I am looking for methods that allow me to do an exploratory factor analysis with missing data. The reason I need to account for missing data is that we will try to collect a large number of variables to figure out which of these are informative/descriptive for a given question. However, since we plan to collect data from human subjects, we cannot present all items, so we have to select a random sub-sample of items for each participant. The rest of the items will be missing data for that subject.
Is there a way to perform a factor analysis on this kind of data, so we can figure out a) which factors are included in our data b) which of these large number of variables are most informative.
Also if you know some better way to detect the relevant variables, then that would also be great.