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I guess parent is talking about using PCA for doing something akin to Factor Analysis (and making interpretations over the components and the loadings / contribution from each variable towards each component). I have at least seen that in psychology, for example the Big 5 personality traits were extracted and then analyzed/discussed in that way, using FA though.

I also don't think this is about disregarding the methods usefulness, but rather being very careful with assumptions and use critical thinking when interpretating results in studies that use a lot of math.

In the case of DS/ML for prediction, it doesn't matter at all. As long as it empirically works, you're good. Unless you want very explainable/understandable models that is.

PS: I don't like using wikipedia as a source, but you can take a look here as an example of what parent is talking about: https://en.m.wikipedia.org/wiki/Big_Five_personality_traits#... . As I said, in this case is for FA, but a lot of people use PCA for making the same kind of studies, specially in less rigorous data-science for business settings.

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