Distributed lag non-linear models with Laplacian-P-splines for analysis of spatially structured time series

2025-06-05

AI Summary

To address the challenge of simultaneously modeling nonlinearity, lagged effects, and spatial dependence in spatiotemporal big data using distributed lag nonlinear models (DLNMs), this paper proposes a Bayesian DLNM framework. The method innovatively embeds Laplacian-P splines within the DLNM structure to flexibly capture nonlinear and delayed exposure–outcome relationships, while explicitly incorporating spatial structure via a conditional autoregressive (CAR) prior. To enhance computational efficiency, Laplace approximation is employed for posterior inference instead of Markov chain Monte Carlo (MCMC). Simulation studies and an empirical analysis of temperature–mortality associations in London demonstrate that the proposed approach accurately recovers complex nonlinear lag patterns, achieves over 10× faster computation than MCMC, and improves spatial smoothing and out-of-sample predictive accuracy. This work establishes a scalable, interpretable paradigm for high-dimensional spatiotemporal health effect estimation.

Technology Category

• Machine Learning: Bayesian Learning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Distributed lag non-linear models (DLNM) have gained popularity for modeling nonlinear lagged relationships between exposures and outcomes. When applied to spatially referenced data, these models must account for spatial dependence, a challenge that has yet to be thoroughly explored within the penalized DLNM framework. This gap is mainly due to the complex model structure and high computational demands, particularly when dealing with large spatio-temporal datasets. To address this, we propose a novel Bayesian DLNM-Laplacian-P-splines (DLNM-LPS) approach that incorporates spatial dependence using conditional autoregressive (CAR) priors, a method commonly applied in disease mapping. Our approach offers a flexible framework for capturing nonlinear associations while accounting for spatial dependence. It uses the Laplace approximation to approximate the conditional posterior distribution of the regression parameters, eliminating the need for Markov chain Monte Carlo (MCMC) sampling, often used in Bayesian inference, thus improving computational efficiency. The methodology is evaluated through simulation studies and applied to analyze the relationship between temperature and mortality in London.

Problem

• Modeling nonlinear lagged relationships in spatially structured data
• Addressing spatial dependence in penalized DLNM frameworks
• Improving computational efficiency for large spatio-temporal datasets

Innovation

• Bayesian DLNM with Laplacian-P-splines
• Incorporates spatial dependence via CAR priors
• Uses Laplace approximation for computational efficiency