I have a school survey dataset which asks teachers, pupils and parents to score (between 0 -10) such variables as;

- Academic Expectations

- Engagement

- Safety and Respect

The dataset includes responses from over 1,500 schools.

Is it correct to apply factor analysis, in the form of principal component analysis (PCA), to validate overarching constructs within the survey - namely determine whether a response to one variable of school life directly impacts other variable responses by a given stakeholder? In other words, is a lower engagement score likely to be strongly positively correlated with low academic expectation, safety and respect scores etc. among teachers?

I found my hypothesis to be correct, with PCA returning three components - one pertaining to teacher responses, one to pupils and the third to parents (see attached).

Is PCA appropriate in this instance?

Thanks in advance.