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I'm analyzing a survey result, which has 50 survey questions in Likert scale of 1-5 and the binary answer of satisfied or not as the target. I'm thinking of applying factor analysis for dimension reduction and use the factors to train a classifier to predict satisfaction. The thing is, the 50 questions are already grouped in 5 topic categories, and I'm wondering if there's any way I can let the model know which question belongs to which topic category, so that I can guide the model to learn the latent variables and thus producing more explainable factors.

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  • $\begingroup$ How do you want the topic categories to guide FA? E.g., do you want the factors to always lie in a subspace defined by the questions of a single topic? If so, why? Why do you think those categories would improve FA? $\endgroup$
    – frank
    Jul 22, 2022 at 12:42
  • $\begingroup$ As I understand FA is a dimension reduction technique, so I'm thinking of using each factor as a linear combination of all the questions within that topic, then I can have fewer features in the model and also better model explainability $\endgroup$
    – crx91
    Jul 22, 2022 at 13:33
  • $\begingroup$ But FA should also find factors that are combinations of topics. $\endgroup$
    – frank
    Jul 22, 2022 at 13:42
  • $\begingroup$ Factors theoretically are not linear combinations of the items (though estimated factor scores are). You may be confusing FA with PCA. $\endgroup$
    – ttnphns
    Jul 24, 2022 at 14:05
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    $\begingroup$ @whuber, Factors in (linear) FA are not conceptualized as linear combinations of the manifest variables. This is because FA model assumes also (besides errors) unique factors (which are not random errors). It is the main distinction with the PCA. I've stressed that in many places, including 1, 2, 3. $\endgroup$
    – ttnphns
    Jul 25, 2022 at 14:59

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Yes, you can "let the model know which questions belong to which topic category." To do this, you would use what is called confirmatory factor analysis (CFA). The factor analysis wiki makes this clear.

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As well as confirmatory factor analysis (CFA), there's an approach called Procrustes rotation to a target matrix, used in exploratory factor analysis. See, for example, https://link.springer.com/article/10.3758/s13428-019-01209-1.

Where CFA is a very strict test of the factor structure, Procrustes rotation is more relaxed. CFA says "your rotation must match this target matrix", Procrustes says "Get this rotation as close as you can to this target matrix".

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    $\begingroup$ Jeremy, how do you think precisely procrustes will help the OP to perform - actually what they seem to me to be after - a hierarchical form of analysis or a so called multiple factor analysis? $\endgroup$
    – ttnphns
    Jul 25, 2022 at 15:04
  • $\begingroup$ When the CFA returns a poor fit, which it almost inevitably will with 50 items, they can give up and declare the structure wrong; attempt to modify the model using CFA, which is often done, but is problematic; use EFA, which completely ignores the structure, or use procrustes - which might indicate that (say) a smaller number of items are problematic. $\endgroup$ Jul 25, 2022 at 16:46

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