Suppose I have a survey that contains 30 items.
The items ask about the relationship between the respondent and their family, in many different realms. For example, the strength of the connection between them, whether they live close to each other, how reliable the family is, etc. (each question is answered in a 1-5 scale)
By looking at my survey, one might say there are some redundancies in the questions asked (too similar questions), or that some questions might be grouped into a new question to reduce survey time, or questions that simply shouldn't be asked. What I am interested in, then, are overlaps in questions and clusters of questions.
My hypothesis is that I have far too many non-differentiating questions that add to the survey length but do not add to insight. In this way, I would be better off removing/combining questions.
In sum, my question is: how would I go about reducing the number of questions down to "just the ones that are relevant" (i.e. that contain most of the information)? How would I know which questions to combine/keep/remove? How can I identify which questions in the survey are redundant, or cluster different questions together?
Would I be using something like Principal Components Analysis (PCA) or Factor Analysis? Which one?
The output of my analysis would be something like a 10-15 item (or however many) questionnaire that gives just as much information as the original questionnaire.
If using PCA, or FA, how would I go about doing so? Examples or links would be very appreciated. (I want to make sure the results are interpretable) I have done some research and it seems that PCA might be hard since results are not so easily interpreted?