The 3-year graduation rate is a rarely measured metric in higher education compared to its 4- or 6- year graduation rate counterparts. For the first time in college (FTIC) students to graduate in three years, they must come with certain skills, abilities, plans, supports, or motivations. This project considers two distinct but interrelated ways of using advanced and novel statistical models, the Log-linear Cognitive Diagnostic Model (LCDM) and the Logistic Regression model (LR), to look at both students' ability to graduate in three years and the characteristics that contribute to this ability. The results indicate that the LCDM is a reliable and efficient statistical model which can provide accurate prediction of students' ability to graduate early. In addition, student enrolled credit hours in the semester, transfer credit hours, student high school GPA, and student socioeconomic status (EFC) were statistically significant predictors contributing to three-year graduation. The significant interaction between students' EFC status and transfer credit hours has a meaningfully practical impact on enrollment strategies and institutional policies. Future studies could use the same LCDM model to consider the degree to which these or other characteristics contribute to 4-, 5-, and 6-year graduation rates. Identification of these characteristics could have policy, student support, and admissions implications. Additionally, the success of the LCDM model in predicting ability could be used for predicting abilities unrelated to graduation, including the ability to pay off loans, succeed in an internship, or give back financially to a university.