Modelling area-wide count outcomes with spatial correlation and heterogeneity: an analysis of London crash data

Count models such as negative binomial (NB) regression models are normally employed to establish a relationship between area-wide traffic crashes and the contributing factors. Since crash data are collected with reference to location measured as points in space, spatial dependence exists among the area-level crash observations. Although NB models can take account of the effect of unobserved heterogeneity (due to omitted variables in the model) among neighbourhoods, such models may not account for spatial correlation areas. It is then essential to adopt an econometric model that takes account of both spatial dependence and uncorrelated heterogeneity simultaneously among neighbouring units. In studying the spatial pattern of traffic crashes, two types of spatial models may be employed: (i) classical spatial models for higher levels of spatial aggregation such as states, counties, etc. and (ii) Bayesian hierarchical models for all spatial units, especially for smaller scale area-aggregations. Therefore, the primary objectives of this paper is to develop a series of relationships between area-wide different traffic casualties and the contributing factors associated with ward characteristics using both non-spatial models (such as NB models) and spatial models and to identify the similarities and differences among these relationships. The spatial units of the analysis are the 633 census wards from the Greater London metropolitan area. Ward-level casualty data are disaggregated by severity of the casualty (such as fatalities, serious injuries, and slight injuries) and by severity of the casualty related to various road users. The analysis implies that different ward-level factors affect traffic casualties differently. The results also suggest that Bayesian hierarchical models are more appropriate in developing a relationship between area-wide traffic crashes and the contributing factors associated with the road infrastructure, socioeconomic and traffic conditions of the area. This is because Bayesian models accurately take account of both spatial dependence and uncorrelated heterogeneity.