cvplogistic: Majorization minimization by coordinate descent for concave...

In cvplogistic: Penalized Logistic Regression Model using Majorization Minimization by Coordinate Descent (MMCD) Algorithm

Description

Compute solution surface for a high-dimensional logistic regression model with concave penalty using MMCD, adaptive rescaling or LLA-CD algorithms

Usage

cvplogistic(y, x, penalty = "mcp", approach = "mmcd", kappa = 1/2.7,
nlambda = 100, lambda.min = 0.01, epsilon = 1e-3, maxit = 1e+3)

Arguments

y	response vector with elements 0 or 1.
x	the design matrix of penalized variables. By default, an intercept vector will be added when fitting the model.
penalty	a character specifying the penalty. One of "mcp" or "scad" should be specified, with "mcp" being the default.
approach	a character specifying the numerical algorithm. One of "mmcd", "adaptive" or "llacda" can be specified, with "mmcd" being the default. See following details for more information.
kappa	a value specifying the regulation parameter kappa. The proper range for kappa is [0, 1).
nlambda	a integer value specifying the number of grids along the penalty parameter lambda.
lambda.min	a value specifying how to determine the minimal value of penalty parameter lambda. We define lambda_min=lambda_max*lambda.min. We suggest lambda.min=0.0001 if n>p; 0.01 otherwise.
epsilon	a value specifying the converge criterion of algorithm.
maxit	an integer value specifying the maximum number of iterations for each coordinate.

Details

The computation for logistic model with concave penalties is not easy. The MMCD package implements the majorization minimization by coordinate descent (MMCD) algorithm for computing the solution path for logistic model with SCAD or MCP penalties. The algorithm is very efficient and stable for high-dimensional data with p>>n. For the MCP penalty, the package also implements the adaptive rescaling and the local linear approximation by coordinate descent algorithms (LLA-CDA) algorithms. For SCAD, only the MMCD algorithm is implemented.

The regularization parameter controls the concavity of the penalty, with larger value of kappa being more concave. When kappa=0, both the MCP and SCAD penalty become Lasso penalty. Hence if zero is specified for kappa, the algorithm returns Lasso solutions.

Value

A list of two elements is returned.

coef	a matrix of dimension (p+1)*nlambda, with p the number of variables (columns) in x. The 1st row is the intercept, which is added by default.
lambdas	a vector of length nlambda for the penalty parameter lambda, ranging from the largest to the smallest.

Author(s)

Dingfeng Jiang

References

Dingfeng Jiang, Jian Huang. Majorization Minimization by Coordinate Descent for Concave Penalized Generalized Linear Models.

Zou, H., Li, R. (2008). One-step Sparse Estimates in Nonconcave Penalized Likelihood Models. Ann Stat, 364: 1509-1533.

Breheny, P., Huang, J. (2011). Coordinate Descent Algorithms for Nonconvex Penalized Regression, with Application to Biological Feature Selection. Ann Appl Stat, 5(1), 232-253.

Jiang, D., Huang, J., Zhang, Y. (2011). The Cross-validated AUC for MCP-Logistic Regression with High-dimensional Data. Stat Methods Med Res, online first, Nov 28, 2011.

See Also

hybrid.logistic, cv.cvplogistic, cv.hybrid, path.plot

Examples

set.seed(10000)
n=100
y=rbinom(n,1,0.4)
p=10
x=matrix(rnorm(n*p),n,p)

## MCP penalty by MMCD algorithm
out=cvplogistic(y, x, "mcp", "mmcd")
## MCP by adaptive rescaling algorithm
## out=cvplogistic(y, x, "mcp", "adaptive")
## MCP by LLA-CD algorith,
## out=cvplogistic(y, x, "mcp", "llacd")
## SCAD penalty
## out=cvplogistic(y, x, "scad")

## Lasso penalty
out=cvplogistic(y, x, kappa =0)

cvplogistic documentation built on May 29, 2017, 11:34 p.m.