Tree-Structured Clustering in Fixed Effects Models

Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of effects that have to be estimated. A recursive partitioning (or tree based) method is proposed that identifies clusters of units that share the same effect. The approach reduces the number of parameters to be estimated and is useful in particular if one is interested in identifying clusters with the same effect on a response variable. It is shown that the method performs well and outperforms competitors like the finite mixture model in particular if the heterogeneity component is correlated with explanatory variables. In two applications the usefulness of the approach to identify clusters that share the same effect is illustrated. Supplementary materials for this article are available online.

固定效应模型(Fixed Effects Models)具有极高的灵活性，其无需对效应的分布作出假设，且在异质性成分与解释变量存在相关性的场景下仍可适用。该方法的缺点在于需要估计的效应数量较多。本文提出一种递归分割（或称基于树的）方法，能够识别拥有相同效应的个体集群。该方法可有效减少待估计参数的数量，尤其适用于需要识别对响应变量具有相同效应的集群的研究场景。研究表明，该方法表现优异，当异质性成分与解释变量存在相关性时，其性能更是优于有限混合模型(Finite Mixture Model)等同类竞争方法。本文通过两项应用实例，展示了该方法在识别共享相同效应的集群方面的应用价值。本文的补充材料可在线获取。