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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.

kjetil b halvorsen
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user1607
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  • Ordered or unordered choices? With designed redundancies to detect bad answers, or a naive questionnaire that may or may not have overlap? – Has QUIT--Anony-Mousse Jul 06 '19 at 11:22
  • @Anony-Mousse the choices are unordered – user1607 Jul 06 '19 at 12:59
  • There is already a fair bit of discussion on this, see f.ex [this](https://stats.stackexchange.com/questions/215404/is-there-factor-analysis-or-pca-for-ordinal-or-binary-data), and links therein. – AkselA Jul 08 '19 at 11:17
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    The link @AkselA pointed out is fairly detailed. Your question would fall under case 1. As an `R` user I recommend you trying the `homals` package; set the rank parameter's value to 1 and you will get something equivalent to a PCA for categorical variables. – Jon Nagra Jul 08 '19 at 14:30

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