---
title: "SURF"
output: rmarkdown::pdf_document
vignette: >
  %\VignetteIndexEntry{SURF}
  %\VignetteEngine{knitr::knitr}
  %\VignetteEncoding{UTF-8}
  
---
title: "SURF:Subsampling ranking forward selection"

author: "Lihui Liu"

package: SURF'

---

## Summary


Performs variable selection based on subsampling, ranking forward
selection. \textrm{Xo} is the matrix of predictor
variables. \textrm{y} is the response variable. \textrm{X} is a
matrix of additional predictors which should be scaled to have sum 1
prior to analysis. \textrm{fold} is the number of folds for
cross-validation. \textrm{Alpha} is the parameter for the elastic net
method used in the subsampling procedure: the default value of 1
corresponds to LASSO. alpha_u is the upper bound of the significance level for the permutation test.\textrm{alpha} is a single or a sequence of significance level of interest.\textrm{prop} is the proportion of variables to
remove in the each subsample. \textrm{weights} indicates whether
observations should be weighted by class size. When the class sizes
are unbalanced, weighting observations can improve results. For binomial family, this paramter should be set to TRUE or FALSE; For other families, the parameter can be FALSE or the user supply the weights vector of the same length of the sample size N.\textrm{B}
is the number of subsamples to use for ranking the
variables. \textrm{C} is the number of permutations to use for
estimating the critical value of the null distribution. If the
\textrm{doParallel} package is installed, the function can be run in
parallel by setting \textrm{ncores} to the number of threads to
use. If the default value of 1 is used, or if the \textrm{doParallel}
package is not installed, the function does not run in
parallel. \textrm{display.progress} indicates whether the function
should display messages indicating its progress.  \textrm{family} is a
family variable for the glm fitting. Note that the \texttt{glmnet}
package does not currently permit the use of non-standard link
functions, so will always use the default link function. However, the
glm fitting will use the specified link. The default is binomial with
logistic regression, because this is a common use case. \textrm{pval}
is the $p$-value for inclusion of a variable in the model and it is discontinued since version 1.1.0. Under the
null case, the number of false positives will be geometrically
distributed with this as probability of success, so if this parameter
is set to $p$, the expected number of false positives should be
$\frac{p}{1-p}$.


```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```
```{r}

set.seed(12345)

library(SuRF.vs)
N=50
p=20
nzc=p/3
X=matrix(rnorm(N*p),N,p)
beta=rnorm(nzc)
fx=X[,seq(nzc)]%*%beta/3
hx=exp(fx)
ty=rexp(N,hx)
tcens=rbinom(n=N,prob=.3,size=1)# censoring indicator (1 or 0)

Xo=NULL
B=20
Alpha=1
fold=5

ncores=1
prop=0.1
C=3
alpha_u=0.2

alpha=seq(0.01,0.1,len=5)


 
 #binomial model
 XX=X[,1:2]
 f=1+XX%*%c(2,1.5)
 p=exp(f)/(1+exp(f))
 y=rbinom(100,1,p)
 weights=FALSE
 family=stats::binomial(link="logit")
 surf_binary=SURF(Xo=X,y=y,X=NULL,fold=5,Alpha=1,prop=0.1,weights=weights,B=50,C=10,ncores=1,display.progress=TRUE,family=family,alpha_u=0.1,alpha=alpha)
 
 
 #linear regression
 y=1+XX%*%c(0.1,0.2)
 
 family=stats::gaussian(link="identity")
 surf_lm=SURF(Xo=X,y=y,X=NULL,fold=5,Alpha=1,prop=0.1,weights=weights,B=100,C=15,ncores=1,display.progress=TRUE,family=family,alpha_u=0.1,alpha=alpha)
 
 
 #cox proportional model
 y=cbind(time=ty,status=1-tcens)
 family=list(family="cox")
 surf_cox=SURF(Xo=X,y=y,X=NULL,fold=5,Alpha=1,prop=0.1,weights=FALSE,B=50,C=5,ncores=1,display.progress=TRUE,family=family,alpha_u=alpha_u,alpha=alpha)
```
