Combining Sub-Samples for Factor Analysis? I am a newbie on the site and a relative newbie to some of the analysis I am trying, so my apologies in advance for any rookie mistakes or for asking what might be obvious to others!
Can I run a single factor analysis if the data is from multiple sub-samples? By this, I mean that some subjects respond to the same items in one situation and others respond to the same items in another situation. For example, suppose that I am looking at the construct of room comfort by measuring temperature, humidity and lighting, and I measure these 3 items from 50 subjects in a cold room, and then I measure these 3 items from 50 different subjects in a hot room. Is it defensible to run a single factor analysis with 100 observations for each of the 3 items (50 observations from hot room subjects and 50 from cold room subjects)? Or can we only do factor analysis if the same subjects provide responses in a cold room and in a hot room (still 100 observations but the same sub-sample providing repeated responses).
I looked on the site and found some answers about missing data (not all subjects respond to all items), but nothing about what I am looking at, so I would be grateful for any inputs.
Thanks for any guidance!
 A: Your question seems to be application-related. If you can or not run factor analysis over different subject populations for each room condition (cold or hot) depends on what questions you want to answer (the objective of your analysis).
If, for example, you want to know how subjects respond to cold rooms independently of how they respond to hot rooms, it is reasonable that you use different subjects. You could do a single factor analysis on the 100 independent subjects, or you could also have a different analysis for each type of room condition. The decision depends, again, on what do you want to answer. You could do both alternatives and investigate the outcomes.
But if it is important for you to know, for example, if subjects that respond 'well' in cold rooms are going to respond 'bad' in hot rooms, then it seems important to have subjects experiencing both types of rooms. In this case, I would further suggest that you use structurally constructed input data. For example, construct a tensor with mode A related to subjects, mode B related to the features of the room (temperature, humidity, and lighting), and mode C related to the type of room (hot or cold). Then you could run a tensor decomposition method (like PARAFAC) to get the relations between subjects and room conditions.
