Description Usage Arguments Details Value Note Author(s) References See Also Examples

Cross-validating generalized linear models with L1 (lasso or fused lasso) and/or L2 (ridge) penalties, using likelihood cross-validation.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
cvl (response, penalized, unpenalized, lambda1 = 0, lambda2= 0, positive = FALSE,
fusedl = FALSE, data, model = c("cox", "logistic", "linear", "poisson"),
startbeta, startgamma, fold, epsilon = 1e-10, maxiter, standardize = FALSE,
trace = TRUE, approximate = FALSE)
optL1 (response, penalized, unpenalized, minlambda1, maxlambda1, base1, lambda2 = 0,
fusedl = FALSE, positive = FALSE, data,
model = c("cox", "logistic", "linear", "poisson"), startbeta, startgamma, fold,
epsilon = 1e-10, maxiter = Inf, standardize = FALSE, tol = .Machine$double.eps^0.25,
trace = TRUE)
optL2 (response, penalized, unpenalized, lambda1 = 0, minlambda2, maxlambda2, base2,
fusedl = FALSE ,positive = FALSE, data,
model = c("cox", "logistic", "linear", "poisson"), startbeta, startgamma,
fold, epsilon = 1e-10, maxiter, standardize = FALSE, tol = .Machine$double.eps^0.25,
trace = TRUE, approximate = FALSE)
profL1 (response, penalized, unpenalized, minlambda1, maxlambda1, base1, lambda2 = 0,
fusedl = FALSE,positive = FALSE, data,
model = c("cox", "logistic", "linear", "poisson"), startbeta, startgamma, fold,
epsilon = 1e-10, maxiter = Inf, standardize = FALSE, steps = 100, minsteps = steps/3,
log = FALSE, save.predictions = FALSE, trace = TRUE, plot = FALSE)
profL2 (response, penalized, unpenalized, lambda1 = 0, minlambda2, maxlambda2, base2,
fusedl = FALSE,positive = FALSE, data,
model = c("cox", "logistic", "linear", "poisson"), startbeta, startgamma, fold,
epsilon = 1e-10, maxiter, standardize = FALSE, steps = 100, minsteps = steps/2,
log = TRUE, save.predictions = FALSE, trace = TRUE, plot = FALSE, approximate = FALSE)
``` |

`response` |
The response variable (vector). This should be a numeric vector for linear regression, a |

`penalized` |
The penalized covariates. These may be specified either as a matrix or as a (one-sided) |

`unpenalized` |
Additional unpenalized covariates. Specified as under |

`lambda1, lambda2` |
The fixed values of 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 |

`minlambda1, minlambda2, maxlambda1, maxlambda2` |
The values of the tuning parameters for L1 or L2 penalization between which the cross-validated likelihood is to be profiled or optimized. For fused lasso penalty |

`base1, base2` |
An optional vector of length equal to the number of covariates in penalized. If supplied, profiling or optimization is performed between |

`fusedl` |
If |

`positive` |
If |

`data` |
A |

`model` |
The model to be used. If missing, the model will be guessed from the |

`startbeta` |
Starting values for the regression coefficients of the penalized covariates. These starting values will be used only for the first values of |

`startgamma` |
Starting values for the regression coefficients of the unpenalized covariates. These starting values will be used only for the first values of |

`fold` |
The fold for cross-validation. May be supplied as a single number (between 2 and n) giving the number of folds, or, alternatively, as a length |

`epsilon` |
The convergence criterion. As in |

`maxiter` |
The maximum number of iterations allowed in each fitting of the model. Set by default at 25 when only an L2 penalty is present, infinite otherwise. |

`standardize` |
If |

`steps` |
The maximum number of steps between |

`minsteps` |
The minimum number of steps between |

`log` |
If |

`tol` |
The tolerance of the Brent algorithm used for minimization. See also |

`save.predictions` |
Controls whether or not to save cross-validated predictions for all values of lambda. |

`trace` |
If |

`approximate` |
If |

`plot` |
If |

All five functions return a list with the following named elements:

`lambda`

:For

`optL1`

and`optL2`

`lambda`

gives the optimal value of the tuning parameters found. For`profL1`

and`profL2`

`lambda`

is the vector of values of the tuning parameter for which the cross-validated likelihood has been calculated. Absent in the output of`cvl`

.`cvl`

:The value(s) of the cross-validated likelihood. For

`optL1`

,`optL2`

this is the cross-validated likelihood at the optimal value of the tuning parameter.`fold`

:Returns the precise allocation of the subjects into the cross-validation folds. Note that the same allocation is used for all cross-validated likelihood calculations in each call to

`optL1`

,`optL2`

,`profL1`

,`profL2`

.`predictions`

:The cross-validated predictions for the left-out samples. The precise format of the cross-validated predictions depends on the type of generalized linear model (see

`breslow`

for survival models. The functions`profL1`

and`profL2`

return a list here (only if`save.predictions = TRUE`

), whereas`optL1`

,`optL2`

return the predictions for the optimal value of the tuning parameter only.`fullfit`

:The fitted model on the full data. The functions

`profL1`

and`profL2`

return a list of`penfit`

objects here, whereas`optL1`

,`optL2`

return the full data fit (a single`penfit`

object) for the optimal value of the tuning parameter only.

