It's a long way to the top (if you wanna biplot): a back-to-basics perspective on the implementation of principal component biplots in R.

Abstract

Principal Component Analysis and biplots are so well-established and readily implemented that it is just too tempting to take for granted their internal workings. In this note we compare how PCA and biplots are implemented in the R language for statistical computing, leveraging a software-agnostic understanding of computational building-blocks that both techniques have in common. We do so with a view to illustrating discrepancies that users might find elusive, as these arise from seemingly innocuous computational choices made under the hood. Wider implications are derived from a simplified case based on real-world clinical trial supply chains data. By getting back to basics, the proposed evaluation grid elevates aspects that are usually disregarded, including relationships that should hold if the computational rationale underpinning each technique is followed correctly. Strikingly, what is expected from these equivalences rarely follows without caveats from the output of specific implementations alone.