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I am trying to understand the paper "A. Langmeyer et al.: Music Preference and Personality". The paper has the following "Structural equation modeling" model:

SEM music preference model In the discussion the paper states that the direction is not ensured:

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.

  1. 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)

  2. Is it important whether the variables correlate or there is a causality necessary for calculating the O, C, E, A, N variables?

  3. edit: If possible, how can I estimate a model where the paths are reversed and what data do I need for it?

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No, you cannot directly infer the values of predictors from the paths in the model. but you could estimate a model where the paths are reversed, and calculate values for the now-dependent O,C,E,A,N variables from that, assuming the model performs well.

Causal inference is about making inferences in the real world. If you stay within a model, you don't have to worry about it. But if you want to make inferences about actual behavior in the population, then you do.

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  • $\begingroup$ "but you could estimate a model" how can I do that? Do I need the raw data for it or can I do it based on a correlations matrix betwen O,C,E,A,N and R&C, I&R, U&C, E&R which is provided by the paper? $\endgroup$
    – simsi
    Feb 25, 2020 at 19:37
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    $\begingroup$ You could estimate paths between factors using the correlation matrix of the factors. If you can assume that all factor means are 0, then you could estimate values of the O,C,E,A,N factors in terms of the other factors. Keep in mind that factor indeterminacy means that it is not possible to derive single best estimates of the values of factor on a case-by-case basis. $\endgroup$
    – Ed Rigdon
    Feb 25, 2020 at 19:52

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