PLS Loadings versus Weights

Analysis
1

Hi,

I’m new to PLS, and I’m getting a bit confused if the values in called myplsobj$loadings$X in the pls mixomics package are either what are called the X “weights” (w vector) or the X “loadings” (p vector) as by Wold et al 2001 PLSR paper. Based on my understanding of the formulas in Le Cao et al 2008 it appears that this is the u vector, which that paper calls loadings but Wold et al call weights.

In addition, are myplsobj$loadings.star[[1]] the PLSR weights transformed to the independent between components (what Wold calls w*)?

Thanks! I’m just getting confused by the different notations used across papers.

2

hi @user2842,
You are right.
myplsobj$loadings$X = direct coefficients to build the components (so the w vector)
myplsobj$loadings.star = the w* (which we use for prediction).

The actual code is a bit tricky to understand, but it is buried in
https://github.com/mixOmicsTeam/mixOmics/blob/master/R/internal_mint.block.R line 721 and called loadings.A then transformed in the call in line 350 as loadings.Astar

Kim-Anh