My data has a nested structure, which is suitable for hierarchical modelling. The categorical variable used as a hierarchical level is county. As the counties are unequally sized (different number of subjects), I use hierarchical modelling for analysing temporal changes.
First, am I correct, that the hierarchical modelling allows reporting temporal changes in a way, where all counties (small and big-sized) have equal contribution to the conditional effects? Or in other words, the results are less affected by the big counties.
Second, which of the following model structures should I use if I am interested in county-level trends only (not country-wide trends):
y ~ time + (time | county)
y ~ (time | county)
When plotting the conditional effects of these models, the results are more or less the same. I use https://cran.r-project.org/web/packages/brms/index.html