SIS (version 0.4)

GLMvanISISscad: (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-5, 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-5,
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 penalize variables selected by the previous step of the ISIS iteration in the following SCAD step. (ISIStypeCumulative= FALSE put penalties on all variables. In this case, the procedure is

DOISIS

DOISIS specifies whether to do iterative SIS.

maxloop

maximum number of loops in iterative SIS.

eps0

an effective zero relative to the scale of the maximum absolute marginal regression coefficients.

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.

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