American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students’ final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation rate method, many studies have applied absorbing Markov chains for estimating graduation rates. In both cases, a frequentist approach is used. For the standard six-year graduation rate method, the frequentist approach corresponds to counting the number of students who finished their program within six years and dividing by the number of students who entered that year. In the case of absorbing Markov chains, the frequentist approach is used to compute the underlying transition matrix, which is then used to estimate the graduation rate. In this paper, we apply a sensitivity analysis to compare the performance of the standard six-year graduation rate method with that of absorbing Markov chains. Through the analysis, we highlight significant limitations with regards to the estimation accuracy of both approaches when applied to small sample sizes or cohorts at a university. Additionally, we note that the Absorbing Markov chain method introduces a significant bias, which leads to an underestimation of the true graduation rate. To overcome both these challenges, we propose and evaluate the use of a regularly updating multi-level absorbing Markov chain (RUML-AMC) in which the transition matrix is updated year to year. We empirically demonstrate that the proposed RUML-AMC approach nearly eliminates estimation bias while reducing the estimation variation by more than 40%, especially for populations with small sample sizes.

Many studies in the field of education analytics have identified student grade point averages (GPA) as an important indicator and predictor of students' final academic outcomes (graduate or halt). And while semester-to-semester fluctuations in GPA are considered normal, significant changes in academic performance may warrant more thorough investigation and consideration, particularly with regards to final academic outcomes. However, such an approach is challenging due to the difficulties of representing complex academic trajectories over an academic career. In this study, we apply a Hidden Markov Model (HMM) to provide a standard and intuitive classification over students' academic-performance levels, which leads to a compact representation of academic-performance trajectories. Next, we explore the relationship between different academic-performance trajectories and their correspondence to final academic success. Based on student transcript data from University of Central Florida, our proposed HMM is trained using sequences of students' course grades for each semester. Through the HMM, our analysis follows the expected finding that higher academic performance levels correlate with lower halt rates. However, in this paper, we identify that there exist many scenarios in which both improving or worsening academic-performance trajectories actually correlate to higher graduation rates. This counter-intuitive finding is made possible through the proposed and developed HMM model.

Simplified classifications have often led to college students being labeled as full-time or part-time students. However, student enrollment patterns can be much more complicated at many universities, as it is common for students to switch between full-time and part-time enrollment each semester based on finances, scheduling, or family needs. While previous studies have identified part-time enrollment as a risk factor to students’ academic success, limited research has examined the impact of enrollment patterns or strategies on academic performance. Unlike traditional methods that use a single-period model to classify students into full-time and part-time categories, in this study, we apply an advanced multi-period dynamic approach using a Hidden Markov Model to distinguish and cluster students’ enrollment strategies into three categories: full-time, part-time, and mixed. We then investigate and compare the academic performance outcomes of each group based on their enrollment strategies while taking into account student type (i.e., first-time-in-college students and transfer students). Analysis of undergraduate student records data collected at the University of Central Florida from 2008 to 2017 shows that the academic performance of first-time-in-college students who apply a mixed enrollment strategy is closer to that of full-time students, as compared to part-time students. Moreover, during their part-time semesters, mixed-enrollment students significantly outperform part-time students. Similarly, analysis of transfer students shows that a mixed-enrollment strategy is correlated with similar graduation rates as the full-time enrollment strategy and more than double the graduation rate associated with part-time enrollment. This finding suggests that part-time students can achieve better overall outcomes by increased engagement through occasional full-time enrollments.