All of the theory I know about factor analysis, scales, etc revolves around separating out indicators into groups that each have (ideally) one underlying dimension. I have a student for whom we'd like to do sort of the opposite of that, and I'm a bit stuck.
He has a whole range of disparate measures of acting-under-social-norms (from alcohol abuse, to registering with a doctor, etc). We don't want to split these into separate factors, but rather to reveal an underlying latent variable that (we hope) is common to all of them, even if it isn't the driving force for any one of them, or for any particular group of them.
Is there a way of doing this? So far, I tried looking at the first principal component, but that seems tilted towards capturing the alcohol use (clearly, a bunch of alcohol abuse indicators clump together to explain a large chunk of the overall variance) and anyway the scree plot does not have as strong an elbow as we'd normally see in factor analysis (reflective of the wide variety of indicators we have gathered). Clearly, we don't want to do a "rotation" because that is doing the exact opposite of what we want: to separate them into cohesive clusters of indicators, whereas we want actually something that (to some extent) can underly all of them.
Is there any reasonable way of doing this?