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I am currently trying to get my head around factor analysis, and especially the difference between factor analysis and PCA. I read most (if not all) questions regarding the difference between these two methods on statsexchange and at the moment study with the book "Principles and Practice of Structural Equation Modeling" by Kline.

I understand what I would consider the most basic difference between those two, which have been already discussed on statsexchange, e.g. the goal is entirely different: reducing dimensionality of data vs. finding a latent construct that is assumed to drive communality.

What I do not seem to graps is: I read repeatedly that (C)FA and PCA come to similar results. How is that possible as their modeling approach is entirely different, isn't it? In PCA, the factors are a linear combination of the input variables. In FA, the input variables (indicators) are modelled as a linear combination of the factors. Therefore, I would say that the method of (C)FA is more like the inverse of PCA - how does this yield same/similar results

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  • $\begingroup$ I do not see how this question is answered in the referenced thread? $\endgroup$
    – Max
    Jul 13, 2021 at 8:14
  • $\begingroup$ Confirmatoty FA is a technique very different from the (exploratory) FA. CFA is a part if SEM or path analysis. When we say just "Factor analysis" we 99% of time mean EFA, not CFA. CFA is in no important way related to PCA. EFA is. $\endgroup$
    – ttnphns
    Jul 17, 2021 at 9:42
  • $\begingroup$ Note that we even have a separate tag for CFA, "confirmatory-factor". $\endgroup$
    – ttnphns
    Jul 17, 2021 at 9:51

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