Abstract
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.