Modelling Heterogeneity Using Bayesian Structured Sparsity
This addresses the challenge of modeling heterogeneity in political science, but it is incremental as it extends existing structured sparsity work to a Bayesian framework.
The paper tackles the problem of estimating heterogeneity in political science by integrating discrete grouping into regression analysis, showing that their Bayesian structured sparsity method outperforms state-of-the-art methods when heterogeneity is grouped and more effectively identifies groups in observational data.
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to draw reliable inferences. This paper allows a common way of simplifying complex phenomenon (placing observations with similar effects into discrete groups) to be integrated into regression analysis. The framework allows researchers to (i) use their prior knowledge to guide which groups are permissible and (ii) appropriately quantify uncertainty. The paper does this by extending work on "structured sparsity" from a traditional penalized likelihood approach to a Bayesian one by deriving new theoretical results and inferential techniques. It shows that this method outperforms state-of-the-art methods for estimating heterogeneous effects when the underlying heterogeneity is grouped and more effectively identifies groups of observations with different effects in observational data.