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I am conducting a cfa (two level, with meaning of level 2;it is staff rating organizations and we care about organizations).

My question is what is the difference is in mplus between type=complex (mlr with sandwich) and type=twolevel if mlr is selected as an estimator with no covariates in the model?

These should be the same corrct?

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If you care about the organizations (the clusters), then use type=twolevel and estimate a within and a between part of your model.

If you were not concerned about the clustering level but wanted to control for within-cluster correlation (you should do that), you would use type=complex to make Mplus use a sandwich estimator.

These two solutions are different in that they will estimate different models (two-level vs single level), and you can expect that they will produce different results for the within part (which would be the only part estimated if you use type=complex model).

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