std: Standardizes a design matrix

In ncvreg: Regularization Paths for SCAD and MCP Penalized Regression Models

Standardizes a design matrix

Description

Accepts a design matrix and returns a standardized version of that matrix (i.e., each column will have mean 0 and mean sum of squares equal to 1).

Usage

std(X, Xnew)

Arguments

X	A matrix (or object that can be coerced to a matrix, such as a data frame or numeric vector).
Xnew	Optional. If supplied, X must be the output of std() and Xnew is to be standardized in the same way. See examples for why this might be useful.

Details

This function centers and scales each column of X so that

\sum_{i=1}^n x_{ij}=0

and

n^{-1} \sum_{i=1}^n x_{ij}^2 = 1

for all j. This is usually not necessary to call directly, as ncvreg internally standardizes the design matrix, but inspection of the standardized design matrix can sometimes be useful. This differs from the base R function scale() in two ways:

1. scale() uses the sample standard deviation sqrt(sum(x^2)/(n-1)), while std() uses the root-mean-square standard deviation ⁠sqrt(mean(sum(x^2))⁠ without the n/(n-1) correction

2. std is faster.

Value

The standardized design matrix, with the following attribues:

center, scale	mean and standard deviation used to scale the columns
nonsingular	A vector indicating which columns of the original design matrix were able to be standardized (constant columns cannot be standardized to have a standard deviation of 1)

Examples

data(Prostate)
S <- std(Prostate$X)
apply(S, 2, sum)
apply(S, 2, function(x) mean(x^2))

# Standardizing new observations
X1 <- Prostate$X[1:90,]
X2 <- Prostate$X[91:97,]
S <- std(X1)
head(std(S, X2))
# Useful if you fit to a standardized X, but then get new obs:
y <- Prostate$y[1:90]
fit <- ncvreg(S, y)
predict(fit, std(S, X2), lambda=0.1)
# Same as
predict(ncvreg(X1, y), X2, lambda=0.1)

ncvreg documentation built on Sept. 11, 2024, 8:31 p.m.