Fit a GLM with a combination of sparse and smooth regularization

Description

Fit a generalized linear model at grids of tuning parameter via penalized maximum likelihood. The regularization path is computed for a combination of sparse and smooth penalty at two grids of values for the regularization parameter lambda1(Lasso or MCP penalty) and lambda2(Laplacian penalty). Fits linear, logistic regression models.

Details

Package: glmgraph
Type: Package
Version: 1.0-0
Date: 2015-03-11
License: GPL-2

The algorithm accepts a design matrix X, a vector of responses Y and a Laplacian matrix L. Produces the regularization path over the grid of tuning parameter lambda1 and lambda2. It consists of the following main functions
glmgraph
cv.glmgraph
plot.glmgraph
coef.glmgraph
predict.glmgraph

Author(s)

Li Chen <li.chen@emory.edu>, Jun Chen <jun.chen2@mayo.edu>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen(2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

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 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## Construct Adjacency and Laplacian matrices
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L,family="gaussian")
 plot(obj)
 betas <- coef(obj)
 betas <- coef(obj,lambda1=c(0.1,0.2))
 yhat <- predict(obj,X,type="response")
 cv.obj <- cv.glmgraph(X,Y,L)
 plot(cv.obj)
 beta.min <- coef(cv.obj)
 yhat.min <- predict(cv.obj,X)