A process convolution model for crash count data on a network.

Crash data observed on a road network often exhibit spatial correlation due to unobserved effects with inherent spatial correlation following the structure of the road network. It is important to model this spatial correlation while accounting for the road network structure. In this study, we introduce the network process convolution (NPC) model. In this model, the spatial correlation among crash data is captured by a Gaussian Process (GP) approximated through a kernel convolution approach. The GP's covariance function is based on path distance computed between a limited set of knots and crash data points on the road network. The proposed model offers a straightforward approach for predicting crash frequency at unobserved locations where covariates are available, and for interpolating the GP values anywhere on the network. Inference procedure is performed following the Bayesian paradigm and is implemented in R-INLA, which offers an estimation procedure that is very efficient compared to Markov Chain Monte Carlo sampling algorithms. We fitted our model to synthetic data and to crash data from Ottawa, Canada. We compared the proposed approach with a proper Conditional Autoregressive (pCAR) model, and with Poisson Regression (PR) and Negative Binomial (NB) models without latent effects. The results of the study indicated that although the pCAR model has comparable fitting performance, the NPC model outperforms pCAR when the main goal is to predict unobserved locations of interest. The proposed model also offers lower mean absolute error rates for cross validated crash counts, latent variable values, fixed-effect coefficients, as well as shorter interval scores for singletons. The NPC provides a natural way to account for the road network structure when considering the inclusion of spatially structured latent random effects in the modelling of crash data. It also offers an improved predictive capability for crash data on a road network.