path.plot: Plot the solution path for the concave 1-norm and 2-norm...

In grppenalty: Concave 1-norm and 2-norm group penalty in linear and logistic regression

Description

Plot the coefficient profiles of each penalized variable for the concave 1-norm and 2-norm group penalties.

Usage

path.plot(out)

Arguments

out	the object return from the grppenalty function

Details

The package implements the concave 1-norm and 2-norm group penalties in linear and logistic regression models. The concave 1-norm group penalty is defined as rho(|beta|_1;d*lambda,kappa) with |beta|_1 being the L1 norm of the coefficients and d being the group size. The concave 2-norm group penalty is defined as rho(|beta|_2;sqrt(d)*lambda,kappa) with |beta|_2 being the L2 norm of the coefficients. Here rho() is the concave function, in current implementation, we only consider the smoothly clipped absolute deviation (SCAD) penalty and minimum concave penalty (MCP).

The concave 1-norm group penalties, i.e. 1-norm gSCAD or gMCP, perform variable selection at group and individual levels under proper tuning parameters. The concave 2-norm group penalties, i.e. 2-norm gSCAD or gMCP selects variable at group level, i.e. the variables in the same group are dropped or selected at the same time. One advantage of of the 1-norm group penalty is that it is robust to mis-specified group information. The 2-norm group penalty is, however, affected by the mis-specified group information. The concave 2-norm group penalty includes group Lasso as a special case when the regularization parameter kappa=0. Hence, setting kappa=0 in the 2-norm group penalty returns the group Lasso solutions.

The solution path plot shows the coefficients profile of variables in x. It illustrates the effect of penalization. Depending on the kappa value specified, a total of nkappa figures will be plotted.

Author(s)

Dingfeng Jiang

References

Jiang, D., Huang, J., Zhang, Y. (2011). The cross-validated AUC for MCP-Logistic regression with high-dimensional data. Statistical Methods in Medical Research, online first.

Yuan, M., Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of Royal Statistical Society Series B, 68 (1): 49 - 67.

Meier, L., van de Geer, S., B\”uhlmann, P., (2008). The group lasso for logistic regression. Journal of Royal Statistical Society Series B, 70 (1): 53 - 71

See Also

grppenalty

Examples

set.seed(10000)
n=100
ybi=rbinom(n,1,0.4)
yga=rnorm(n)
p=20
x=matrix(rnorm(n*p),n,p)
index=rep(1:10, each =2)
out=grppenalty(yga, x, index, "gaussian", "l1", "mcp",  c(0,1/2.7))
path.plot(out)

grppenalty documentation built on May 30, 2017, 4:33 a.m.