simulateDCSIS {VariableScreening}

Simulate a dataset for demonstrating the performance of screenIID with the DC-SIS method

Description

Simulates a dataset that can be used to demonstrate variable screening for ultrahigh-dimensional regression with the DC-SIS option in screenIID. The simulated dataset has p numerical predictors X and a categorical Y-response. The data-generating scenario is a simplified version of Example 3.1a (homoskedastic) or 3.1d (heteroskedastic) of Li, Zhong & Zhu (2012). Specifically, the X covariates are normally distributed with mean zero and variance one, and may be correlated if the argument rho is set to a nonzero value. The response Y is generated as either Y = 6*X1 + 1.5*X2 + 9*1X12 < 0 + exp(2*X22)*e if heteroskedastic=TRUE, or Y = 6*X1 + 1.5*X2 + 9*1X12 < 0 + 6*X22 + e if heteroskedastic=FALSE, where e is a standard normal error term and 1 is a zero-one indicator function for the truth of the statement contained. Special thanks are due to Wei Zhong for providing some of the code upon which this function is based.

Usage

simulateDCSIS(n = 200, p = 5000, rho = 0, heteroskedastic = TRUE)

Arguments

n

Number of subjects in the dataset to be simulated. It will also equal to the number of rows in the dataset to be simulated, because it is assumed that each row represents a different independent and identically distributed subject.

p

Number of predictor variables (covariates) in the simulated dataset. These covariates will be the features screened by DC-SIS.

rho

The correlation between adjacent covariates in the simulated matrix X. The within-subject covariance matrix of X is assumed to has the same form as an AR(1) autoregressive covariance matrix, although this is not meant to imply that the X covariates for each subject are in fact a time series. Instead, it is just used as an example of a parsimonious but nontrivial covariance structure. If rho is left at the default of zero, the X covariates will be independent and the simulation will run faster.

heteroskedastic

Whether the error variance should be allowed to depend on one of the predictor variables.

Value

A list with following components: X Matrix of predictors to be screened. It will have n rows and p columns. Y Vector of responses. It will have length n.

References

Li, R., Zhong, W., & Zhu, L. (2012) Feature screening via distance correlation learning. Journal of the American Statistical Association, 107: 1129-1139. <DOI:10.1080/01621459.2012.695654>

Examples

set.seed(12345678)
results <- simulateDCSIS()