Fitting generalized linear models with L1 (lasso and fused lasso) and/or L2 (ridge) penalties, or a combination of the two.
penalized (response, penalized, unpenalized, lambda1=0,
lambda2=0, positive = FALSE, data, fusedl=FALSE,
model = c("cox", "logistic", "linear", "poisson"),
startbeta, startgamma, steps =1, epsilon = 1e-10,
maxiter, standardize = FALSE, trace = TRUE)The response variable (vector). This should be a numeric vector for linear regression, a Surv object for Cox regression and factor or a vector of 0/1 values for logistic regression.
The penalized covariates. These may be specified either as a matrix or as a (one-sided) formula object. See also under data.
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.
The tuning parameters for L1 and L2 penalization. Each must be either a single positive numbers or a vector with length equal to the number of covariates in penalized argument. In the latter case, each covariate is given its own penalty weight.
If TRUE, constrains the estimated regression coefficients of all penalized covariates to be non-negative. If a logical vector with the length of the number of covariates in penalized, constrains the estimated regression coefficients of a subset of the penalized covariates to be non-negative.
A data.frame used to evaluate response, and the terms of penalized or unpenalized when these have been specified as a formula object.
If TRUE or a vector, the penalization method used is fused lasso. The value for lambda1 is used as the tuning parameter for L1 penalization on the coefficients and the value for lambda2 is used as the tuning parameter for L1 penalization on the differences of the coefficients. Default value is FALSE.
The model to be used. If missing, the model will be guessed from the response input.
Starting values for the regression coefficients of the penalized covariates.
Starting values for the regression coefficients of the unpenalized covariates.
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).
The convergence criterion. As in glm. Convergence is judged separately on the likelihood and on the penalty.
The maximum number of iterations allowed. Set by default at 25 when only an L2 penalty is present, infinite otherwise.
If TRUE, standardizes all penalized covariates to unit central L2-norm before applying penalization.
If TRUE, prints progress information. Note that setting trace=TRUE may slow down the algorithm up to 30 percent (but it often feels quicker)
penalized returns a penfit object when steps = 1 or a list of such objects if steps > 1.
The penalized function fits regression models for a given combination of L1 and L2 penalty parameters.
Goeman J.J. (2010). L-1 Penalized Estimation in the Cox Proportional Hazards Model. Biometrical Journal 52 (1) 70-84.
penfit for the penfit object returned, plotpath
for plotting the solution path, and cvl for cross-validation and
optimizing the tuning parameters.
# NOT RUN {
# More examples in the package vignette:
# type vignette("penalized")
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)
# A fused lasso fit predicting survival
pen <- penalized(Surv(time, event), penalized = nki70[,8:77], data = nki70,
lambda1 = 1, lambda2 = 2, fusedl = TRUE)
plot(coefficients(pen, "all"),type="l",xlab = "probes",ylab = "coefficient value")
plot(predict(pen,penalized=nki70[,8:77]))
# }
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