They are very different:
- "converged" is indeed about the optimizer only; most algorithms in
lavaan are iterative (using the nlminb() function) and the optimizer may
simply not converge, implying that it did not find a (reasonable) solution
- "post.check" is only relevant if the model converged; this is a check
to see if the estimated parameter values are all 'admissible' (i.e., no
negative variances, all covariance matrices positive-definite); this is
a very different type of information; not everyone wants to 'exclude'
improper (but converged) solutions in a simulation study, because not
everybody feels that, say, a tiny negative variance is problematic (in
particular when the sample size is small)
Yves.
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