  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.
