Principal component analysis is not the same as clustering. Some of the post seems to make that distinction, while other parts appear to blur it.
If there are clusters, PCA might find them, but PCA might tell you something interesting even if there are no clusters. But if there are clusters, the factors that PCA finds won’t be the clusters, but the differences between them. In the simplest case, if there are two clusters, a left-wing party and a right-wing party, PCA will say that there is one interesting factor, the factor that distinguishes the two parties. But PCA will also say that is an interesting factor if there is no cluster, but a clump of people in the middle, thinning towards extremists.
Actually, factor analysis pretty much assumes that there aren’t clusters. If factor 1 put you in a cluster, that would tell pretty much all there is to say and would pin down your factor 2, but the idea in factor analysis is that your factor 2 is designed to be as free as possible, despite knowing factor 1.
Just about to say this. ‘Cluster’ is very much the wrong word to use to describe the components. A reasonable word would be ‘dimension’. Someone can be more or less realist/anti-realist, rationalist/anti-rationalist, externalist/anti-externalist, and each of those dimensions is relatively independent of the others.
The main point of conducting a principal component / factor analysis is dimension reduction. A philosopher can be fairly well described by how strongly they endorse each component rather than keeping track of each individual answer. This is the same math behind the Big 5 personality model.
This confusion seems to be why the post claims the LW-ish position isn’t represented. It’s not that there is a well-defined group of anti-naturalists that LWers don’t fit into; instead, the dimension just happens to be defined with anti-naturalist on the high end. Then, LW roughly endorses being low on each dimension, except maybe externalism and objectivism.
Thanks, Douglas! I was worried about this too, but I rushed the post a bit too much and didn’t think of obvious better terms. I’ll edit the post to speak of ‘dimensions’ so I don’t perpetuate any misunderstandings. If there are any other improvements you’d make, let me know.
Principal component analysis is not the same as clustering. Some of the post seems to make that distinction, while other parts appear to blur it.
If there are clusters, PCA might find them, but PCA might tell you something interesting even if there are no clusters. But if there are clusters, the factors that PCA finds won’t be the clusters, but the differences between them. In the simplest case, if there are two clusters, a left-wing party and a right-wing party, PCA will say that there is one interesting factor, the factor that distinguishes the two parties. But PCA will also say that is an interesting factor if there is no cluster, but a clump of people in the middle, thinning towards extremists.
Actually, factor analysis pretty much assumes that there aren’t clusters. If factor 1 put you in a cluster, that would tell pretty much all there is to say and would pin down your factor 2, but the idea in factor analysis is that your factor 2 is designed to be as free as possible, despite knowing factor 1.
Just about to say this. ‘Cluster’ is very much the wrong word to use to describe the components. A reasonable word would be ‘dimension’. Someone can be more or less realist/anti-realist, rationalist/anti-rationalist, externalist/anti-externalist, and each of those dimensions is relatively independent of the others.
The main point of conducting a principal component / factor analysis is dimension reduction. A philosopher can be fairly well described by how strongly they endorse each component rather than keeping track of each individual answer. This is the same math behind the Big 5 personality model.
This confusion seems to be why the post claims the LW-ish position isn’t represented. It’s not that there is a well-defined group of anti-naturalists that LWers don’t fit into; instead, the dimension just happens to be defined with anti-naturalist on the high end. Then, LW roughly endorses being low on each dimension, except maybe externalism and objectivism.
Thanks, Douglas! I was worried about this too, but I rushed the post a bit too much and didn’t think of obvious better terms. I’ll edit the post to speak of ‘dimensions’ so I don’t perpetuate any misunderstandings. If there are any other improvements you’d make, let me know.