Q:

Can Y-aware PCA be performed with binary independent variables?

I came across this tutorial for Y-aware PCA using the vtreat R package. In short, Y-aware PCA is PCA on variables that have been scaled to be in y-units. 
Is it valid to scale categorical independent variables in y-units? 
All of my independent variables are dichotomous. It seems inconsistent to implement this y-scaling on them and then run PCA, since, typically, a method like multiple correspondence analysis would be used on categorical variables.     

A:

You need to run independent component analysis (ICA), which is used for performing (essentially) PCA on categorical or binary variables.  One reason that PCA is unwise to use is because the covariance or correlation for binary data results in a departure from normality.   That is, means and variances are biased (wrong) for binary data.   

