Is it useful to include cross-level-interaction in multilevel (hierarchical) models without varying slopes (only varying intercept)? A short example in R:
m1 <- lme(y~x_1+x_2+z_1+z_2+x_1:z_1, random = ~1|county, data = data)
Where:
- y = Response variable
- x = covariate from individual-Level
- z = covariate from group-Level
Technically these models can be fitted in R without warnings. But is it useful from a theoretical point of view? I once read that cross-level-interactions are only possible with individual-Level variables that possess a varying slope. Is that correct?