Timeline for What are the differences between Factor Analysis and Principal Component Analysis?
Current License: CC BY-SA 3.0
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| Jan 14 at 23:25 | comment | added | aiwl | @ttnphns Would PCA or FA be more appropriate prior to visualization with t-SNE/UMAP, for psychology questionnaires? PCA/SVD is the typical approach; however, FA is more widely used in psychology due to the assumption of latent personality traits. They do look very similar in this example, however I'm not sure if they're still similar when reducing to higher dimensions. Which is more suited to t-SNE/UMAP's goal of preserving distances between neighbouring points? | |
| Jul 3, 2017 at 22:30 | history | edited | amoeba | CC BY-SA 3.0 |
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Mar 8, 2017 at 14:28 | comment | added | amoeba | @ttnphns Thanks for these comments. This answer of mine requires some additional work but I keep postponing it... Whenever I get to edit it, I will take your points into consideration. | |
| Dec 3, 2015 at 17:53 | comment | added | ttnphns | (cont.) Of course, one is in full right to draw "biplots" in FA like the right one of yours. It is not a mistake. Rather one should just keep in mind that on such a plot we blend two different types of axes: factors as true (which load) and factors as estimated scores. | |
| Dec 3, 2015 at 17:47 | comment | added | ttnphns | (cont.) But the right pic (FA) is actually not a true biplot, it is rather an overlay of two distinct scatterplots, different spaces: the loading plot (where axes are true factors) and the object scores plot (where axes are the estimated factors as scores). True factor space overruns the "parental" variable space but factor scores space is its subspace. You superimposed two heterogeneous pairs of axes, but they bear the same labels ("factor1" and "factor2" in both pairs) which circumstance is strongly misleading and persuades us to think that is a bona fide biplot, like the left one. | |
| Dec 3, 2015 at 17:47 | comment | added | ttnphns | (cont.) A subtle and insidious nuance which potentially misleads a viewer of your two plots arises from the fact that both are drawn by you as a biplot, not simply a plot of loadings. When we speak of PCA (left pic), the biplot is justified, because both variable loadings and object scores are embedded in the same analytic space - the space of principal axes which are in turn the subspace of the space spanned by the variables. | |
| Dec 3, 2015 at 4:27 | comment | added | ttnphns | (cont.) Factors are transcendent latent traits; pr. components are immanent derivations. Despite your two loading plots appear practically similar, theoretically they are fundamentally different. The components plane on the left was produced as a subspace of the variables which project themselves on it. The factor plane was produced as a space different from the space of the variables, and so they project themselves on an "alien" space on the right plot. | |
| Dec 3, 2015 at 4:25 | comment | added | ttnphns | It is true that PCA and FA sometimes and not at all seldom give similar results (loadings), and so PCA can be seen as a specific case of FA, when factor analysis is defined broadly. Still FA (sensu stricto) and PCA are theoretically quite different. | |
| Mar 30, 2015 at 22:21 | comment | added | amoeba | I used Matlab. I was thinking of pasting the code into my answer (as is normally my habit), but did not want to clutter this busy thread even more. But come to think of it, I should post it on some external website and leave a link here. I will do that. | |
| Mar 30, 2015 at 17:36 | comment | added | rnso | Which software did you use to create the PCA and factor analysis plots? | |
| Jan 31, 2015 at 22:56 | history | edited | amoeba | CC BY-SA 3.0 |
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| Jan 17, 2015 at 14:23 | history | edited | amoeba | CC BY-SA 3.0 |
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| Jan 17, 2015 at 0:33 | history | answered | amoeba | CC BY-SA 3.0 |