Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors

The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.

Investigating the Existence of Second Order Spatial Autocorrelation in Crash Frequency across Adjacent Freeway Segments

This study developed spatial Poisson model to incorporate spatial autocorrelation in crash frequency across contagious freeway segments. Spatial autocorrelation is the presence of spatial pattern in crash frequency over space due to geographic proximity. Usually crash caused congestion on a freeway segment propagates upstream and creates chance of occurring secondary crashes. This phenomenon makes the crash frequency on the contiguous freeway segments correlated. This correlation makes the distributional assumption of independence of crash frequency invalid. The existence of spatial autocorrelation is investigated by using Conditional autoregressive models (CAR models). The models are set up in a Bayesian modeling framework, to include terms which help to identify and quantify residual spatial autocorrelation for neighboring observation units. Models which recognize the presence of spatial dependence help to obtain unbiased estimates of parameters quantifying safety levels since the effects of spatial autocorrelation are accounted for in the modeling process. Based on CAR models, approximately 51% of crash frequencies across contiguous freeway segments are spatially auto-correlated. The incident rate ratios revealed that wider shoulder and weaving segments decreased crash frequency by factors of 0.84 and 0.75 respectively. The marginal impacts graphs showed that an increase in longitudinal space for segments with two lanes decreased crash frequency. However, an increase of facility width above three lanes results in more crashes, which indicates an increase in traffic flows and driving behavior leading to crashes. These results call an important step of analyzing contagious freeway segments simultaneously to account for the existence of spatial autocorrelation.