Educational success measured by retention leading to graduation is an essential component of any academic institution. As such, identifying the factors that contribute significantly to success and addressing those factors that result in poor performances are important exercises. By success, we mean obtaining a semester GPA of 3.0 or better and a GPA of 2.0 or better. We identified these factors and related challenges through analytical models based on student performance. A large dataset obtained from a large state university over three consecutive semesters was utilized. At each semester, GPAs were nested within students and students were taking classes from multiple instructors and pursuing a specific major. Thus, we used multiple membership multiple classification (MMMC) Bayesian logistic regression models with random effects for instructors and majors to model success. The complexity of the analysis due to multiple membership modeling and a large number of random effects necessitated the use of Bayesian analysis. These Bayesian models identified factors affecting academic performance of college students while accounting for university instructors and majors as random effects. In particular, the models adjust for residency status, academic level, number of classes, student athletes, and disability residence services. Instructors and majors accounted for a significant proportion of students' academic success, and served as key indicators of retention and graduation rates. They are embedded within the processes of university recruitment and competition for the best students.