I know that they are different but I am kind of at a loss for how to explain the difference, but I may be overthinking it. In simple terms, my understanding is that a latent mean(intercept) is an estimation of a theoretical construct that is equal to 0. You can rescale the latent mean by fixing the variance to 1 and setting the intercept of one of the indicators to 0. In this case the latent mean will take on the scale of the indicator. An observed composite mean is simply the mean of the indicators of the factor. The main difference between the two is that the composite mean includes the measurement error of the observed variables, while the latent mean adjusts for this.
Am I missing anything else here? Also, I assume that it would be inappropriate to compare the latent mean from one study with a composite mean from another study?
Dear Lendi,
if you allow some self-ad: Here are to sources that focus on the difference:
Steinmetz, H. (2010). Estimation and comparison of latent means across cultures. In P. Schmidt, J. Billiet, & E. Davidov (Eds.), Cross-cultural analysis: Methods and applications (pp. 85-116). Taylor & Francis Group: Routledge.
Steinmetz, H. (2013). Analyzing observed composite differences across groups: Is partial measurement invariance enough? Methodology, 9(1), 1-12. doi:10.1027/1614-2241/a000049
With best regards
--Holger
What software did you use in this regard?
This will give you an important idea.
Yes, you are right. Also, the latent variable consists of factor loadings, which are weighting each indicators differently. In contrast to sum scores with all indicators weighted equally.
Best,
Rolf
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