I have a model of vignettes nested in respondents. In my simulation, I would like to replace respondents (level 2) as well as vignettes (level 1) within respondents.
How could I bootstrap at both levels simultaneously? Ideally using Stata, but any recommendation in other software is welcome.
Not sure that I really understand the question as it is not usual for the bootstrap to be used to estimate hierarchical models, as there are good general purpose algorithms.
That being said the MLwiN software uses likelihood , Bayesian MCMC procedures and the iterated bootstrap to estimate models. The latter is used with discrete response outcomes where it is known that quasi-likelihood procedures can give biased estimates in certain circumstances (when there are important higher level effects and there are few lower level units in a typical higher- level unit). But these days most people use MCMC to get better estimates rather than the iterated bootstrap
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html
MLwiN can be run from within Stata but you need both sets of software on your machine
http://www.bristol.ac.uk/cmm/software/runmlwin/
" The multilevel models fitted by runmlwin are often considerably faster than those fitted by the Stata's xtmixed, xtmelogit and xtmepoisson commands. The range of models which can be fitted by runmlwin is also much wider than those commands. runmlwin also allows fast estimation on large data sets for many of the more complex multilevel models available through the user written gllamm command. "
Is bootstrap not in your software, i cant help. It is in Sas, Mplus, Stats, R. Dont know about Spss.
You can check this link https://journals.sagepub.com/doi/suppl/10.1177/0013164416678980/suppl_file/Online_Appendix.pdf
supplementary files for https://journals.sagepub.com/doi/suppl/10.1177/0013164416678980