Researchers often have to deal with heterogeneous population with mixed regression relationships, increasingly so in the era of data explosion. In such problems, when there are many candidate predictors, it is not only of interest to identify the predictors that are associated with the outcome, but also to distinguish the true sources of heterogeneity, that is, to identify the predictors that have different effects among the clusters and thus are the true contributors to the formation of the clusters. We clarify the concepts of the source of heterogeneity that account for potential scale differences of the clusters and propose a regularized finite mixture effects regression to achieve heterogeneity pursuit and feature selection simultaneously. We develop an efficient algorithm and show that our approach can achieve both estimation and selection consistency. Simulation studies further demonstrate the effectiveness of our method under various practical scenarios. Three applications are presented, namely, an imaging genetics study for linking genetic factors and brain neuroimaging traits in Alzheimer's disease, a public health study for exploring the association between suicide risk among adolescents and their school district characteristics, and a sport analytics study for understanding how the salary levels of baseball players are associated with their performance and contractual status.

中文翻译：

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在集群人口建模中寻找异质性的来源

研究人员经常不得不处理具有混合回归关系的异质人群，在数据爆炸的时代越来越多。在这样的问题中，当候选预测变量很多时，不仅要识别与结果相关的预测变量，还要区分异质性的真正来源，即识别出具有不同影响的预测变量。集群，因此是集群形成的真正贡献者。我们阐明了解释集群潜在规模差异的异质性来源的概念，并提出了一个正则化的有限混合效应回归同时实现异质性追求和特征选择。我们开发了一种有效的算法，并表明我们的方法可以实现估计和选择的一致性。仿真研究进一步证明了我们的方法在各种实际场景下的有效性。提出了三个应用程序，即一项将阿尔茨海默病的遗传因素和脑神经影像学特征联系起来的成像遗传学研究，一项探索青少年自杀风险与其学区特征之间关联的公共卫生研究，以及一项了解如何进行的运动分析研究。棒球运动员的工资水平与他们的表现和合同状况有关。