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 \(\lambda\), the one optimizing the
criterion specified in tune.
tune.fit(x, y, family = c("gaussian", "binomial", "poisson", "cox"),
penalty = c("SCAD", "MCP", "lasso"), concavity.parameter = switch(penalty,
SCAD = 3.7, 3), tune = c("cv", "aic", "bic", "ebic"), nfolds = 10,
type.measure = c("deviance", "class", "auc", "mse", "mae"),
gamma.ebic = 1)The design matrix, of dimensions n * p, without an intercept. Each row is an observation vector.
The response vector of dimension n * 1. Quantitative for
family='gaussian', non-negative counts for family='poisson',
binary (0-1) for family='binomial'. For family='cox', y
should be an object of class Surv, as provided by the function
Surv() in the package survival.
Response type (see above).
The penalty to be applied in the regularized likelihood subproblems. 'SCAD' (the default), 'MCP', or 'lasso' are provided.
The tuning parameter used to adjust the concavity of the SCAD/MCP penalty. Default is 3.7 for SCAD and 3 for MCP.
Method for selecting the regularization parameter along the
solution path of the penalized likelihood problem. Options to provide a
final model include tune='cv', tune='aic', tune='bic',
and tune='ebic'. See references at the end for details.
Number of folds used in cross-validation. The default is 10.
Loss to use for cross-validation. Currently five
options, not all available for all models. The default is
type.measure='deviance', which uses squared-error for gaussian models
(also equivalent to type.measure='mse' in this case), deviance for
logistic and poisson regression, and partial-likelihood for the Cox model.
Both type.measure='class' and type.measure='auc' apply only to
logistic regression and give misclassification error and area under the ROC
curve, respectively. type.measure='mse' or type.measure='mae'
(mean absolute error) can be used by all models except the 'cox';
they measure the deviation from the fitted mean to the response. For
penalty='SCAD' and penalty='MCP', only
type.measure='deviance' is available.
Specifies the parameter in the Extended BIC criterion
penalizing the size of the corresponding model space. The default is
gamma.ebic=1. See references at the end for details.
Returns an object with
The vector of indices of the
nonzero coefficients selected by the maximum penalized likelihood procedure
with tune as the method for choosing the regularization parameter.
The intercept of the final model selected by tune.
The vector of coefficients of the final model selected by
tune.
The fitted penalized regression object.
The corresponding lambda in the final model.
The index on the solution path for the final model.
Jerome Friedman and Trevor Hastie and Rob Tibshirani (2010) Regularization Paths for Generalized Linear Models Via Coordinate Descent. Journal of Statistical Software, 33(1), 1-22.
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), 1-13.
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, 232-253.
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.), 267-281.
Gideon Schwarz (1978) Estimating the Dimension of a Model. The Annals of Statistics, 6, 461-464.
Jiahua Chen and Zehua Chen (2008) Extended Bayesian Information Criteria for Model Selection with Large Model Spaces. Biometrika, 95, 759-771.
# NOT RUN {
set.seed(0)
data('leukemia.train', package = 'SIS')
y.train = leukemia.train[,dim(leukemia.train)[2]]
x.train = as.matrix(leukemia.train[,-dim(leukemia.train)[2]])
x.train = standardize(x.train)
model = tune.fit(x.train[,1:3500], y.train, family='binomial', tune='bic')
model$ix
model$a0
model$beta
# }
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