One or two factor analyses?

Question

I'm in the process of planning a scale development project and stuck with a question:

I have two constructs that will each form an axis of a matrix. Both constructs can correlate and can be related, but don't need to. They don't form a total score together at the end. I will use a scale for each construct to determine the organization's position on each axis of the matrix. If I'm developing items for each construct, do I need two or one exploratory factor analyses? My idea was a different factor analysis for each construct to find out the domains/factors of each construct. However, I saw a paper that analyzed two different constructs within one factor analysis. Won't items in both constructs just cross-load, so basically form a cluster in my matrix if I do it in one factor analysis?

Sorry if this might seem to be a trivial question for some, I'm just confused at the moment. Thank you!

Answer 1

One factor analysis can consider items from many scales at once. Doing so may be useful as a test of convergent and discriminant validity. If, in one factor analysis, items cross-load strongly (roughly $\lambda>.3\ \text{or}\ .4$, depending partly on how strong your loadings get in general) on multiple factors, this reveals a potential problem for your measurement model, assuming it wouldn't otherwise score those multiple latent constructs using the same items. Some measurement models don't require each item to have only one primary loading. If, for instance, you were interested in comparing the evidence for a single "general" factor against the evidence for multidimensionality, you could perform an exploratory bifactor analysis to compare the items' loadings on the general factor and the group factors. Reise and colleagues (2010) offer a good introduction to that approach. By the way, if these are Likert ratings you're using, you may want to see a related question, Factor analysis of questionnaires composed of Likert items.