Since some people have asked, I should say that “Overton Paradox” is the name I am giving this phenomenon. It’s named after the Overton window, for reasons that will be clear if you read my explanation.
Here’s a visualization of explained variance versus number of components.
With one component, we can capture 44% of the variation in the measurements. With two components, we’re up to 62%. After that, the gains are smaller (as we expect), but with 10 measurements, we get up to 78%.
Looking at the loadings, we can see which measurements contribute the most to each of the components, so we can get a sense of which characteristics each component captures.
I won’t explain all of the measurements, but if there are any you are curious about, you can look them up in The Measurer’s Handbook, which includes details on “sampling strategy and measuring techniques” as well as descriptions and diagrams of the landmarks and measurements between them.
Here’s my interpretation of the first few components.
Not surprisingly, the first component is loaded with measurements of height. If you want to predict someone’s measurements, and can only use one number, choose height.
The second component is loaded with measurements of girth. No surprises so far.
The third component seems to capture torso length. That makes sense — once you know how tall someone is, it helps to know how that height is split between torso and legs.
The fourth component seems to capture hand and foot size (with sitting height thrown in just to remind us that PCA is not obligated to find components that align perfectly with the axes we expect).
Component 5 is all about the shoulders.
Component 6 is mostly about the head.
After that, things are not so neat. But two things are worth noting:
Component 7 is mostly related to the dimensions of the pelvis, but…
Components 7, 8, and 10 are surprisingly loaded up with ear measurements.
As we saw in the previous article, there seems to be something special about ears. Once you have exhausted the information carried by the most obvious measurements, the dimensions of the ear seem to be strangely salient.