PCA for categorical variables

[Ayushi Basoya]

I am trying to perform PCA for a mix of categorical and binary variables. Is it advised to conduct PCA for the categorical variables as it or alternatively, I have tried converting categorical variables by taking a dummy variable for each category. Kindly let me know what would be the ideal approach while dealing with categorical variables in PCA.

[Nick Cox]

This is contentious. Indeed, some researchers think PCA for any kind of categorical variables doesn't usually work well, and some of those would recommend instead correspondence analysis or a variant.

If categorical means, or includes, nominal scale variables, there isn't a defensible alternative to treating those as a bundle of indicator variables (dummy variables in your terminology).

If categorical means, or includes, ordinal scale variables, then treating their grades or codes literally is either a bold or a foolish step, depending on who you ask.

I've rarely seen any multivariate analysis working well with a mix of different kinds of variables. I'd welcome specific references to success stories to the contrary.