can I cluster standard errors within a multilevel model?

Question

I recognise this is similar to this but I couldn't understand the answer to the question and hence am asking again.

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. 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. Is this possible? If so how does one do this in R together with a multilevel model set up?

Answer 1

Edit: I'm adding more detail now per the comment below.

If you have a conjoint experiment and you're estimating logit models, you can cluster your standard errors with the logitr package: https://jhelvy.github.io/logitr/

To cluster standard errors at the individual level for your data, set the clusterID argument equal to a variable that identifies the individual.

For example, in the basic MNL models article, you could specify a cluster ID like this using the id variable (identifies the individual):

library("logitr")

mnl_pref <- logitr(
  data    = yogurt,
  outcome = 'choice',
  obsID   = 'obsID',
  pars    = c('price', 'feat', 'brand'),
  clusterID = 'id'
)