I am trying to understand the paper "A. Langmeyer et al.: Music Preference and Personality". The paper has the following "Structural equation modeling" model:
The first is that the analyses are based on cross-sectional data, so that no causal conclusions could be made. It is therefore possible that personality influences music pref-erences. Yet, according to self-expression theory (Rentfrow & Gosling, 2007), it is also just as likely that music preferences can influence personality.
Is it possible to calculate the variables O, C, E, A, N by using R&C, I&R, U&C, E&R? (e.g.
O = 0.42 * R&C + 0.21 * I&R + 0.35 * U&C)
Is it important whether the variables correlate or there is a causality necessary for calculating the O, C, E, A, N variables?
edit: If possible, how can I estimate a model where the paths are reversed and what data do I need for it?