Principle component analysis (PCA) distributes the variation in a multivariate dataset across components. The PCA allows us to visualize patterns that would not be apparent with common graphical techniques. Linear algebra is at the heart of the PCA, but this discussion will be light on mathematical theory. Instead, you can expect a gentle introduction to the topic, which will include how this ordination technique is carried out in R.

Accomplishing the PCA Manually

With the powerful tools available to us in R, there is no need to conduct a PCA manually. Contained within one line of code, R has native functions which can handle the heavy-lifting for us. My goal for the manual PCA is to expose you to the terminology and concepts in PCA. As such, you will be better prepared to defend your analysis.

Motivating example - wolf spider morphometrics

The original motivation for this analysis was to establish a standard algorithm to determine the “size” of a wolf spider. One way to accomplish this is with a PCA of morphometric characteristics. The parameters which possess the highest degree of variation will be the most optimal predictor of animal size.