SIS: (Iterative) Sure Independence Screening ((I)SIS) and Fitting...

In SIS: Sure Independence Screening

(Iterative) Sure Independence Screening ((I)SIS) and Fitting in Generalized Linear Models and Cox's Proportional Hazards Models

Description

This function first implements the Iterative Sure Independence Screening for different variants of (I)SIS, and then fits the final regression model using the R packages ncvreg, glmnet, and msaenet plus an internal Cox adaptive elastic-net implementation for the SCAD/MCP/LASSO/ENET/AENET regularized loglikelihood for the variables picked by (I)SIS.

Usage

SIS(
  x,
  y,
  family = c("gaussian", "binomial", "poisson", "cox", "multinom"),
  penalty = c("SCAD", "MCP", "lasso", "enet", "aenet", "msaenet"),
  concavity.parameter = switch(penalty, SCAD = 3.7, 3),
  tune = c("bic", "ebic", "aic", "cv"),
  nfolds = 10,
  type.measure = c("deviance", "class", "auc", "mse", "mae"),
  gamma.ebic = 1,
  nsis = NULL,
  iter = TRUE,
  iter.max = ifelse(greedy == FALSE, 10, floor(nrow(x)/log(nrow(x)))),
  varISIS = c("vanilla", "aggr", "cons"),
  perm = FALSE,
  q = 1,
  greedy = FALSE,
  greedy.size = 1,
  seed = NULL,
  standardize = TRUE,
  covars = NULL,
  boot_ci = FALSE,
  parallel = TRUE
)

Arguments

x	The design matrix, of dimensions n * p, without an intercept. Each row is an observation vector. SIS standardizes the data and includes an intercept by default.
y	The response vector of dimension n * 1. Quantitative for family='gaussian', non-negative counts for family='poisson', binary (0-1) for family='binomial', factor for family='multinom'. For family='cox', y should be an object of class Surv, as provided by the function Surv() in the package survival.
family	Response type (see above).
penalty	The penalty to be applied in the regularized likelihood subproblems. 'SCAD', 'MCP', or 'lasso' are provided. 'lasso' is the default for family = 'multinom' or 'cox', 'SCAD' is the default for other families.
concavity.parameter	The tuning parameter used to adjust the concavity of the SCAD/MCP penalty. Default is 3.7 for SCAD and 3 for MCP.
tune	Method for tuning the regularization parameter of the penalized likelihood subproblems and of the final model selected by (I)SIS. Options include tune='bic', tune='ebic', tune='aic', and tune='cv'.
nfolds	Number of folds used in cross-validation. The default is 10.
type.measure	Loss to use for cross-validation. Currently five options, not all available for all models. The default is type.measure='deviance', which uses squared-error for gaussian models (also equivalent to type.measure='mse' in this case), deviance for logistic and poisson regression, and partial-likelihood for the Cox model. Both type.measure='class' and type.measure='auc' apply only to logistic regression and give misclassification error and area under the ROC curve, respectively. type.measure='mse' or type.measure='mae' (mean absolute error) can be used by all models except the 'cox'; they measure the deviation from the fitted mean to the response. For penalty='SCAD' and penalty='MCP', only type.measure='deviance' is available.
gamma.ebic	Specifies the parameter in the Extended BIC criterion penalizing the size of the corresponding model space. The default is gamma.ebic=1. See references at the end for details.
nsis	Number of pedictors recuited by (I)SIS.
iter	Specifies whether to perform iterative SIS. The default is iter=TRUE.
iter.max	Maximum number of iterations for (I)SIS and its variants.
varISIS	Specifies whether to perform any of the two ISIS variants based on randomly splitting the sample into two groups. The variant varISIS='aggr' is an aggressive variable screening procedure, while varISIS='cons' is a more conservative approach. The default is varISIS='vanilla', which performs the traditional vanilla version of ISIS. See references at the end for details.
perm	Specifies whether to impose a data-driven threshold in the size of the active sets calculated during the ISIS procedures. The threshold is calculated by first decoupling the predictors x_i and response y_i through a random permutation \pi of (1,...,n) to form a null model. For this newly permuted data, marginal regression coefficients for each predictor are recalculated. As the marginal regression coefficients of the original data should be larger than most recalculated coefficients in the null model, the data-driven threshold is given by the qth quantile of the null coefficients. This data-driven threshold only allows a 1-q proportion of inactive variables to enter the model when x_i and y_i are not related (in the null model). The default is here is perm=FALSE. See references at the end for details.
q	Quantile for calculating the data-driven threshold in the permutation-based ISIS. The default is q=1 (i.e., the maximum absolute value of the permuted estimates).
greedy	Specifies whether to run the greedy modification of the permutation-based ISIS. The default is greedy=FALSE.
greedy.size	Maximum size of the active sets in the greedy modification of the permutation-based ISIS. The default is greedy.size=1.
seed	Random seed used for sample splitting, random permutation, and cross-validation sampling of training and test sets.
standardize	Logical flag for x variable standardization, prior to performing (iterative) variable screening. The resulting coefficients are always returned on the original scale. Default is standardize=TRUE. If variables are in the same units already, you might not wish to standardize.
covars	Names of the factor variables.
boot_ci	Logical flag for computing bootstrap confidence intervals. Default = FALSE.
parallel	Specifies whether to conduct parallel computing

Value

A list with components:

sis.ix0

The vector of indices selected by only SIS.

ix

The vector of indices selected by (I)SIS with the regularization step.

coef.est

The vector of coefficients of the final model selected by (I)SIS.

fit

A fitted object of type ncvreg, cv.ncvreg, glmnet, or cv.glmnet for the final model selected by the (I)SIS procedure. If tune='cv', the returned fitted object is of type cv.ncvreg if penalty='SCAD' or penalty='MCP'; otherwise, the returned fitted object is of type cv.glmnet. For the remaining options of tune, the returned object is of type glmnet if penalty='lasso', and ncvreg otherwise.

path.index

The index along the solution path of fit for which the criterion specified in tune is minimized.

ix0

The vector of indices ordered by decreasing importance.

ix_list

The list of vectors of indices ordered by decreasing importance, for each screening step.

cis

A data frame with columns coef, CI_low, CI_up, Est, CI_low_perc, and CI_up_perc.

