I am new to this. I have a set of survey data with 18 questions (columns/features) with 165 observations. Responses are ternary: True, False, Don't Know. Each question has a correct response, which may be either True or False. I would like to choose a subset of survey questions in order to send out a new survey. I want a simpler survey of about two to five questions, so I can hopefully get more observations.
What would be the suggested method(s) for performing preliminary feature selection on the survey data?
Initially, I thought to use PCA and select the features like in this answer. But I've read that PCA is geared towards continuous data, so I am unsure if it would be correct to use it. I've read the MCA is a categorical analogue to PCA, but I don't know if it can be used for feature selection.