Browsing by Subject "Multivariate normal distribution"
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Item Generalizing the multivariate normality assumption in the simulation of dependencies in transportation systems(2010-05) Ng, Man Wo; Waller, S. Travis; Hasenbein, John J.By far the most popular method to account for dependencies in the transportation network analysis literature is the use of the multivariate normal (MVN) distribution. While in certain cases there is some theoretical underpinning for the MVN assumption, in others there is none. This can lead to misleading results: results do not only depend on whether dependence is modeled, but also how dependence is modeled. When assuming the MVN distribution, one is limiting oneself to a specific set of dependency structures, which can substantially limit validity of results. In this report an existing, more flexible, correlation-based approach (where just marginal distributions and their correlations are specified) is proposed, and it is demonstrated that, in simulation studies, such an approach is a generalization of the MVN assumption. The need for such generalization is particularly critical in the transportation network modeling literature, where oftentimes there exists no or insufficient data to estimate probability distributions, so that sensitivity analyses assuming different dependence structures could be extremely valuable. However, the proposed method has its own drawbacks. For example, it is again not able to exhaust all possible dependence forms and it relies on some not-so-known properties of the correlation coefficient.Item A novel approach to modeling and predicting crash frequency at rural intersections by crash type and injury severity level(2013-12) Deng, Jun, active 2013; Bhat, Chandra R. (Chandrasekhar R.), 1964-Safety at intersections is of significant interest to transportation professionals due to the large number of possible conflicts that occur at those locations. In particular, rural intersections have been recognized as one of the most hazardous locations on roads. However, most models of crash frequency at rural intersections, and road segments in general, do not differentiate between crash type (such as angle, rear-end or sideswipe) and injury severity (such as fatal injury, non-fatal injury, possible injury or property damage only). Thus, there is a need to be able to identify the differential impacts of intersection-specific and other variables on crash types and severity levels. This thesis builds upon the work of Bhat et al., (2013b) to formulate and apply a novel approach for the joint modeling of crash frequency and combinations of crash type and injury severity. The proposed framework explicitly links a count data model (to model crash frequency) with a discrete choice model (to model combinations of crash type and injury severity), and uses a multinomial probit kernel for the discrete choice model and introduces unobserved heterogeneity in both the crash frequency model and the discrete choice model, while also accommodates excess of zeros. The results show that the type of traffic control and the number of entering roads are the most important determinants of crash counts and crash type/injury severity, and the results from our analysis underscore the value of our proposed model for data fit purposes as well as to accurately estimate variable effects.