## 5 Results  
In this section, we present the main results of the stages of discovery and analysis of the PM2 methodology. Findings are enumerated to ease their discussion later. **(F1)** Among students who took a stopout while having high-failure rate courses they must retake, late dropout is more frequent than late graduation. Figure 2 shows that 64.60% of students who took a stopout with high-failure rate courses they must retake ended in LATE-DROPOUT, compared to only 35.40% who ended in LATE-GRAD. Moreover, educational trajectories that include MUST-RETAKE-COURSES > STOPOUT transitions are mostly unsatisfactory. This can be seen in that they include a high proportion of transitions MUST-RETAKE-COURSES > MUST-RETAKE-COURSES (84.66%), STOPOUT > MUST-RETAKE-COURSES (73.55%), and MUST-RETAKE-COURSES > LATE-DROPOUT (59.82%). **(F2)** Differences were found among ISCED fields for the educational trajectories of students who took a stopout while having high-failure rate courses they must retake. Figure 3a shows educational trajectories that are clearly unsatisfactory. It groups the following ISCED fields: Agriculture; Science; Social Sciences, Business and Law; and Engineering, Manufacturing, and Construction. Furthermore, 54.95% of students had ENR > MUST-RETAKE-COURSES transitions; 88.32% had consecutive semesters with MUST-RETAKE COURSES; 82.42% had STOPOUT > MUST-RETAKE-COURSES transitions; and 72.94% ended in LATE-DROPOUT. On the other hand, Figure 3b shows more satisfactory educational trajectories. It groups the following ISCED fields: Education; Arts and Humanities; and Health and Welfare. Overall, 85.49% of students had ENR > NO-RETAKE-COURSES transitions, 81.18% had consecutive semesters with NO-RETAKE-COURSES, and 59.22% ended in LATE-GRAD. Figure 2: Educational trajectories in high-failure rate courses, according to the RETAKE-STOPOUT model, including only students who had at least one MUST-RETAKE-COURSES > STOPOUT transition, did not have NO-RETAKE-COURSES > STOPOUT transitions, and ended in LATE-DROOPOUT or LATE-GRAD. 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 the model. **(F3)** Among students who took a stopout without having high-failure rate courses they must retake, late graduation is more frequent than late dropout. Figure 4 shows that 83.07% of students who took a stopout without high-failure rate courses they must retake, ended in LATE-GRAD, compared to only 16.93% who ended in LATE-DROPOUT. Moreover, educational trajectories that include NO-RETAKE-COURSES > STOPOUT transitions are mostly satisfactory. This can be seen in that they include a high proportion of transitions ENR > NO-RETAKE-COURSES (81.37%), NO-RETAKE-COURSES > NO-RETAKE-COURSES (96.31%), STOPOUT > NO-RETAKE-COURSES (92.63%). Moreover, they have also a very little proportion of transitions MUST-RETAKE-COURSES > LATE-DROPOUT (6.08%). Contrary to what was presented in (F4), no significant differences were found for educational trajectories grouped by ISCED field. Figure 4: Educational trajectories in high-failure rate courses, according to the RETAKE-STOPOUT model, including only students who had at least one NO-RETAKE-COURSES > STOPOUT transition, did not have MUST-RETAKE-COURSES > STOPOUT transitions, and ended in LATE-DROPOUT or LATE-GRAD. 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.