still, if you transform your variables into z-scores you end up modelling the *correlation* matrix and not the covariance matrix. and that's a big no-no because the standard errors of the loadings when modelling correlations take larger sample sizes to stabilize.

we only model correlation matrix (and standardized variables) when we have no way around it (i.e. Muthen's categorical variable methodology where we model the polychoric correlation matrix by virtue of how the latent error variances are defined).