http://www.stat.columbia.edu/~gelman/stuff_for_blog/Lord%20AA&P%202006.pdf

Modeling motor vehicle crashes using Poisson-gamma models: examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter.

This paper describes how there has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution. When crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the “low mean problem” (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of a mis-specified dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used for estimating the dispersion parameter of Poisson-gamma models of motor vehicle crashes were evaluated: the method of moments (MM), the weighted regression (WR) and the Maximum Likelihood method (ML). In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes mis-specified increases significantly as the sample mean and sample size decrease. Consequently, the results show that a mis-specified dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with a mis-specified dispersion parameter for modeling motor vehicle crashes.

Modeling Motor Vehicle Crashes Using Poisson-Gamma Models: Examining Effects of Low Sample Mean Values and Small Sample Size on Estimation of Fixed Dispersion Parameter

http://ceprofs.tamu.edu/dlord/Papers/Lord_et_al._COM-Poisson.pdf

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

Traffic accident segmentation by means of latent class clustering.

In order to achieve sustainable long-term transport infrastructure development, there is a growing need for fast, reliable and effective methods to evaluate and predict the impact of traffic safety measures. Recognising this need, and the need for an active traffic safety approach, this thesis focuses on traffic safety assessment and prediction based on the use of safety indicators that measure the spatial and/or temporal proximity of safety critical events. The main advantage of such measures is that they occur more frequently than accidents, and therefore require relatively short periods of study to establish values that can later be used for comparison, or for accident prediction purposes. There are a number of more generally accepted safety indicators including: Time-to-Accident, Time-to-Collision, and Post-Encroachment Time. These are based on different underlying principles and measurement techniques, including both on-site subjective estimation, and objective photometric measures. A major part of the work presented in this thesis, concerns identifying the potential and limitations of the different safety indicators with regard to their validity and reliability, and practical use for safety assessment and prediction purposes. This is done in conjunction with field studies in the urban and suburban environment, at both signalised and unsignalised intersections. Results from these studies indicate that on-site observation methods provide useful quantitative and qualitative information relatively quickly and efficiently, provided that they are used correctly. On the other hand, the methods based on photometric measurement (video-analysis) proved arduous and time-consuming. Furthermore, there are questions regarding the abilities of the Time-to-Collision and Post-Encroachment Time safety indicators to adequately represent interaction severity, suggesting possible flaws in fundamental concepts related to construct validity. Importantly, results showed that the relationship between safety indicators and traffic accidents is complex and equivocal, where many different factors and processes can impose a significant influence on safety. This makes generalised predictive modelling a particularly difficult task for safety analysts. The potential of micro-simulation for traffic safety and performance estimation based on the use of safety indicators was investigated in the second part of this thesis. Microscopic traffic simulation has become increasingly popular among transport planners, due to the fact that it serves as a safe and flexible off-line test environment for the estimation of dynamic and complex traffic system effects. It is useful and cost-effective in relation to the evaluation of issues concerning roadway design, and technological systems that influence road-user behaviour and vehicle performance. For reasons related to modelling fidelity and data quality, simulation has seldom been used for traffic safety estimation. Simulation model development is however, undergoing rapid development and the area of ‘safety-simulation’ and is recognised as having a high potential in the field of transport planning and traffic engineering. As part of the work in this thesis, practical simulation experiments were carried out to investigate this potential, and identify limitations. Based on the data from one of the earlier studies, and knowledge regarding important safety-influencing factors and behavioural processes, one of the simulation experiments showed evidence to suggest that realistic safety critical events could be generated and measured using safety indicators in a simulation environment, without making unnecessary and unrealistic behavioural assumptions. Furthermore, a second application of this methodology revealed the safety potential of a rear-end incident-reduction function used in standard vehicle actuated signalling. While both of these simulation studies highlighted the potential of this type of approach, the need for more flexible and realistic models of interactive behavioural processes could be identified in addition to the general need for greater active research into the field of safety simulation.

/pdf/indicators-for-traffic-safety-assessment-and-prediction-and-2bqp7cdjo0.pdf

Indicators for traffic safety assessment and prediction and their application in micro-simulation modelling : a study of urban and suburban intersections

https://stat.mq.edu.au/wp-content/uploads/2014/05/Confidence_and_prediction_intervals.pdf

Confidence and prediction intervals for generalised linear accident models.

Generalised linear models, with "log" link and either Poisson or negative binomial errors, are commonly used for relating accident rates to explanatory variables. This paper adds to the toolkit for such models. It describes how confidence intervals (for example, for the true accident rate at given flows) and prediction intervals (for example, for the number of accidents at a new site with given flows) can be produced using spreadsheet technology.

Graham Wood

Papers

Confidence and prediction intervals for generalised linear accident models.

Confidence and prediction intervals for generalised linear accident models