I have answers from 16 multiple-choice questions, each with 4 unordered options, and I would like to apply a dimensionality reduction method on them. I was thinking of going for PCA, but then I learned that it works only with numerical values.
What is an appropriate reduction method for factor variables?
The reason why I want to apply a reduction method on my questions is to extract the latent phenomena of the questionnaire. Once I have the latent phenomena, I will apply a clustering method for the respondents according to their answers on the reconstructed variables. The ultimate goal is to cluster the respondents according to their answers in the questionnaire.