Using the glmnet and ncvreg packages, fits a Generalized Linear Model or Cox Proportional Hazards Model using various methods for choosing the regularization parameter λ
Description
This function fits a generalized linear model or a Cox proportional hazards
model via penalized maximum likelihood, with available penalties as
indicated in the glmnet and ncvreg packages. Instead of
providing the whole regularization solution path, the function returns the
solution at a unique value of λ, the one optimizing the
criterion specified in tune
.
Usage
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Arguments
x 
The design matrix, of dimensions n * p, without an intercept. Each row is an observation vector. 
y 
The response vector of dimension n * 1. Quantitative for

family 
Response type (see above). 
penalty 
The penalty to be applied in the regularized likelihood subproblems. 'SCAD' (the default), 'MCP', or 'lasso' are provided. 
concavity.parameter 
The tuning parameter used to adjust the concavity of the SCAD/MCP penalty. Default is 3.7 for SCAD and 3 for MCP. 
tune 
Method for selecting the regularization parameter along the
solution path of the penalized likelihood problem. Options to provide a
final model include 
nfolds 
Number of folds used in crossvalidation. The default is 10. 
type.measure 
Loss to use for crossvalidation. Currently five
options, not all available for all models. The default is

gamma.ebic 
Specifies the parameter in the Extended BIC criterion
penalizing the size of the corresponding model space. The default is

Value
Returns an object with
ix 
The vector of indices of the
nonzero coefficients selected by the maximum penalized likelihood procedure
with 
a0 
The intercept of the final model selected by 
beta 
The vector of coefficients of the final model selected by

fit 
The fitted penalized regression object. 
lambda 
The corresponding lambda in the final model. 
lambda.ind 
The index on the solution path for the final model. 
Author(s)
Jianqing Fan, Yang Feng, Diego Franco Saldana, Richard Samworth, and Yichao Wu
References
Jerome Friedman and Trevor Hastie and Rob Tibshirani (2010) Regularization Paths for Generalized Linear Models Via Coordinate Descent. Journal of Statistical Software, 33(1), 122.
Noah Simon and Jerome Friedman and Trevor Hastie and Rob Tibshirani (2011) Regularization Paths for Cox's Proportional Hazards Model Via Coordinate Descent. Journal of Statistical Software, 39(5), 113.
Patrick Breheny and Jian Huang (2011) Coordiante Descent Algorithms for Nonconvex Penalized Regression, with Applications to Biological Feature Selection. The Annals of Applied Statistics, 5, 232253.
Hirotogu Akaike (1973) Information Theory and an Extension of the Maximum Likelihood Principle. In Proceedings of the 2nd International Symposium on Information Theory, BN Petrov and F Csaki (eds.), 267281.
Gideon Schwarz (1978) Estimating the Dimension of a Model. The Annals of Statistics, 6, 461464.
Jiahua Chen and Zehua Chen (2008) Extended Bayesian Information Criteria for Model Selection with Large Model Spaces. Biometrika, 95, 759771.
Examples
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