Hello!

First, thank you to all who have contributed to this package and this forum - it has been an invaluable resource for me.

Second, my question. In short, I am wondering if someone might provide an explanation of the “Explained Variance” generated from a PLS or sPLS model. (I am currently working with a PLS model in regression mode.)

The manual states “This function calculates the variance explained by variates.” I am wondering how it is calculated? How ought it be interpreted? Importantly, I am wondering how it relates to Q^2? (E.g., in some models I run that have a negative Q^2, the Explained Variance is positive.)

Some example output provided, in case that is of any help. Here, let X be metabolomics1 and Y be metabolomics2. (And yes, sadly I am aware that my model is a poor fit…)

tune.pls$Q2.total

Q2.total

1 comp 0.001666725

2 comp 0.007492810

explained_variance(pls$X, pls$Y, ncomp = 2)

comp 1 comp 2

0.008908663 0.017972628

explained_variance(pls$Y, pls$X, ncomp = 2)

comp 1 comp 2

0.010692957 0.006996459

pls$explained_variance$X

comp 1 comp 2

0.41078514 0.08263149

pls$explained_variance$Y

comp 1 comp 2

0.09326141 0.27158469

Any help would be much appreciated! Thank you.