The model-based approach (aka design based) has been shown to perform equally well as the multi-level approach. Primarily it adjusts the SE for the presence of bias resulting from grouped participants (e.g., students in classes).

A good read on the comparison b/w the two approaches is:

Wu, J.-Y., & Kwok, O.-m. (2012). Using SEM to analyze complex survey data: A comparison between design-based single-level and model-based multilevel approaches. Structural Equation Modeling: A Multidisciplinary Journal, 19(1), 16-35. doi:10.1080/10705511.2012.634703

To my understanding, there is no need to center the items when using TYPE=COMPLEX, or for any model-based approach in general. It will simply change the scale of your latent variable -- which may or may not be meaningful in its own right.

Hope this is helpful, and wishing you well in your research.

Tim

For me there is a real difference between these two - Robust SEs are a technical fix, multilevel addresses the substantive problem that there there might be different constructs at each level. Imagine individuals at level 1 and neighborhoods at level 2; the constructs of deprivation might be quite different at each level with quite different loadings.

So it depends on what you want to find out. I am surprised that you have been advised to de-mean as that would remove the higher-level (neighbourhood) variation and reduce any variables measured at the higher level to be, in effect, all zeros.

For discussion about these two different viewpoints in regression-like analysis , see this recent exchange:

https://www.researchgate.net/post/When_should_I_use_multilevel_modellings_vs_cluster_robust_standard_errors

Thank you very much for your explanations and references! This helps a lot!