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

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.

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

Leandro