I've been recently learning about mixed effects models (e.g. via Fitzmaurice, Laird, and Ware 's book Applied Longitudinal Analysis) as well as Bayesian hierarchical models (e.g. via Gelman and Hill's book Data Analysis Using Regression and Multilevel/Hierarchical Models)
One curious thing I've noticed: The Bayesian literature tends to emphasize that their models can handle covariates at multiple level of analysis. For example, if the clustering is by person, and each person is measured in multiple "trials," then the Bayesian hierarchical models can investigate the main effects of covariates both at the subject and trial level, as well as interactions across "levels."
However, I have not seen these kinds of models in the textbooks introducing frequentist methods.
I'm not sure if this is a coincidence, or an example of where Bayesian methods can do "more complicated things." Is it possible to use mixed effects models (e.g. the lme4 or nlme packages in the R statistical software) to investigate interactions of covariates across "levels" of analysis?