CFA: Collapsing data set with mean standardized factor score by group

[Tarjei W. Havneraas]

Hi

I am working on a confirmatory factor analysis (CFA) where the aim is to measure a latent attitude toward a medical practice. We are using a data set with items on attitudes towards this practice. We believe the average attitude towards the medical practice may vary by institutions.

To examine this, it would be interesting to plot the average standardized value of the latent factor score by institution. However, I wonder if we run into problems by using the mean of a standardized latent factor score by institution?

We proceed as follows:

1. Specify CFA model in standardized form
2. Extract standardized latent factor score (L1) with predict L1, latent
3. collapse (mean) L1 (semean) sem1 = L1, by(institution)
4. Calculate 95% CI
5. Plot average L1 by institution with 95% CI

Intuitively the plot makes sense as the scale is still in SD with the same range as the individual-level data set. While the mean value of aggregated L1 is ~0, the SD is ~.3 (=considerably lower than ~1). I have not seen any posts addressing this specific issue and would be happy for any feedback.