A New Spatial Count Data Model with Time-varying Parameters

TL;DR

This paper introduces a novel spatiotemporal count data model with time-varying parameters and a conjugate Gibbs sampler, enabling better understanding of crash frequency dynamics over time.

Contribution

The paper proposes a new count data model that captures temporal variation in parameters and spatial correlation, with a Gibbs sampler ensuring efficient Bayesian inference.

Findings

Model reveals significant temporal instability in crash data.

Safety benefits of pavement quality increase over time.

Gibbs sampler performs well in Monte Carlo validation.

Abstract

Recent crash frequency studies incorporate spatiotemporal correlations, but these studies have two key limitations: i) none of these studies accounts for temporal variation in model parameters; and ii) Gibbs sampler suffers from convergence issues due to non-conjugacy. To address the first limitation, we propose a new count data model that identifies the underlying temporal patterns of the regression parameters while simultaneously allowing for time-varying spatial correlation. The model is also extended to incorporate heterogeneity in non-temporal parameters across spatial units. We tackle the second shortcoming by deriving a Gibbs sampler that ensures conditionally conjugate posterior updates for all model parameters. To this end, we take the advantages of P\'olya-Gamma data augmentation and forward filtering backward sampling (FFBS) algorithm. After validating the properties of the Gibbs sampler in a Monte Carlo study, the advantages of the proposed specification are demonstrated in an empirical application to uncover relationships between crash frequency spanning across nine years and pavement characteristics. Model parameters exhibit practically significant temporal patterns (i.e., temporal instability). For example, the safety benefits of better pavement ride quality are estimated to increase over time.