Population-wide county-based data: reasonable to report temporal trends using hierarchical modelling? I have a population-wide data, including county-level information. Subjects are unequally distributed between the 10 counties in the dataset, resulting in multifold differences. The problem is that crude estimates would depend mostly on large counties. However, would it be reasonable to report country-wide temporal trends using hierarchical modelling y ~ predictor + (1|county)?
 A: I think that using a multilevel model for this task makes a lot of sense. A critical issue is how time enters the model. Most typically it would enter as a "fixed" predictor treated as a continuous variable to estimate a linear association between time passed and the outcome:
In lmer:
m1 <- lmer(y ~ time + (1|county), df)

Depending on your goal for the analysis, you might be interested in whether the time trend varies across counties, in which case you can augment the model to allow for county variation in the linear relation between time and y:
m2 <- lmer(y ~ time + (time|county), df)

m1 is nested within m2 and you can use a likelihood ratio test to determine whether the added complexity of m2 (a random slope for time and the random covariance between the time slopes and the county intercepts) provides a better fit to the data than just a single random intercept for county in m1:
anova(m2, m1)

A completely different direction would be to think of the time effect as being crossed with county such that all counties are affected similarly by some event or characteristics that are tracked in the occasions of measurement. This is called a two-way error components model by economists because there are two random intercepts for different clustering units. Psychologists and others call this a cross-classified model:
m3 <- lmer(y ~ 1 + (1|county) + (1|time), df)

The residual from this model ($e_{ij}$) captures any interaction between occasion and county as well as other county effect specific to county$_i$ on occasion$_j$. This model is less common, but is just as valid, especially if you expect the occasion effect to have similar influences on all counties. Note that this model is not nested within either m1 or m2 so you cannot use likelihood ratio testing to compare it to either of them.
