Are CIs from fitting a SEM with a survey-resampling similar to se = bootstrap?

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Aug 1, 2018, 4:09:29 AM8/1/18
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Dear lavaan-fans and -friends!

I have a question which is hopefully not too trivial.
I am using lavaan.survey to account for the fact that in my data teams are nested in teams. I also know that most of my variables are lacking normal distribution and that there are a lot of missings in the data. Therefore, I adjusted the standard errors to the data structure and I apply bootstrapping to the resulting data before fitting them with the model.

 design <- svydesign(ids=~team, probs = ~1, data =
 design.boot <- as.svrepdesign(design, type = "bootstrap", replicates = 5000)

The actual goal of the analysis is to fit a moderated mediation with multiple mediators and multiple moderators.
Now, I have also read that under these circumstances (lacking normality, mediaiton) it is better to assess indirect effects by looking at the bootstrap-CIs instead of p-values.

 fit.main.d.c <- lavaan(sem1,, fixed.x = F,
            estimator = "MLM",
            meanstructure = T,
   = T,
            auto.var = T,
            auto.fix.first =T,
   = T) <- lavaan.survey(fit.main.d.c, design.boot) 
 summary(, fit.measures = T, standardized = T, ci = T)

My question is whether the CIs I request in the summary-function are already the same as the ones I would get if set "se = bootstrap" in the fit function?
can get when I request bootstrap = T in the first fit-function? The reason why I am asking is that I need to set MLM as estimator in the first fit function (lavaan-function) to be able to use the lavaan-object in the lavaan.survey-function but setting "se = bootstrap" in the lavaan-function requires that the estimator in the same is set to "ML".
If it is not equal, I would be grateful for any advice on how I can get around this issue somehow.

Thank you in advance!
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