# Backpack Process Model (BPPM): A Process Mining Approach for Curricular Analytics
## 5 Application Case: First Engineering Courses  
This section illustrates the usefulness of the BPPM and BPPM-S models through a real application case that analyzes the backpack trajectories for N = 4466 engineering students from a Latin American university. Specifically, the trajectories they followed to take the first four courses of the curriculum were analyzed. The courses are calculus (C), algebra (A), chemistry (Q) and innovation (D). All four courses are automatically enrolled at the beginning of the first semester. The N = 4466 correspond to the students of the 2013 to 2019 cohorts, who passed the four courses or dropped out after having failed any of these courses. Specifically, the following three perspectives are analyzed: (P1) BPPM trajectories, ending either in retention (at the undergraduate program) or in dropout; (P2) most frequent backpacks; and (P3) the size of the backpack. 1. BPPM trajectories ending either in retention or in dropout  
The BPPM model allows us to compare the backpack trajectories between dropout students and those who remained. In particular, the differences can be seen in the distribution of the variants, the relative frequency of each backpack, the elapsed time in the entire trajectory and the average time students spend with each backpack. Table 4 shows three groups of trajectories. The first of these corresponds to those that include only the empty backpack (No BP). This is the most frequent variant (2504 cases)  
Figure 10: Educational trajectories that ended in DROPOUT, according to the BPPM-S model. (**a**) Shows only students who started with only one course in the backpack. (**b**) Shows only students who started with two courses in the backpack. (**c**) Shows only students who started with three courses in the backpack. (**d**) Shows only students who started with four courses in the backpack. The darker color of the nodes represents a higher percentage of students who went through a state. The thickness of the arrows represents the percentage of students who had transitions between both states. All values are percentages in relation to the total number of students included in each model. and also the shortest (a single event). The second group corresponds to those students who, having failed one or more courses, manage to empty the backpack and remain in the study program. The third group corresponds to those students who, having failed one or more courses, drop out of the study program without having managed to empty the backpack. Table 4 also shows that, for the trajectories that include backpacks, both those that drop out and those who remain show a high variability (51 and 40 variants, respectively). In the same way, the number of backpack events is similar between students who remain and those who drop out. However, the average time that students who drop out stay with a non-empty backpack is significantly lower (\(p<0.01\)). Figure 4 shows that the first backpack of students who remain in their undergraduate programs are more evenly distributed, compared to the first backpack of students who dropped out, where close to half (50.25% of cases) began with backpack ACQ. An institution seeking to reduce the early dropout risk could use this information, for example, to implement support mechanisms for students who have failed certain courses simultaneously or change the design of its curricula to prevent certain combinations of failed courses from occurring at high frequencies. When the average time that the students stay with each backpack is compared, it is possible to see that the average time that the dropout students stay with each backpack is less than the average time for students who remain. Figure 5 shows that the average time that students who ended in RETENTION stay with each backpack, varies from 166.35 to 275.1 days. In contrast, Figure 5 also shows that the average time that students who ended in DROPOUT stay with each backpack, varies from 0 to 129.6 days.