Multilevel regression and post-stratification (MRP) is a popular use of hierarchical models in political science. Multiple papers have suggested that relying on machine learning methods can provide substantially better performance than traditional approaches that use hierarchical models. However, these comparisons are often unfair to traditional techniques as they omit possibly important interactions or nonlinear effects. I show that complex (“deep”) hierarchical models that include interactions can nearly match or outperform state-of-the-art machine learning methods. Combining multiple models into an ensemble can improve performance, although deep hierarchical models are themselves given considerable weight in these ensembles. The main limitation to using deep hierarchical models is speed. This paper derives new techniques to further accelerate estimation using variational approximations. I provide software that uses weakly informative priors and can estimate nonlinear effects using splines. This allows flexible and complex hierarchical models to be fit as quickly as many comparable machine learning techniques.

Pepinsky, Goodman, and Ziller (2024, American Political Science Review, PGZ) reassess a recent study on the long-term consequences of concentration camps in Germany. The authors conclude that accounting for contemporary (i.e., post-treatment) state heterogeneity in the models provides unbiased estimates of the effects of camps on current-day outgroup intolerance. In this note, we show that PGZ’s empirical strategy rests on (a) a mischaracterization of what regional fixed effects capture and (b) two unrealistic assumptions that can be avoided with pre-treatment state fixed effects. We further demonstrate that results from the original article remain substantively the same when we incorporate regional fixed effects correctly. Finally, simulations reveal that camp proximity consistently outperforms spatially correlated noise in this specific study. The note contributes to the growing literature on legacy studies by advancing the discussion about the correct modeling choices in this challenging field.