On R, I use the
mixOmics package to run a repeated measures ("multilevel") Partial Least Squares analysis. I'm able to plot the 2-dimensional PLS projections such that I get the following for two samples:
Visually, you can see that there seems to be greater group separation in the second sample, as compared to the first sample. However, since PLS doesn't quantify group separation (it does elucidate which variables have the greatest loadings per latent variable, which can be conceptualized as a measure of variable importance for each latent variable), I compared the difference in the distribution of predictors between the two outcome groups by calculating a within-subject variation version of an energy statistic, called a V statistic. For this, I used the
EDMeasure package in R.
As you can see, the V-statistic is higher (more significant) in Sample 1 despite the PLS projections presenting less group separation. I'm still trying to understand the details behind the calculation of a V-statistic, but I'm wondering if someone has any ideas about what's driving this inconsistency between the two (independent) methods.
Note: The two samples have equal # of particpiants n and equal # of predictors k.