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.
翻译:如何估计异质性,例如,不同观测之间某些差异的影响,是政治科学中的一个关键问题。这样做的方法简化了对异质性基本性质的假设,以得出可靠的推论。本文件允许一种简化复杂现象的共同方法(将具有类似效果的观测结果纳入离散群体)纳入回归分析。框架允许研究人员(一) 利用其先前的知识来指导哪些群体是允许的,(二) 适当量化不确定性。本文这样做的方式是通过产生新的理论结果和推断技术,将“结构化的宽度”工作从传统的惩罚性可能性方法扩大到贝叶斯人,从而将“结构化的宽度”工作从新的理论结果和推断技术扩大到巴伊斯人。它表明,当基本异质性被分组时,这一方法优于最先进的估计多种效应的方法,并更有效地确定观测数据具有不同效果的观察组。