Question

true or false Categorical variables can be used for PCA.

Answer 1

False

PCA works well with binary data, the only constraint is having not too sparse data. In my experience PCA results in this casde are practically coincident with correspondence analysis and or multidimensinal scaling. My suggestion in any case is to apply these different methods and loo at the convergence of the results.

The challenge with categorical variables is to find a suitable way to represent distances between variable categories and individuals in the factorial space. To overcome this problem, you can look for a non-linear transformation of each variable--whether it be nominal, ordinal, polynomial, or numerical--with optimal scaling.