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Is it possible to use both cluster standard errors and multilevel models together and how does one implement this in R?

In my set up I am running a conjoint experiment in 26 countries with 2000 participants per country. Like any conjoint experiment each participant is shown two vignettes and asked to choose/rate each vignette. The same participants is then shown two fresh vignettes for comparison and asked to repeat the task. In this case each participant performs two comparisons. The hierarchy is thus comparisons nested within individuals nested within countries. I am currently running a multilevel model with each comparison at level 1 and country is the level 2 unit. Obviously comparisons within individuals are likely to be correlated so I'd like to cluster standard errors at the individual level as well. It seems overkill to add another level in the MLM for this since the size of my clusters are extremely small (n=2) and it makes more sense to do my analysis at the individual level (not to mention unnecessarily complicating the model since with 2000 individuals*26 countries the parameter space becomes crazy huge). Is this possible? If so how does one do this in R together with a multilevel model set up?

jonnyf
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The cluster size of 2 is not an issue, and I don't see any issue with the parameter space either. If you fit random intercepts for participants, and countries, these are estimated as latent normally distributed variables. A model such as:

lmer(outomce ~ fixed effects + (1|country/participant)

This will handle the dependencies within clusters (at the participant level and the country level) so there will be no need to use cluster standard errors.

Robert Long
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  • Thanks for the comment. So I thought about doing that and ended up fitting a random intercept per participant. But I was given feedback by my prof that this doesn't solve the issue that the betas for the fixed effects are still correlated within individuals. To my mind it seems like the only way to solve this would be to run lmer(outcome ~ fixed effects + (1 + fixed effects | country/participant)) However this immediately becomes a very computationally expensive model with so many random effects to run – jonnyf May 20 '22 at 08:43
  • There is a paper by Schuessler and Freitag (2020) https://osf.io/preprints/socarxiv/9yuhp/ In section 5 they talk about clustering SEs for conjoint experiments, and that actually it's not a big deal if you don't cluster it. According to them the only valid reason for clustering is if one is interested in population ATE > sample ATE, which we are, but even then the authors show that clustering in conjoints increases SEs by merely 2% or so. I'm not sure how much comfort I can take in that – jonnyf May 20 '22 at 08:50