In this tutorial we present the use of R package mgcv to implement Distributed Lag Non-Linear Models (DLNMs) in a flexible way. Interpretation of smoothing splines as random quantities enables approximate Bayesian inference, which in turn allows uncertainty quantification and comprehensive model checking. We illustrate various modeling situations using open-access epidemiological data in conjunction with simulation experiments. We demonstrate the inclusion of temporal structures and the use of mixture distributions to allow for extreme outliers. Moreover, we demonstrate interactions of the temporal lagged structures with other covariates with different lagged periods for different covariates. Spatial structures are also demonstrated, including smooth spatial variability and Markov random fields, in addition to hierarchical formulations to allow for non-structured dependency. Posterior predictive simulation is used to ensure models verify well against the data.

中文翻译：

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使用 mgcv 的计数数据的灵活分布式滞后模型

在本教程中，我们将介绍如何使用 R 包 mgcv 以灵活的方式实现分布式滞后非线性模型 （DLNM）。将平滑样条解释为随机量可实现近似贝叶斯推理，从而实现不确定性量化和全面的模型检查。我们使用开放获取的流行病学数据结合模拟实验来说明各种建模情况。我们演示了时间结构的包含和使用混合分布来允许极端异常值。此外，我们证明了时间滞后结构与其他协变量的交互作用，不同协变量具有不同的滞后周期。此外，还演示了空间结构，包括平滑空间可变性和马尔可夫随机场，以及允许非结构化依赖关系的分层公式。后验预测模拟用于确保模型根据数据进行良好验证。