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

[franz...@gmail.com]

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 = fin.team)

 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, fin.team, fixed.x = F,
            estimator = "MLM",
            meanstructure = T,
            int.ov.free = T,
            auto.var = T,
            auto.fix.first =T,
            auto.cov.lv.x = T)

 fit.team.main.d.c <- lavaan.survey(fit.main.d.c, design.boot) 

 summary(fit.team.main.d, 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!

Best,

Franzi