I have data from a multiple choice question with 10 possible answers. Respondents were asked to select up to 3 answers that applied. Can I do a factor analysis on the answers, considering each possible answer as one item? How would I do that (in Stata)?
No, and there actually very little that you can do with this kind of question, other than to report descriptive statistics.
Hello Mark,
As you limited the responses to 3 (of 10 options), there will almost inevitably be negative intercorrelations among many of the options. That alone will make your quest for finding any sensible structure quite a challenge.
Had you offered no upper limit for choices, then you could have treated the responses as a set of 10 dichotomously scored items (yes/no; 1/0), that wouldn't suffer from negative intercorrelations as an artifact of a semi forced-choice response system.
Factoring generally requires continuous scores, though you'll find plenty of instances of persons doing FA on dichotomous variables. Some suggest that using tetrachoric correlations as a starting point (instead of ordinary Pearson correlations) is a good idea in that instance.
Good luck with your work.
Dear Mark Olsthoorn ,
Treating each response separately as a unit breaks the assumption of independence of the observations.
For multiple choice questions you consider a multivariate analysis of variance MANOVA.
I give the following statistical methods for consideration and ask for comments in particular David Morse . I have no other ideas at this time.
In MANOVA, the dependent variables will be: first choice, second choice, third choice . The dependent variables must take different values for a given unit, they are not independent.
There is ambiguity in the data due to the arbitrary order in which the respondent's answers are recorded. To solve the data problem, you can permute and multyplicate the data.
When the dependent variable will be a single response choice (one-dimensional analysis) and the choice values are grouped by respondent, you fit a GLMM.
What are you wanting to do with the "factors"? I assume this is not something like an academic assessment where the response patterns with each item (each choose 3 of 10) can can be mapped onto something like wrong, a little right, almost correct, correct, where things like the partial credit model is often used and available in freeware like the mirt package in R. If the questions are something like "choose up to 3 of these 10 fruits for a fruit salad" the key is likely how to map the 10 choose 3 + 10 choose 2 + 10 choose 1 + 1 =176 possible patterns for each item onto something simpler, and how to do that will depend on more details. Once aggregated so that there are a smaller number things like the nominal response model (in mirt) could be used. But, since you have already marked a response as providing the answer, I won't go any further.
Hello Hanna,
Had the task been presented with the chance to select as many possible options as the respondent deemed suitable, then I'd argue that the individual choices to select or omit each option are independent.
Opting for manova doesn't appear to make sense to me in this situation, as the DV would be an option number (e.g., respondent chose option #6 as the first selection, followed by option #1), and not a measurement or score, but maybe I didn't get where you were going with this suggestion.
Best regards to all.
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