Hurdle Network Model With Latent Dynamic Shrinkage For Enhanced Edge Prediction in Zero-Inflated Directed Network Time Series

Abstract

This article aims to model international trade relationships among 29 countries in the apparel industry between 1994 and 2013. Bilateral trade flows can be represented as a directed network, where nodes correspond to countries and directed edges indicate trade flows (i.e., whether one country exported to another in a given year). Additionally, node (e.g., GDP) and edge-specific (e.g., labor provision) covariates are also available. The study focuses on two key challenges: (1) capturing multiple forms of temporal and network dependence, and dependence on covariates; and (2) accounting for potential trade volume as an important but partially observed edge-specific covariate, which is only available for country pairs that engaged in trade. To address these challenges, we introduce the dynamic hurdle network model (Hurdle-Net) for zero-inflated directed network time series that incorporates several novel features. First, it represents the time series as a paired binary and continuous time series and utilizes a hurdle model that effectively handles sparsity in edge occurrence. Second, the model captures evolving network dependencies using node-specific latent variables governed by a dynamic shrinkage process. Third, it leverages a shared latent structure across the binary and continuous components, reflecting the fact that both networks involve the same nodes. Finally, the model employs a generalized logistic link function to relate edge occurrence to edge weight, allowing for a parsimonious and coherent hierarchical Bayesian framework that jointly models both network components. Compared to static or independent models, Hurdle-Net provides improved model selection, estimation, and prediction performance for analyzing international trade patterns. Its effectiveness is demonstrated through simulation studies and an application to bilateral trade flow data.