Panel Data Analysis via Mechanistic Models

Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared parameters while also having unit-specific parameters. To give the scientist flexibility in model specification, we are motivated to develop a framework for inference on panel data permitting the consideration of arbitrary nonlinear, partially observed panel models. We build on iterated filtering techniques that provide likelihood-based inference on nonlinear partially observed Markov process models for time series data. Our methodology depends on the latent Markov process only through simulation; this plug-and-play property ensures applicability to a large class of models. We demonstrate our methodology on a toy example and two epidemiological case studies. We address inferential and computational issues arising due to the combination of model complexity and dataset size. Supplementary materials for this article are available online.

面板数据（Panel data）又称纵向数据（longitudinal data），是一类时间序列（time series）的集合。每条时间序列本身可为多元序列，由针对某一不同个体的一系列测量值构成。机理建模（Mechanistic modeling）指通过基于科学原理的方程，对驱动每个个体观测值的动态系统集合进行描述。面板系统的核心特征为：个体间的动态交互可忽略不计，因此面板模型由一系列独立随机过程（stochastic processes）构成，这类过程通常通过共享参数实现关联，同时亦包含个体专属参数。为给研究者提供模型设定层面的灵活性，我们致力于开发一套面向面板数据的推断框架，以支持任意非线性、部分可观测的面板模型的研究。我们基于迭代滤波技术（iterated filtering techniques）开展研究，该技术可针对时间序列数据的非线性部分可观测马尔可夫过程（Markov process）模型实现基于似然的推断。我们的方法仅通过模拟依赖于隐马尔可夫过程（latent Markov process），这一即插即用（plug-and-play）特性确保了其可适用于大量模型类别。我们通过一个玩具示例（toy example）与两项流行病学案例研究验证了所提方法的有效性，并针对模型复杂度与数据集规模结合所引发的推断与计算问题展开了探讨。本文的补充材料可在线获取。