Could someone please explain when FA is used or when PCA is used, as I understood FA do dimensionality reduction, however PCA - the main goal is the same. Then which one should I use and in which cases?
Topic exploratory-factor-analysis pca dimensionality-reduction
Category Data Science
Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance.
Factor analysis is a way to condense the data in many variables into a just a few variables. For this reason, it is also sometimes called “dimension reduction.” You can reduce the “dimensions” of your data into one or more “super-variables.”
PCA is used to decompose the data into a smaller number of components and therefore is a type of Singular Value Decomposition (SVD). Factor Analysis is used to understand the underlying 'cause' which these factors (latent or constituents) capture much of the information of a set of variables in the dataset data.
For More,
What are the differences between Factor Analysis and Principal Component Analysis?
In terms of a simple rule of thumb, I'd suggest that you:
Run factor analysis if you assume or wish to test a theoretical model of latent factors causing observed variables.
Run principal component analysis If you want to simply reduce your correlated observed variables to a smaller set of important independent composite variables.
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