mvnorm.l2boost: multivariate normal data simulations.

In l2boost: Exploring Friedman's Boosting Algorithm for Regularized Linear Regression

Description

Create simulated dataset from a multivariate normal. Used to recreate data simulations from Ehrlinger and Ishwaran (2012).

Usage

mvnorm.l2boost(n = 100, p = 100, beta = NULL, which.beta = NULL, rho = 0)

Arguments

n	number of observations
p	number of coordinate directions in the design matrix
beta	a "true" beta vector of length p (default=NULL) See details.
which.beta	indicator vector for which beta coefficients to include as signal in simulation (default=NULL) see details
rho	correlation coefficient between coordinate directions

Details

By default, mvnorm.l2boost creates a data set of n multivariate normal random observations of p covariates (see MASS:mvrnorm). The correlation matrix is constructed with 1 on the diagonals and the correlation coefficient rho on the off diagonals.

The response is constructed as follows: If a true beta vector is not supplied, the first 10 beta coefficients carry the signal with a value of 5, and the remaining p-10 values are set to zero. Given a beta.true vector, all values are used as specified. The coefficent vector is truncated to have p signal terms if length(beta.true) > p, and noise coordinates are added if length(beta.true) < p.

It is possible to pass an indicator vector which.beta to select specific signal elements from the full vector beta.true.

Value

• call Matched function call

• x design matrix of size n x p

• y response vector of length n

References

Ehrlinger J., and Ishwaran H. (2012). "Characterizing l2boosting" Ann. Statist., 40 (2), 1074-1101

Examples

#--------------------------------------------------------------------------
# Example: Multivariate normal data simulation

# Create a (reproducable) data set of size 100 x 100
set.seed(1024)
n<- 100
p<- 100

# Set 10 signal variables using a uniform beta=5, the remaining (p-10)=90 are
# set to zero indicating random noise.  
beta <- c(rep(5,10), rep(0,p-10))

# Example with orthogonal design matrix columns (orthogonal + noise)
ortho.data <- mvnorm.l2boost(n, p, beta)
cbind(ortho.data$y[1:5],ortho.data$x[1:5,])

# Example with correlation between design matrix columns
corr.data <- mvnorm.l2boost(n, p, beta, rho=0.65)
cbind(corr.data$y[1:5],corr.data$x[1:5,])

l2boost documentation built on Feb. 11, 2022, 5:10 p.m.