standard: Standardizes a design matrix

In SSLASSO: The Spike-and-Slab LASSO

Standardizes a design matrix

Description

The function 'standard' 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). The code has been adapted from the 'ncvreg' package (Breheny and Huang, 2011).

Usage

standard(X)

Arguments

X	A matrix (or object that can be coerced to a matrix, such as a data frame).

Details

This function centers and scales each column of 'X' so that

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

and

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

for all j. This is usually not necessary to call directly, as 'SSLASSO' 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 'standard' uses the root-mean-square, or population, standard deviation 'sqrt(mean(sum(x^2)))', and (2) 'standard' is faster. The reason for using the population standard deviation is that 'SSLASSO' assumes that the columns of the design matrix have been scaled to have norm 'sqrt(n)'.

Value

A standardized matrix with attributes for center, scale, and non-singular columns.

SSLASSO documentation built on Nov. 5, 2025, 7:40 p.m.