I am using coarsened exact matching (CEM) to match my treatment-control groups. As a result, the matches are grouped in strata. I would like to use both fixed effects model and mixed effects model next. I’m setting up my mixed effects model as following:

mixed dep indep treatment [fweight = cem_weight] || cem_strata: || firm:
  1. Is it sensible to use cem_strata as a level in the mixed effects model? I’m aware of people using match_id above firm_id in mixed model after propensity score matching.
  2. Is it ok to use cem_weight as a frequency weight? I read somewhere that cem_weight, usually used as iweight or aweight, can be used as fweight. Even though xtreg requires fweight to be an integer, mixed accepts non integer fweight. Can I directly feed fweight like I have done above?