Structural Equation Modeling: When and why do you use Z-scores instead of Mean.

#1
Hi.

Can anyone help me answer the question why some people who do SEM use z-scores as opposed to using mean scores?

(articles and books are welcomed)

Thank you.
 

Lazar

Phineas Packard
#2
Do we? Can you give a bit more context to the question?

The only thing I can think you might be getting at is that there is often advice given to put all variables on a similar metric to help facilitate maximum likelihood (gradient descent can struggle when variables are on vastly different metrics)
 

spunky

Smelly poop man with doo doo pants.
#3
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).
 
#4
we were instructed (classroom setting) to use Mean scores, similar to the regression. But I encountered this study that used Zscores. The study made use of different measures for their latent variables and some had 5-point scales and 7-point ones.
 

spunky

Smelly poop man with doo doo pants.
#5
we were instructed (classroom setting) to use Mean scores, similar to the regression. But I encountered this study that used Zscores. The study made use of different measures for their latent variables and some had 5-point scales and 7-point ones.
care to share what "this study" is? is it a published article we could have access to? if these people did things right, they fitted their SEM model using a method specifically designed for (ordered) categorical data and there is a (very) tangential relationship between z-scores and SEM through the probit link function.