How to interpret results from X block, Y block and X-Y block

Analysis
1

Good morning,

studing the articles regarding pls and your tutorial (which is very clear, thank you so much <3 ) I don’t understand how to interpret different sample dispositions in X block, Y block and X-Y block (e.g. plot Arrow). If I got it right, the X block take in account the influence of both X and Y data thanks to their covariance but it’s focusing on X data set primarily while the X-Y plot allow to plot a disposition which reflects both the hyperplanes? How to explain an exclusive clustering in X-Y plot only?

Thank you really much for your help,

Leandro

2

Hello again @Leandro

If I got it right, the X block take in account the influence of both X and Y data thanks to their covariance but it’s focusing on X data set primarily

This is sort of right. As you know, PLS, CCA and related methods produce two sets of components - one for each input dataframe (X and Y). If we look at the output of plotIndiv() where rep.space = "X-variate", we will see the projection of the samples onto the components associated with the X dataframe., whereas if rep.space = "Y-variate", then the same samples will be projected onto the components associated with the Y dataframe.

plotArrow() essentially combines these two and for a given sample, draws an arrow between where the sample is found in the X space and in the Y space.

When looking at the X-Y space (rep.space = "XY-variate"), the samples are projected onto the average of the two components. In other words, for the first component, the projection of a sample on first component from the X set and the projection of the same sample on the first component from the Y set are calculated. These two values are then averaged, producing a single value. This is the sample’s projection on the first component in the combined, X-Y space.

How to explain an exclusive clustering in X-Y plot only?

Clustering within the X-Y space is a little trickier to interpret. In the simplest terms, it represents the average of the clustering within the X space and the clustering in the Y space.

Hope this answered helped.

Cheers,
Max.

3

Thank you really much! Now it’s much more clear.

Leandro