Motor vehicle crashes have increasingly become a serious concern for highway safety engineers and transportation agencies over the past few decades. This serious concern has led to a great deal of research activities. One of these activities is to develop safety analysis tools, specifically crash prediction models, for the purpose of reducing crashes and enhancing highway safety.Crash prediction models based on statistical or econometric modeling techniques are used for a variety of purposes; most commonly to estimate the expected crash frequencies from various roadway entities (highways, intersections, interstates, etc.) and also to identify geometric, environmental, and operations factors that are associated with crashes. A comprehensive review of prior literature indicates that many researchers have mainly focused on the development of aggregate crash prediction models based on single equation estimation techniques to identify the influences of geometric, environmental, and traffic variables on a single counted outcome. In some cases, however, more than one dependent variable might be of interest and hence several equations are formulated at the same time. Such a multiple equation structure may require simultaneous (or joint) estimation techniques under some situations.This dissertation research develops simultaneous estimation approaches to account for contemporaneous correlation and endogeneity problems in crash data. Specifically, seemingly unrelated negative binomial models and simultaneous equation models are developed to account for contemporaneous correlation between the disturbance terms across crash type models and to control for the endogenous relationship between the presence of left-turn lanes and angle crashes.Modeling crash types may provide certain advantages to gain insights as to 1) identification of high-risk sites with respect to specific types of crashes, which is not revealed through crash totals, and 2) the differences between conditions that lead to various crash types, but the disturbance terms across crash types might be contemporaneously correlated due to the unobserved common characteristics. Therefore, individual and simultaneous crash type models were estimated and the results of both models were compared. The results showed that a simultaneous estimation approach provides more efficient estimators relative to a single equation estimation technique.The presence of left-turn lanes has been treated as exogenous in crash prediction models, but in fact they are affecting each other. The bi-directional relationship between left-turn lanes and crashes results in endogeneity. This research investigated the endogenous relationship between left-turn lanes and crashes and developed simultaneous equation models to control for the endogeneity. The findings indicated that the presence of left-turn lanes is endogenously associated with crashes and the real effect of left-turn lanes on crashes can be obtained by controlling for endogeneity.