Bootstrap hierarchical data at both level 1 and level 2

[Johannes Muller]

Dear All,

I am using hierarchically nested data of 5,000 individuals (level 1) nested in 50 regions (level 2) to estimate a multilevel mediation. An earlier threat discusses how to set up the gsem estimation and how to derive the indirect effects etc here: https://www.statalist.org/forums/for...cts-after-gsem

One issue that's left largely undiscussed there (aside from the last comment and warning of @Mike Zyphur) is that the bootstraping required to obtain credible confidence intervals for a multilevel mediation is not straightforward, i.e. simply bootstrapping individuals / at level 1 is not an ideal solution.

I am wondering whether there are any implementations or advice that would help with first sampling regions (i.e. at level 2) and then sampling individuals (level 1), i.e. a "joint two-stage bootstrap".

Many thanks in advance!

[Felix Bittmann]

I see two potential options here. Either stratify on the region so you know the size of each resample is equal to the original size of the regions. Or view the regions as clusters and sample entire clusters and not individuals. Both options are easy to set up. However I am not sure which is better and if there is any statistical validation for these techniques.

[Johannes Muller]

Hi Felix, thanks for this.
I am not entirely sure I follow #1. Could you help me with a few more pointers there?
Me sense is that #2, sampling regions, may not be desireable given the underline data-generating process. Ideally, I would like to combine level 2 and level 1 sampling in the bootstrap if at all possible...
Many thanks again!!

[Felix Bittmann]

Regarding #1, you can do it like:

bootstrap ..., strata(region): command

Regarding #2, i am not sure how this could work. You would need to write a command that first samples regions and then, in a second step, samples individuals from the regions.