties, or a combination of the two.

Usage


penalized (response, penalized, unpenalized, lambda1 = 0, lambda2 = 0,
    positive = FALSE, data, model = c("cox", "logistic", "linear",
    "poisson"), startbeta, startgamma, steps = 1, epsilon = 1e-10,
    maxiter, standardize = FALSE, trace = TRUE)

Arguments

response The response variable (vector). This should be a numeric vector for linear regression, a Surv object for Cox regression and a vector of 0/1 values for logistic regression.
penalized The penalized covariates. These may be specified either as a matrix or as a (one-sided) formula object. See also under data.
unpenalized Additional unpenalized covariates. Specified as under penalized. Note that an unpenalized intercept is included in the model by default (except in the Cox model). This can be suppressed by specifying unpenalized = ~0.
lambda1, lambda2 The tuning parameters for L1 and L2 penalization.
positive If TRUE, constrains the estimated regression coefficients of all penalized covariates to be positive.
data A data.frame used to evaluate response, and the terms of penalized or unpenalized when these have been specified as a formula object.
model The model to be used. If missing, the model will be guessed from the response input.
startbeta Starting values for the regression coefficients of the penalized covariates.
startgamma Starting values for the regression coefficients of the unpenalized covariates.
steps If greater than 1, the algorithm will fit the model for a range of steps lambda1-values, starting from the maximal value down to the value of lambda1 specified. This is useful for making plots as in plotpath. With steps = "Park" it is possible to choose the steps in such a way that they are at the approximate value at which the active set changes, following Park and Haste (2007).
epsilon The convergence criterion. As in glm. Convergence is judged separately on the likelihood and on the penalty.
maxiter The maximum number of iterations allowed. Set by default at 25 when only an L2 penalty is present, infinite otherwise.
standardize If TRUE, standardizes all penalized covariates to unit central L2-norm before applying penalization.
trace If TRUE, prints progress information. Note that setting trace=TRUE may slow down the algorithm up to 30 percent (but it often feels quicker)

Details

The penalized function fits regression models for a given combination of L1 and L2 penalty parameters.

Value

penalized returns a penfit object when steps = 1 or a list of such objects if steps > 1.

Note

The response argument of the function also accepts formula input as in lm and related functions. In that case, the right hand side of the response formula is used as the penalized argument or, if that is already given, as the unpenalized argument. For example, the input penalized(y~x) is equivalent to penalized(y, ~x) and penalized(y~x, ~z) to penalized(y, ~z, ~x).

In case of tied survival times, the function uses Breslow's version of the partial likelihood.

Author(s)

Jelle Goeman: j.j.goeman@lumc.nl

See Also

penfit for the penfit object returned, plotpath for plotting the solution path, and cvl for cross-validation and optimizing the tuning parameters.

Examples


data(nki70)

# A single lasso fit predicting survival
pen <- penalized(Surv(time, event), penalized = nki70[,8:77],
    unpenalized = ~ER+Age+Diam+N+Grade, data = nki70, lambda1 = 10)
show(pen)
coefficients(pen)
coefficients(pen, "penalized")
basehaz(pen)

# A single lasso fit using the clinical risk factors
pen <- penalized(Surv(time, event), penalized = ~ER+Age+Diam+N+Grade,
    data = nki70, lambda1=10, standardize=TRUE)

# using steps
pen <- penalized(Surv(time, event), penalized = nki70[,8:77],
    data = nki70, lambda1 = 1, steps = 20)
plotpath(pen)

[Package penalized version 0.9-23 Index]