Author(s)

Jianqing Fan, Yang Feng, Diego Franco Saldana, Richard Samworth, Arce Domingo-Relloso and Yichao Wu

References

Diego Franco Saldana and Yang Feng (2018) SIS: An R package for Sure Independence Screening in Ultrahigh Dimensional Statistical Models, Journal of Statistical Software, 83, 2, 1-25.

Jianqing Fan and Jinchi Lv (2008) Sure Independence Screening for Ultrahigh Dimensional Feature Space (with discussion). Journal of Royal Statistical Society B, 70, 849-911.

Jianqing Fan and Rui Song (2010) Sure Independence Screening in Generalized Linear Models with NP-Dimensionality. The Annals of Statistics, 38, 3567-3604.

Jianqing Fan, Richard Samworth, and Yichao Wu (2009) Ultrahigh Dimensional Feature Selection: Beyond the Linear Model. Journal of Machine Learning Research, 10, 2013-2038.

Jianqing Fan, Yang Feng, and Yichao Wu (2010) High-dimensional Variable Selection for Cox Proportional Hazards Model. IMS Collections, 6, 70-86.

Jianqing Fan, Yang Feng, and Rui Song (2011) Nonparametric Independence Screening in Sparse Ultrahigh Dimensional Additive Models. Journal of the American Statistical Association, 106, 544-557.

Jiahua Chen and Zehua Chen (2008) Extended Bayesian Information Criteria for Model Selection with Large Model Spaces. Biometrika, 95, 759-771.

Domingo-Relloso, Arce, Yang Feng, Zulema Rodriguez-Hernandez, Karin Haack, Shelley A. Cole, Ana Navas-Acien, Maria Tellez-Plaza, and Jose D. Bermudez (2024) Omics feature selection with the extended SIS R package: identification of a body mass index epigenetic multimarker in the Strong Heart Study. American Journal of Epidemiology, 193, no. 7: 1010-1018.

See Also

predict.SIS

Examples

set.seed(0)
n <- 400
p <- 50
rho <- 0.5
corrmat <- diag(rep(1 - rho, p)) + matrix(rho, p, p)
corrmat[, 4] <- sqrt(rho)
corrmat[4, ] <- sqrt(rho)
corrmat[4, 4] <- 1
corrmat[, 5] <- 0
corrmat[5, ] <- 0
corrmat[5, 5] <- 1
cholmat <- chol(corrmat)
x <- matrix(rnorm(n * p, mean = 0, sd = 1), n, p)
x <- x %*% cholmat

# gaussian response
set.seed(1)
b <- c(4, 4, 4, -6 * sqrt(2), 4 / 3)
y <- x[, 1:5] %*% b + rnorm(n)


# SIS without regularization
model10 <- SIS(x, y, family = "gaussian", iter = FALSE)
model10$sis.ix0
# The top 10 selected variables
model10$ix0[1:10]
# The top 10 selected variables for each step
lapply(model10$ix_list, f <- function(x) {
  x[1:10]
})
# ISIS with regularization
model11 <- SIS(x, y, family = "gaussian", tune = "bic")
model12 <- SIS(x, y, family = "gaussian", tune = "bic", varISIS = "aggr", seed = 11)
model11$ix
model12$ix
## Not run: 
# binary response
set.seed(2)
feta <- x[, 1:5] %*% b
fprob <- exp(feta) / (1 + exp(feta))
y <- rbinom(n, 1, fprob)
model21 <- SIS(x, y, family = "binomial", tune = "bic")
model22 <- SIS(x, y, family = "binomial", tune = "bic", varISIS = "aggr", seed = 21)
model21$ix
model22$ix

# poisson response
set.seed(3)
b <- c(0.6, 0.6, 0.6, -0.9 * sqrt(2))
myrates <- exp(x[, 1:4] %*% b)
y <- rpois(n, myrates)
model31 <- SIS(x, y,
  family = "poisson", penalty = "lasso", tune = "bic", perm = TRUE, q = 0.9,
  greedy = TRUE, seed = 31
)
model32 <- SIS(x, y,
  family = "poisson", penalty = "lasso", tune = "bic", varISIS = "aggr",
  perm = TRUE, q = 0.9, seed = 32
)
model31$ix
model32$ix


# Cox model
set.seed(4)
b <- c(4, 4, 4, -6 * sqrt(2), 4 / 3)
myrates <- exp(x[, 1:5] %*% b)
Sur <- rexp(n, myrates)
CT <- rexp(n, 0.1)
Z <- pmin(Sur, CT)
ind <- as.numeric(Sur <= CT)
y <- survival::Surv(Z, ind)
model41 <- SIS(x, y,
  family = "cox", penalty = "lasso", tune = "bic",
  varISIS = "aggr", seed = 41
)
model42 <- SIS(x, y,
  family = "cox", penalty = "lasso", tune = "bic",
  varISIS = "cons", seed = 41
)
model41$ix
model42$ix

# SIS with bootstrap confidence intervals
sis <- SIS(x, y, family = "cox", penalty='aenet', tune='cv', varISIS='cons',
seed = 41, boot_ci=FALSE)
sis$cis

## End(Not run)

SIS documentation built on March 14, 2026, 9:07 a.m.