This function computes the lower bound for the the Degrees of Freedom of PLS with 1 component.

compute.lower.bound(X)

## Arguments

X matrix of predictor observations.

## Value

bound

logical. bound is TRUE if the decay of the eigenvalues is slow enough

lower.bound

if bound is TRUE, this is the lower bound, otherwise, it is set to -1

## Details

If the decay of the eigenvalues of cor(X) is not too fast, we can lower-bound the Degrees of Freedom of PLS with 1 component. Note that we implicitly assume that we use scaled predictor variables to compute the PLS solution.

## References

Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

pls.model

Nicole Kraemer

## Examples


# Boston Housing data
library(MASS)
data(Boston)
X<-Boston[,-14]
my.lower<-compute.lower.bound(X)