Analysis of Bus Speed Using a Multivariate Conditional Autoregressive Model: Contributing Factors and Spatiotemporal Correlation

Bus speed indicates the performance of bus systems. Exploring the impact of contributing factors to bus speed can provide public transit agencies insights into developing improvement strategies. Bus speed observations can be correlated both spatially and temporally, but their dependence has generally been neglected. This paper proposes a novel multivariate conditional autoregressive (MCAR) model to jointly account for spatial and temporal correlations of bus speeds extracted from large-scale Global Positioning System data. The proposed MCAR model is compared with the univariate conditional autoregressive model, which only accounts for spatial correlation, and the linear regression model, which assumes independent speed observations. Results show that the MCAR model outperforms the other models by presenting a much lower deviance information criterion (DIC) value and smaller prediction errors. This confirms the necessity of addressing the spatiotemporal correlation when modeling bus speeds. Driveway density, number of bus routes, bus stop density, signal effect, and bus volume are found to affect bus speed significantly in the MCAR model. Furthermore, how the distance affects the spatial correlation is investigated by specifying different spatial correlation weight (SCW) matrices. It is found that the MCAR model with SCWs generated from the radial basis function (RBF) can yield better outcomes than one using inverse distance. The optimal shape parameter of the RBF is found to be within a range of 1–2 km. Specifically, if the shape parameter equals 2 km, the SCW of two road segments is approximately 0.88 when their midpoints are 1 km from each other.