If I perform PCA on a simple table, I can take the resulting principal component scores as variables and then perform regression to predict an outcome from my original data. I would do this for dimension and noise reduction and to see if I could reduce my pc's to less than the number of variables I originally had.
However, I don't understand what I can do with the results from Multi Factor Analysis (MFA), Partial Triadic Analysis (PTA) and other multitable PCA extensions. Can I take the principal components from the common space and use those for regression? Or is the only thing I can do with them is to make biplots and other visuals to compare the different tables (time periods, variable groups, etc) to one another? I know that PCA is partly a visual exploratory tool, but it can also be used to get new variables that are orthogonal from one another to eliminate collinearity.
I understand the math behind PCA fairly well so I understand that its just a linear transformation of the original data using orthogonal new basis vectors. However, The math behind MFA/PTA is less clear to me. From what I understand I would think I could use pc's form the common space in MFA for regression as I might with a standard pca, but ever paper I've read about MFA ends with just visual plots and a discussion about what is in the plots. A couple papers mentioned something about using principal components from MFA in further analyses but I have yet to see a single example of this.
