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 sophisticated statistical approaches to help local authorities implement new policies and mitigate the problem. These models are typically developed taking into account a set of socio-economic or demographic variables, such as population density and traffic volumes. However, they usually ignore that the external factors may be suffering from measurement errors, which can severely bias the statistical inference. This paper presents 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 considering all road collisions 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 corrected using a measurement error model. Our results show that omitting measurement error considerably worsens the model's fit and attenuates the effects of imprecise covariates.