Hi,
I have a nonnested 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) + (1year) + (1country)

Does this model formula / approach make sense in terms of modelling this nonnested 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:year
groups? (I ask because it also possible, apparently, to treat country:years
as crossclassified within countries
and years
along with individual firms as strictly nested in country:years.)***
Many thanks,
Ilan
*** Alexander W. SchmidtCatran 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.
Thanks for this, Paul.
Could you expand a little on your point .1 if you have a moment?
Point 2. Fairbrother (below) describes Model F as follows: “Model F treats countryyears as crossclassified within countries and years, and individuals as strictly nested in countryyears.”
And to your Point 1. above, Fairbrother says of Model A: " This structure implicitly treats any timeinvariant countrylevel variable as a timevarying one, and thus as having 100 unique values [20 countries each with 5 unique values]. Conversely, the model does not regard repeated observations on countries as nested within countries".
Many thanks,
With regard to (1) I would probably write
1 + x1 + ( 1 + x1  year:country) + (1 + x1  year) + (1 + x1  country)
if x1 is varying both within year and country.
The nested structure presented in the paper is likely equivalent to the sort of nonnested formulation that you use in brms. This can be checked by taking the hierarchical equations from the paper (if they are some) and writing down all within the same linear predictor.
2 Likes
Sorry, one more thing, would this equation below, as estimated by brms():
1 + x1 + ( 1 + x1  year:country) + (1 + x1  year) + (1 + x1  country)
be considered to be a crossclassified data structure with firms nested separately within countries
, and then separately within years
, and then separately within country:years
? Just wondering how best to understand it hierarchically within brms().
Since I would speculate that we would want years
to be nested within year:country
; and same with our country
groups: surely they should also be thought of as being nested within year:country
? But not sure if that would make a difference theoretically and practically…
Thanks,
I would say you could call that structure crossclassified in the way you described.
I would personally speak of year:country
being nested within year and country (not the other way round) in the same way as students are nested within classes.