Factor Analysis - multiple answers from same respondents i am conducting an Exploratory Factor Analysis. I asked 100 subjects to rate the credibility of 4 marketing tactics. I examined 8 tactics in total and 4 tactics were allocated randomly to every subject to answer.
Now I want to conduct a factor analysis to find the number and nature of constructs underlying the eight items.

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*Is it even ok to have multiple answers by the same respondents? (I have 100 x 4 answers -> translate to 400 rows of data in my SPSS output) Because one assumption of FA is, that "the answers are independent to each other", isn't it?


*If it is ok, do I use the dataset with 400 rows or do I have to reduce the dataset with mean averages of some kind? What would be the advantage?
Thank you so much, I really need the help for my finals!
 A: Factor analysis (FA) is a statistical method to describe variability among observed, correlated variables in terms of a potentially lower number of underlying, unobserved variables. The FA does not assume that the answers are independent - quite the opposite, FA assumes that the responses are dependent because a few (sometimes, a single) latent factors are assumed to generate the observed variation in your responses. You could say that, given the latent factors, the responses are assumed to be independent. This is just a way of saying that there is some shared variation (latent factors) and some unique variation (independent residual errors).
If your question is really about whether one or few factor(s) underlie the ratings (it's hard to tell from your question), then FA is the right approach. Since you have eight ratings but randomly assessed only four per person, you have used a planned missing data design. That is, the shape of your data is really 100 x 8 with half of the values being missing. Since the pattern of missing data is missing completely at random_ by design, there should be no bias in your estimates with modern missing data approaches (such as full-information maximum likelihood or multiple imputation).