A named list. See details.

The `optL1`

and `optL2`

functions use Brent's algorithm for minimization without derivatives (see also `optimize`

). There is a risk that these functions converge to a local instead of to a global optimum. This is especially the case for `optL1`

, as the cross-validated likelihood as a function of `lambda1`

quite often has local optima. It is recommended to use `optL1`

in combination with `profL1`

to check whether `optL1`

has converged to the right optimum.

See also the notes under `penalized`

.

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

Goeman J.J. (2010). L-1 Penalized Estimation in the Cox Proportional Hazards Model. Biometrical Journal 52 (1) 70-84.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# More examples in the package vignette:
# type vignette("penalized")
data(nki70)
attach(nki70)
# Finding an optimal cross-validated likelihood
opt <- optL1(Surv(time, event), penalized = nki70[,8:77], fold = 5)
coefficients(opt$fullfit)
plot(opt$predictions)
# Plotting the profile of the cross-validated likelihood
prof <- profL1(Surv(time, event), penalized = nki70[,8:77],
fold = opt$fold, steps=10)
plot(prof$lambda, prof$cvl, type="l")
plotpath(prof$fullfit)
``` |

```
Loading required package: survival
Welcome to penalized. For extended examples, see vignette("penalized").
lambda= 4.133719 12345cvl= -254.3604
lambda= 6.688499 12345cvl= -257.6856
lambda= 2.554779 12345cvl= -252.6971
lambda= 1.57894 12345cvl= -258.902
lambda= 3.157881 12345cvl= -252.3473
lambda= 3.029548 12345cvl= -252.2689
lambda= 2.971872 12345cvl= -252.2501
lambda= 2.812557 12345cvl= -252.3046
lambda= 2.947776 12345cvl= -252.2516
lambda= 2.966433 12345cvl= -252.2502
lambda= 2.97557 12345cvl= -252.2501
lambda= 2.975587 12345cvl= -252.2501
lambda= 2.996199 12345cvl= -252.2535
lambda= 2.98346 12345cvl= -252.2502
lambda= 2.978594 12345cvl= -252.2501
lambda= 2.976806 12345cvl= -252.2501
lambda= 2.976188 12345cvl= -252.2501
QSCN6L1 SCUBE2 ZNF533 IGFBP5 PRC1 ESM1
0.06546981 -0.07450513 -0.54863441 0.58674788 1.31951640 0.05861560
lambda= 10.82222 12345cvl= -258.4229
lambda= 9.619749 12345cvl= -258.4968
lambda= 8.417281 12345cvl= -258.4897
lambda= 7.214812 12345cvl= -257.9279
lambda= 6.012343 12345cvl= -257.4077
lambda= 4.809875 12345cvl= -255.957
lambda= 3.607406 12345cvl= -252.9509
lambda= 2.404937 12345cvl= -253.1057
lambda= 1.202469 12345cvl= -258.234
lambda= 0 12345cvl= -Inf
```

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