I have a simple path model with several latent variables that are ostensibly well enough indicated by survey items (that is chi2 versus saturated model / CFI / SRMR / RMSEA are satisfactory in the measurement model), but yield non-normal distributions for the latent variable (e.g. see below).

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The final path model is below.



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I have both independent and dependent variables with such skewed distributions.

At present, I wish to stick with a covariance-based SEM for analysis, rather than revert to variance based SEM via SmartPLS, but am concerned about theses distributions.

My 2 questions are below, but based on the tenet that I have to transform the factor score somehow. If this is wrong, please tell me why and that's that :-)

1) Can someone give me a steer how I transform the factor score for the measurement analysis part of the model, when I estimate the whole path model. I presume I can use - predict - somewhere along the line to estimate a seperate factor score, but this make the predicted factor score an observed variable within the final model and does not allow estimation of the measurement model and the structural model in one hit. Moreover, it seems very laborious. Is there an option whereby one can specify that the model estimation handles a latent variable in a transformed manner?

2) Assuming I can transform the variables that I believe need transforming, how do I handle the interpretation of path estimates (such as ones in red). Is it the same as a simple regression that uses transformed dependent or independent variables (e.g. dependent variable transformed then exponentiate coefficient, subtract one, divide by 100 etc)? I am not sure about this since the coefficients displayed are standardised, and of course I would like to keep it this way given the increased comprehensibility of the model.

Thanks for giving me a steer.