I have a non-nested panel data structure of firms across 24 different countries and 24 different years. Not every firm has data for every year. Every firm belongs to one country. I model this data structure using the following brms() syntax.
y ~ 1 + x1 + ( 1 + x1 | year:country) + (1|year) + (1|country)
Does this model formula / approach make sense in terms of modelling this non-nested multiple membership structure?
Is it correct to say that this structure implies that individual firms are nested within all three groups (
country, year, country:year), rather than only within
country:yeargroups? (I ask because it also possible, apparently, to treat
country:yearsas cross-classified within
yearsalong with individual firms as strictly nested in country:years.)***
*** Alexander W. Schmidt-Catran and Malcolm Fairbrother, `The Random Effects in Multilevel Models: Getting Them Wrong and Getting Them Right’, European Sociological Review, 2016, Vol. 32, No. 1, 23–38.