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. / text