Dear Community,
I have a messy dataset that contains survey questions rated on 5-point Likert scales (e.g. Totally acceptable, Fairly acceptable, Not very acceptable, Totally unacceptable, Don’t know) and 3-point categorical scales (e.g. Yes, No, don't know), and binary scales (yes/no). So the sub-questions are as follows:
1) I understand I'll have to do EFA using tetrachoric/polychoric correlations. So the question is whether I need to do separate EFAs on polychoric/tetrachoric correlation on questions rated on 5-point Likert scales, 3-point categorical scales and binary scales? Or do I need to calculate a polychoric matrix for all the questions and do a single EFA.
2) In the case of later, how do we calculate composite variables (factor scores) if for example a question with a 3-point scale loads on a factor with all 5-point scales?
3) How to finally do a CFA on the above data?
Help highly appreciated.
Hello Kamal,
0. The Don't know option situation is the hardest one to address, as some respondents may consider "Don't know" as an intermediate, but neutral, response option compared to "Yes" or "No," (or "Totally acceptable...") whereas others may consider it as analogous to a "Not applicable (to me)" response. The two perspectives are not interchangeable.
The first offers an ersatz, ordinal scale: e.g., No, Don't know, Yes. The second would require that any instance of "Don't know" be treated as no response (e.g., the participant was not qualified to respond). You'll have to decide which approach is more defensible for your work. In the future, try to replace such options with more explicit choices.
1.& 2. If you want to explore an EFA solution for all items, then you'll have to include them all in the analysis (a single correlation matrix). While polychoric values are possible, you'll have to figure out what sort of mapping of the 2 to 3 to 5 option values makes sense. For example, does a "Yes" on the two or three option scale map to "Totally acceptable," "Fairly acceptable," or both?
If the nature of the questions was such that different response scales made sense, then you might be better off evaluating the dimensionality of those sections individually.
3. CFA is no different, though your choices are:
1) Treat the scores as ordinal (many sem/cfa software packages allow you to do this);
2) Go with polychoric correlations;
3) Consider item response model options with allow for polytomous scoring (such as the graded response model).
Good luck with your work.
David Morse. Thank you very much for your comprehensive answer, David. It's actually a survey conducted by an organization and understandably lacks academic rigor. Hence, I have to deal with yes, no, don't know kinds of choices. I am trying to see what kind of validated scales if any we can get out of the survey.
Another question please: What kind of extraction and rotation do you recommend in such a scenario? Also please share references if you can. I'll be really grateful.
Regards
Kamal Badar
the methods of factor retention and rotation have been commented on in many threads on RG:
https://www.researchgate.net/post/Exploratory_Factor_Analysis_and_Comformatory_Factor_analysis
https://www.researchgate.net/post/Factor-Analysis-Which-method-and-rotation-should-i-use
Best
Marcel
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