We propose a novel marginal additive model (MAM) for modeling cluster-correlated data with nonlinear population-averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between-cluster variability and cluster-specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (a) a longitudinal study of beaver foraging behavior and (b) a spatial analysis of Loa loa infection in West Africa.

中文翻译：

---

纵向和聚类相关数据中总体平均推理的边际加性模型

我们提出了一种新颖的边际加性模型（MAM），用于对具有非线性总体平均关联的聚类相关数据进行建模。所提出的 MAM 是一个统一的框架，用于边际均值模型的估计和不确定性量化，并结合集群间变异性的推断和集群特定的预测。我们提出了一种拟合算法，可以有效计算标准误差并纠正惩罚项的估计。我们在模拟中展示了所提出的方法，并将其应用于（a）海狸觅食行为的纵向研究和（b）西非罗阿罗阿感染的空间分析。