## 8 Academic Performance Clustering Analysis
### Graduation Rate Analysis  
Another important metric in assessing academic performance for different enrollment strategies is graduation rate. To compute this metric, American universities use the six-year graduation rate approach. Based on the federal definition, the six-year graduation rate refers to the percentage of FTIC students who complete their program within 150% of the standard enrollment time to degree [46]. For example, for a four-year program, students who earn degrees within six years are considered graduates. Despite its popularity, the six-year graduation rate approach has two main blind spots. First, no distinction exists between students with different enrollment strategies. PES students often take fewer courses each semester compared to MES and FES. Therefore, they are more likely to finish their program in more than six years. All such students are considered halting their program in the six-year graduation rate method, leading to underestimating the actual graduation rate. Second, the six-year graduation rate is only computed for FTIC students, excluding transfer students. In this paper, we apply two alternative methodologies for computing the graduation rate. In the first methodology, we calculate the halt rate as a substitute for the graduation rate. The halt rate refers to the percentage of FTIC students who halt enrollment at UCF within six years. Students are considered as halted if they do not register at UCF for three consecutive semesters. This measure helps us avoid the underestimation caused by excluding students who take more than six years to graduate. In the second approach, we use an absorbing Markov Chain to compute the graduation rates. This approach does not exclude students who graduate after six years, as it can calculate the graduation/halt rate probability for any duration of time that students spend in their program. Moreover, it makes it possible to consider transfer students by inserting them into the Markov chain model, taking into account their academic level when they join the new program. This approach is explained in detail by [47]. Table 15 reports the six-year graduation and halt rates for FTIC students who start their program in Fall 2008, 2009, and 2010. As indicated in the table, PES students have a higher six-year halt rate than FES and MES students. Table 16 shows the graduation rate for FTIC students with different types of enrollment strategies using the absorbing Markov chain method. Aligned with prior studies, FES students have the highest graduation rate for any academic level, this is followed by MES and PES, respectively. Furthermore, for FTIC students with any enrollment strategy, higher academic levels correspond to higher graduation rates. For example, Senior students have a higher graduation rate compared to Junior, Sophomore, and Freshman students; that is to say persistence is a critical factor. Columns _Time to graduate_ and _Time to halt_ in Tables 15 and 16 provide the expected time it takes for students to graduate and halt enrollment, respectively. As shown in the tables, regardless of metric, the time to graduate for the FES group is notably shorter than for MES and PES groups. For example, students in the FES group with the _Freshman_ academic level need an average of 11.09 semesters to graduate from their program, while for students in the MES and PES groups, it takes 12.74 and 13.26 semesters on average, respectively. However, the comparisons between enrollment strategies differ when considering Time to halt. As an example, time to halt for freshman students in the MES (4.70) group is longer than FES (3.82) and PES (3.15) groups. This could be explained as some full-time students may decide to alternate between full-time and part-time semesters as a strategy to decrease imposed workload and avoid halting enrollment. Table 17 provides the same measures in Table 16 for transfer students. For both FTIC and transfer groups, FES students have the highest graduation rate, followed by MES, and PES, respectively.