In PCA and Factor Analysis, there is the term loadings, which refers to factor loadings (onto the original variable).
Does the term (original) variable loading (onto the latent factor) exist?
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$\begingroup$ Perhaps you could show some usage - I'm not sure I understand what you're asking. $\endgroup$– Jeremy MilesSep 14, 2018 at 20:44
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1 Answer
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This is just a situation where terminology is being used interchangeably. It is more customary to say that a variable "loads on a factor" or principal component (PC), rather than a factor loads on a variable (PC). Specifically, however, it's the same thing. Loadings are correlation coefficients, essentially between an original variable $X$ and a factor or principal component $F$.
It's better to get into the habit of saying that an "original $X$ variable loads on a factor (or PC) with loading 0.65" (and not ever saying a factor(PC) loads on a variable).
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$\begingroup$ Thanks, but just to be clear I have another question: The interpretation of the loading is: 1. The higher the loading of a PC, the more influence it has in the formation of the variable. 2. The higher the loading of a variable, the more influence it has in the formation of the principal component score. 3. Both ? So you say the answer is 1? $\endgroup$ Sep 15, 2018 at 5:14
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$\begingroup$ If it matters, the longer post of mine regarding the question is: stats.stackexchange.com/questions/366970/… $\endgroup$ Sep 15, 2018 at 5:27
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$\begingroup$ The answer to the comment is 2. The higher the loading of a variable, the more influence it has in the formation of the principal component score. For option 1, factors and PCs don't create variables, since all the data comes from the variables. $\endgroup$– user32398Sep 15, 2018 at 17:42