When I read about exploratory factor analyses, I saw equations showing that each variable is a linear composite of different factors - with loadings correspond to the coefficient in front of each factor in the linear equation. I think this makes sense because loadings refer to "how each factor loads on each variable" instead of the other way around.
Interestingly, when I read about PCA, I saw descriptions such as "each component is a linear composite of variables".
Then I am confused. I know PCA and EFA are conducted for different purposes, but the computation processes of the two were supposed to be pretty similar. I thought the biggest difference computation-wise between the two analyses was that EFA extracts factors only based on common variance while PCA uses total variance. And I have been equating "factor" in EFA to be somewhat the same as "component" in PCA. Here is my question: If EFA "factor" and PCA "component" are computed in the same way, then how come people say "each variable is a linear composite of factors" in EFA but "each component is a linear composite of variables" in PCA?
