Measurement error models for spatial network lattice data: analysis of car crashes in Leeds

Road casualties represent an alarming concern for modern societies, especially in poor and developing countries. In the last years, several authors developed a series of statistical approaches to help authorities implement new policies and mitigate the problem. These models are typically developed taking into account socio-demographic variables such as population density or traffic volumes, but they usually ignore that these external factors may be suffering from measurement error which can severely bias the statistical inference. Therefore, we propose a Bayesian hierarchical model to analyse car crashes occurrences at the network lattice level taking into account measurement error in the spatial covariates. The suggested methodology is exemplified by considering the collisions that occurred in the road network of Leeds (UK) from 2011 to 2019. Traffic volumes are approximated at the street segment level using an extensive set of road counts obtained from mobile devices and the estimates are adjusted using a spatial measurement error correction. Our results show that ignoring the measurement error considerably worsens the model’s fit and attenuates the effects of the imprecise covariates.