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I have a survey data that asked multiple-choice questions. For example, one of the questions asked why you decided to live in the current house. Respondents can select multiple choices (there are 25 options in total). The answer is recorded like a dummy variable, 1 is the selection of the option and 0 is not. I looks like this:$$ {\rm Answer\ for \ Question \ 1} =({\rm Option}_1, {\rm Option}_2, \cdots, {\rm Option}_n) = (0,1,0,0,\cdots,1) $$

I conducted a factor analysis and found that there are four factors. I want to know what people think important in deciding house. For example, if factors are space, cost, area, and security, I want to say people in the sample prioritize cost over all other factors, space is the second most important and so on.

Is there any method to do so?

user51966
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  • Can you say a little more about what your survey/data looks like? How did you deal with questions where a person can pick more than one option? – Ian_Fin Aug 09 '16 at 12:52
  • @Ian_Fin Thanks for the comment. I added the explanation. – user51966 Aug 09 '16 at 13:01
  • And did you subject only the answers to question 1 to the factor analysis, or were there more questions? If the latter, form form did these questions take? – Ian_Fin Aug 09 '16 at 13:11
  • @Ian_Fin Thanks for the follow-up question. Since each question asks different topic, I want to know the ranking of factors (according to importance) for each question. – user51966 Aug 09 '16 at 13:22
  • If the only information you have is the options each person selected, then it sounds like you may have to assume that the more options a person selected per factor (as a proportion of available options) the more important the person thought that factor was. It's a rather crude metric. – Ian_Fin Aug 09 '16 at 13:44
  • @Ian_Fin Thanks. If I use other methods other than factor analysis, is there any way using the same data? What I want to do ultimately is grouping choices into several groups (or assuming latent features for choices) and then rank them according to the sample preferences. It is awkward to show the ranking of 25 options, so I think the ranking of groups is better regarding understandability. – user51966 Aug 09 '16 at 13:50
  • Unfortunately the problem lies in the data, rather than the method. You've not really asked people how much a priority something is. You've only asked them to list what the priorities were. I think you're right to want to reduce your 25 options to a small set of factors, and it's possible to rank them as I described (by proportion of options selected) but you may just have to accept that, e.g., saying 5/5 area options are important and saying 1/5 cost options does not necessarily mean area is more important than cost to people. – Ian_Fin Aug 09 '16 at 13:56
  • @Ian_Fin I understand following your description, we can say priority ranking under the assumption (more options a person selected per factor the more important the person thought that factor was). Is this same when we talk about ranking in the sample in total? It is enough for me to know what the sample think. – user51966 Aug 09 '16 at 14:24
  • If you took the mean of all the people's priority ranking for each factor then you could say (at least descriptively) that on average people consider, e.g., cost to be more important than area. – Ian_Fin Aug 09 '16 at 14:35
  • @Ian_Fin Thanks for your help again! I understand. We need to calculate each unit's ranking under the assumption anyway. – user51966 Aug 09 '16 at 14:39
  • `I conducted a factor analysis`. Were you conducting classic linear FA on the binary data? If yes, it isn't a good practice at all. [See](http://stats.stackexchange.com/q/16331/3277). [See](http://stats.stackexchange.com/q/215404/3277). – ttnphns Aug 09 '16 at 17:01

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