Is Multiple Correspondence Analysis applicable to Multi-valued Categorical Variables?

Question

I have a data-set containing only Categorical Variables. I needed to do Principal Component Analysis on the data set. Eventually, I found Multiple Correspondence Analysis and learnt it. But, in MCA, it's assumed that, each of the Categorical variable has only one of the levels as True and others as False, i.e an observation can not belong more than 1 category of the same variable.

But in my data-set, I have multiple value for a categorical variable. For example, a disease has a set of symptoms, so, symptoms feature is a multi-valued categorical variable, where each of the symptom creates a different level. So for a disease, symptom feature can have multiple levels as true.

How do I run PCA/MCA/FAMD on such data-set? Is there any solution to this issue?

Thanks a lot for helping.

Answer 1

Non-mutually exclusive categories may be an issue for multiple correspondence analysis (MCA) if you don't treat your dataset adequately.

The commonplace solution is simply to treat these non-mutually exclusive categories as binary variables (e.g. instead of "symptoms: fever/dizziness/sneezing" -> "fever: yes/no", "dizziness: yes/no", etc.).

Now, if you converted these categories as distinct binary variables, you might still want to consider them as belonging to the same group of variables. In this case, an option is to use multiple factor analysis as an extension of MCA.

For mutually exclusive categories (e.g. blood group), this is not a problem at all for MCA, and statistical software generally deal internally with that. So in this case, you generally don't have to convert these categories to binary variables, though it may be a good idea to look at the software documentation to avoid bad surprises.