cmenet {cmenet}

Bi-level selection of conditional main effects (fixed parameters)

Description

cmenet performs variable selection of conditional main effects (CMEs) via a bi-level penalization framework, given fixed penalty parameters.

Usage

cmenet(xme, xcme, y,
          lambda.sib=exp(seq(from=log(max.lambda),to=log(max.lambda*1e-6),length=20)),
          lambda.cou=exp(seq(from=log(max.lambda),to=log(max.lambda*1e-6),length=20)),
          max.lambda=lambda0.cme(cbind(xme,xcme),y),
          gamma=1/(0.5-tau)+0.001, tau=0.01,
          act.vec=rep(1,ncol(xme)+ncol(xcme)),
          beta0=rep(0,ncol(xme)+ncol(xcme)),
          it.max=250, lambda.flg=T)

Arguments

xme

An n x p binary model matrix for MEs.

xcme

An n x (4*choose(p,2)) model matrix for CMEs.

y

An n-length response vector.

lambda.sib

Penalty vector for sibling CMEs.

lambda.cou

Penalty vector for cousin CMEs.

max.lambda

Maximum penalty value.

gamma

Bridge parameter in MC+ penalty.

tau

Coupling parameter for CMEs.

act.vec

A (p+4*choose(p,2))-length binary vector for setting which variables are always active in optimization.

beta0

Initial regression coefficients.

it.max

Number of optimization iterations.

lambda.flg

Use the default option TRUE (unless within cv.cmenet).

Value

coefficients

Array of regression coefficients (over different lambda.sib and lambda.cou).

residuals

Array of regression residuals (over different lambda.sib and lambda.cou).

inter

Matrix of intercept estimates (over different lambda.sib and lambda.cou).

References

Mak and Wu (2018). cmenet: a new method for bi-level variable selection of conditional main effects. Journal of the American Statistical Association, to appear.

Examples

## Not run: 
    library(MASS)
n <- 50 #number of observations
p <- 50 #number of main effects

## Simulate model matrix for MEs and CMEs
set.seed(1)
rho <- 0 #correlation
ones <- matrix(1,p,p)
covmtx <- rho*ones+(1-rho)*diag(p)
latmtx <- mvrnorm(n,p,mu=rep(0,p),Sigma=covmtx) #equicorrelated cov. matrix
memtx <- (latmtx>=0)-(latmtx<0) #simulate model matrix for MEs
model.mtx <- full.model.mtx(memtx)$model.mtx #generate model matrix for MEs and CMEs

## Set true model and generate response
num.act <- 2 # two siblings active
num.grp <- 4 # ... within four active groups
ind <- c()
for (ii in 1:num.grp){
  eff <- sample(seq(2*(p-1)),num.act)
  ind <- c(ind, p + eff + (ii-1)*(2*(p-1)))
}
colnames(model.mtx)[ind] # active CMEs

des.mtx <- model.mtx[,ind]
inter <- 12 #intercept
xbtrue <- inter + rowSums(des.mtx)
y <- xbtrue + rnorm(n,sd=1) #response
xme <- model.mtx[,1:p]
xcme <- model.mtx[,(p+1):ncol(model.mtx)]

## Run cmenet
cv.cme <- cv.cmenet(xme, xcme, y, var.names=colnames(model.mtx))

## End(Not run)