ttest.ppls: t-Test for Penalized PLS Regression Coefficients

Description

Computes two-sided t-tests and p-values for the regression coefficients of a penalized PLS model based on jackknife estimation.

Usage

ttest.ppls(
  ppls.object,
  ncomp = ppls.object$ncomp.opt,
  index.lambda = ppls.object$index.lambda
)

Value

A list with:

tvalues: Numeric vector of t-statistics.
pvalues: Numeric vector of two-sided p-values.

Arguments

ppls.object: An object returned by penalized.pls.cv, containing the jackknife array coefficients.jackknife.
ncomp: Integer. Number of PLS components to use. Default is ppls.object$ncomp.opt.
index.lambda: Integer. Index of the penalty parameter lambda to use. Default is ppls.object$index.lambda.

Details

This function calls jack.ppls to estimate:

The mean of the jackknife coefficients (point estimates),
The covariance matrix (for standard errors),
The degrees of freedom, equal to k - 1, where k is the number of cross-validation folds.

It then performs standard two-sided t-tests: $$t_j = \frac{\hat{\beta}_j}{\text{SE}_j}, \quad \text{df} = k - 1$$ and computes associated p-values.

These p-values can be used for variable selection or inference, although they are based on cross-validation folds and should be interpreted with caution.

Examples

Run this code

set.seed(123)
X <- matrix(rnorm(20 * 100), ncol = 20)
y <- rnorm(100)
result <- penalized.pls.cv(X, y, lambda = c(0, 1), ncomp = 3)
tstats <- ttest.ppls(result)
print(tstats$pvalues)