Yu Han, Jiang Shanhe, Huang Hong
Department of Applied Statistics and Research Methods, University of Northern Colorado, Greeley, CO, USA.
Department of Criminal Justice, Wayne State University, Detroit, MI, USA.
J Appl Stat. 2021 Feb 16;49(8):1979-2000. doi: 10.1080/02664763.2021.1887101. eCollection 2022.
We extend the existing group-based trajectory modeling by proposing the network-based trajectory modeling based on judicious design and analysis of a spatio-temporal parse network (STPN) as a representation of neighborhood structure that evolves in time. The STPN offers a principled qualitative specification for an explicit paradigm framework to deal with complex real-world problems. The framework is completed by developing a quantitative specification of latent field representation to merge seamlessly on or alongside the established STPN via hierarchical modeling. The models adopt spatial random effects to characterize the heterogeneity and autocorrelation over the locations where nonlinear trajectories were observed. The trajectories are then investigated in the presence of the operational constraints of the dependence structure induced by the spatial and temporal dimensions. With the framework, complex developmental trajectory problems can be discerned, communicated, diagnosed and modeled in a relatively simple way that interpretation is accessible to nontechnical audiences and quickly comprehensible to technically sophisticated audiences. The proposed modeling is applied to address the challenges of the trajectory modeling of nonlinear dynamics arising from a motivating criminal justice empirical process.
我们通过提出基于网络的轨迹建模来扩展现有的基于群体的轨迹建模，该建模基于对时空解析网络（STPN）的审慎设计和分析，STPN作为随时间演变的邻域结构的一种表示。STPN为处理复杂现实世界问题的显式范式框架提供了一个有原则的定性规范。通过开发潜在场表示的定量规范，通过分层建模在已建立的STPN上或与之无缝合并，从而完善该框架。这些模型采用空间随机效应来表征在观察到非线性轨迹的位置上的异质性和自相关性。然后，在由空间和时间维度引起的依赖结构的操作约束存在的情况下研究这些轨迹。借助该框架，复杂的发展轨迹问题可以以一种相对简单的方式被识别、交流、诊断和建模，非技术受众可以理解其解释，技术精湛的受众也能快速理解。所提出的建模方法被应用于应对源于一个具有启发性的刑事司法实证过程的非线性动力学轨迹建模的挑战。
