Re-Evaluating Machine Learning for MRP Given the Comparable Performance of (Deep) Hierarchical Models

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.