Dimension reduction - find a conveniently small subset of linear combinations of the mass of observed variables which captures a suitably large fraction of the total variance.

As hypothesis-testing goes, that strikes me as putting the cart before the horse. If they have a hypothesis for how the data should behave, then why are they not just fitting directly to their hypothesis? And if they don't have a hypothesis, then it sounds suspiciously like a fishing expedition. Which, like all fishing expeditions, runs a large risk of bycatch. Are they modeling signal, or are they modeling noise here?

Because linear algebra is the only thing we humans know how to work with...

And it is, after all, better to be very precisely wrong than to be roughly right...

- Jake

Friends come and go. Enemies accumulate.