GLMvanISISscad {SIS}R Documentation

(Iterative) Sure Independence Screening ((I)SIS) in Generalized Linear Models

Description

These functions implement the iterative sure independence screening with GLMvanISISscad for vanilla ISIS and GLMvarISISscad for variant ISIS in Generalized Linear Models.

Usage

GLMvanISISscad(x, y, nsis=NULL, family=binomial(), folds=folds, 
rank.method="obj", eps0=1e-3, inittype='NoPen', tune.method="AIC",  
ISIStypeCumulative=FALSE, DOISIS=TRUE, maxloop=5)
  
GLMvarISISscad(x, y, nsis=NULL, family=binomial(), folds=folds, 
rank.method="obj", tune.method="AIC", vartype="First", eps0=1e-3, 
inittype='NoPen',  ISIStypeCumulative=FALSE, DOISIS=TRUE, maxloop=5)

Arguments

x an (n * p) matrix of features.
y an (n) vector of response.
nsis number of pedictors recuited by (I)SIS.
family a description of the error distribution and link function to be used in the model.
folds fold information for cross validation.
rank.method the criterion for ranking predictor variables in (I)SIS. It can be either obj or coeff.
tune.method method for tuning regularization parameter.
inittype inittype specifies the type of initial solution for the one-step SCAD. It can be either NoPen or L1.
vartype vartype specifies variant (I)SIS of first type or second type.
ISIStypeCumulative ISIStypeCumulative specifies whether to allow variable deletion in each step of ISIS. (ISIStypeCumulative= FALSE allows variable deletion)
DOISIS DOISIS specifies whether to do iterative SIS.
maxloop maximum number of loops in iterative SIS.
eps0 an effective zero.

Value

Returns an object with

initRANKorder initial predictor ranking order for vanilla SIS.
detail.pickind, detail.ISISind details of each loop of ISIS.
normal.exit indicator of normal exit.
SISind the vector of indices selected by SIS.
ISISind the vector of indices selected by ISIS.
initRANKorder1, initRANKorder2 initial predictor ranking order for variant SIS.

Author(s)

Jianqing Fan, Yang Feng, Richard Samworth, and Yichao Wu

References

Jianqing Fan and Jinchi Lv (2008) Sure independence screening for ultra-high dimensional feature space (with discussion) Journal of Royal Statistical Society B, 36, 849-911.

Jianqing Fan, Richard Samworth, and Yichao Wu (2009) Ultrahigh dimensional variable selection: beyond the linear model Journal of Machine Learning Research, to appear.

Jianqing Fan and Rui Song (2009) Sure Independence Screening in Generalized Linear Models with NP-Dimensionality, technical report.

See Also

scadglm, fullscadglm

Examples

set.seed(0)
b <- c(4,4,4,-6*sqrt(2))
n=150
p=200
truerho=0.5
corrmat=diag(rep(1-truerho, p))+matrix(truerho, p, p)
corrmat[,4]=sqrt(truerho)
corrmat[4, ]=sqrt(truerho)
corrmat[4,4]=1
cholmat=chol(corrmat)
x=matrix(rnorm(n*p, mean=0, sd=1), n, p)
x=x%*%cholmat
feta=x[, 1:4]%*%b
fprob=exp(feta)/(1+exp(feta))
y=rbinom(n, 1, fprob)

nsis=floor(n/log(n)/4)

binom.van.sis=GLMvanISISscad(x, y, nsis, family=binomial(), tune.method='BIC')
binom.var.sis=GLMvarISISscad(x, y, nsis, family=binomial(), vartype='Second', 
tune.method='BIC')

#####compare the result
binom.van.sis$SIS

binom.van.sis$ISIS

binom.var.sis$SIS

binom.var.sis$ISIS

[Package SIS version 0.2 Index]