A flexible multivariate conditional autoregression with application to road safety performance indicators.

Abstract

There is a dearth of models for multivariate spatially correlated data recorded on a lattice. Existing models incorporate some combination of three correlation terms: (i) the correlation between the multiple variables within each site, (ii) the spatial autocorrelation for each variable across the lattice, and (iii) the correlation between each variable at one site and a different variable at a neighbouring site. These may be thought of as correlation, spatial autocorrelation and spatial cross-correlation parameters respectively. This thesis develops a exible multivariate conditional autoregression model where the spatial cross-correlation is asymmetric. A comparison of the performance of the FMCAR with existing MCARs is performed through a simulation exercise. The FMCAR compares well with the other models, in terms of model fit and shrinkage, when applied to a range of simulated data. However, the FMCAR out performs all of the existing MCAR models when applied to data with asymmetric spatial crosscorrelations. To demonstrate the model, the FMCAR model is applied to road safety performance indicators. Namely, casualty counts by mode and severity for vulnerable road users in London, taken from the STATS19 dataset for 2006. However, by exploiting correlation between multiple performance indicators within local authorities and spatial auto and cross-correlation for the variables across local authorities, the FMCAR results in considerable shrinkage of the estimates of local authority performance. Whilst this does not enable local authorities to be differentiated based upon their road safety performance it produces a considerable reduction in the uncertainty surrounding their rankings. This is consistent with previous attempts to improve performance rankings. Further, although the findings of this thesis indicate that there is only mild evidence of asymmetry in the spatial cross-correlations for road casualty counts, the thesis provides a demonstration of the applicability of this model to real world social and economic problems