Statistics show that signalized intersections are among the most dangerous locations of a roadway network. Different approaches including crash frequency and severity models have been used to establish the relationship between crash occurrence and intersection characteristics. In order to model crash occurrence at signalized intersections more efficiently and eventually to better identify the significant factors contributing to crashes, this dissertation investigated the temporal, spatial, and site correlations for total, rear-end, right-angle and left-turn crashes. Using the basic regression model for correlated crash data leads to invalid statistical inference, due to incorrect test statistics and standard errors based on the misspecified variance. In this dissertation, the Generalized Estimating Equations (GEEs) were applied, which provide an extension of generalized linear models to the analysis of longitudinal or clustered data. A series of frequency models are presented by using the GEE with a Negative Binomial as the link function. The GEE models for the crash frequency per year (using four correlation structures) were fitted for longitudinal data; the GEE models for the crash frequency per intersection (using three correlation structures) were fitted for the signalized intersections along corridors; the GEE models were applied for the rear-end crash data with temporal or spatial correlation separately. For right-angle crash frequency, models at intersection, roadway, and approach levels were fitted and the roadway and approach level models were estimated by using the GEE to account for the "site correlation"; and for left-turn crashes, the approach level crash frequencies were modeled by using the GEE with a Negative Binomial link function for most patterns and using a binomial logit link function for the pattern having a higher proportion of zeros and ones in crash frequencies. All intersection geometry design features, traffic control and operational features, traffic flows, and crashes were obtained for selected intersections. Massive data collection work has been done. The autoregression structure is found to be the most appropriate correlation structure for both intersection temporal and spatial analyses, which indicates that the correlation between the multiple observations for a certain intersection will decrease as the time-gap increase and for spatially correlated signalized intersections along corridors the correlation between intersections decreases as spacing increases. The unstructured correlation structure was applied for roadway and approach level right-angle crashes and also for different patterns of left-turn crashes at the approach level. Usually two approaches at the same roadway have a higher correlation. At signalized intersections, differences exist in traffic volumes, site geometry, and signal operations, as well as safety performance on various approaches of intersections. Therefore, modeling the total number of left-turn crashes at intersections may obscure the real relationship between the crash causes and their effects. The dissertation modeled crashes at different levels. Particularly, intersection, roadway, and approach level models were compared for right-angle crashes, and different crash assignment criteria of "at-fault driver" or "near-side" were applied for disaggregated models. It shows that for the roadway and approach level models, the "near-side" models outperformed the "at-fault driver" models. Variables in traffic characteristics, geometric design features, traffic control and operational features, corridor level factor, and location type have been identified to be significant in crash occurrence. In specific, the safety relationship between crash occurrence and traffic volume has been investigated extensively at different studies. It has been found that the logarithm of traffic volumes per lane for the entire intersection is the best functional form for the total crashes in both the temporal and spatial analyses. The studies of right-angle and left-turn crashes confirm the assumption that the frequency of collisions is related to the traffic flows to which the colliding vehicles belong and not to the sum of the entering flows; the logarithm of the product of conflicting flows is usually the most significant functional form in the model. This study found that the left-turn protection on the minor roadway will increase rear-end crash occurrence, while the left-turn protection on the major roadway will reduce rear-end crashes. In addition, left-turn protection reduces Pattern 5 left-turn crashes (left-turning traffic collides with on-coming through traffic) specifically, but it increases Pattern 8 left-turn crashes (left-turning traffic collides with near-side crossing through traffic), and it has no significant effect on other patterns of left-turn crashes. This dissertation also investigated some other factors which have not been considered before. The safety effectiveness of many variables identified in this dissertation is consistent with previous studies. Some variables have unexpected signs and a justification is provided. Injury severity also has been studied for Patterns 5 left-turn crashes. Crashes were located to the approach with left-turning vehicles. The "site correlation" among the crashes occurred at the same approach was considered since these crashes may have similar propensity in crash severity. Many methodologies and applications have been attempted in this dissertation. Therefore, the study has both theoretical and implementational contribution in safety analysis at signalized intersections.