Kate, I will refer to the latent variable part of your question as Patrick already answered your question with regard to composite variables.

In order to justify using an estimator based on the assumption of multivariate normality, you would only investigate the distribution of the observed variables, such as indicators in measurement models, and not the latent variables. You would of course assume that the errors are normally distributed (these are also latent variables). When the observed variables are MVN distributed, then the latent variables should be normally distributed, too, as each observed variable consists of (normally distributed) errors and true scores.

Does this help?

Regards, Karin

Kate,

Item-level indicators are considered endogenous manifest variables, as they are "caused by" their factors. So a composite would address only the distribution of the composite--it would not give you information about MVN for a full measurement model.

Pat

Kate, I will refer to the latent variable part of your question as Patrick already answered your question with regard to composite variables.

In order to justify using an estimator based on the assumption of multivariate normality, you would only investigate the distribution of the observed variables, such as indicators in measurement models, and not the latent variables. You would of course assume that the errors are normally distributed (these are also latent variables). When the observed variables are MVN distributed, then the latent variables should be normally distributed, too, as each observed variable consists of (normally distributed) errors and true scores.

Does this help?

Regards, Karin

Dear all, 

When we become applying SEM we can do the exploration of data doing the analysis of mutlivariate normality, symetry, kurtosis, outliers .

Ususally i try to see if there are outliers,...i.e i try to "clean the variables. Then i will see again how is performing SEM. if the model continue not being good, i do the usual things: i analyse MI. We do the correction one by one..until the model become good.

Have a nice time

Helena

I forget to  say the the use of MI must have support in theory. You should never decide the improvement of your model based only in statistics, but should have always support on theory, if not you would have a very very good fit but your model has nothing to do with reality. There are also others measures of qualitiy of adjustment.

Thanks to all contributors, so far.  You have each given me food for thought. 

I've seen a few published articles using the aggregate score for a latent variable in Mardia's Test.  So, that's a "no-no," right?  

Kate, that depends, as is often the case. For example, if you have a small sample size you may not be able to analyze a large model. Then it would be an option to build an index of the observed variables measuring the same construct and to include the aggregate in you model. In this case, when you treat the latent variable as if it were a manifest variable, you may wish to know whether this variable is normally distributed.

Regards, Karin