# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 5 Results
### Analysis of the Evolution of Local Persistence over Time  
In the previous section, local persistence was evaluated using all the available interactions. However, it is also relevant to discover whether or not students can be more/less persistent at the local level in some parts of the course. In order to delve into this issue, the evolution of local persistence over the time has been computed. Figure 3 shows the evolution of the local persistence over the 16 weeks of the SPOCs taken in the first semester in 2018/2019. From the 13 SPOCs taken in that semester, only the six in which there were interactions in the first two weeks and in the last two weeks are considered (i.e., SPOCs whose interactions do not comprise the whole semester are excluded), although there can be intermediate weeks where no student attempts the exercises. The rest of them are excluded for this analysis as they are probably designed for a specific part of the course and they do not allow evaluating local persistence during the whole semester. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Profile** & **No. Students (\%)** & **Local\_Pers** & **Per\_Attempt** & **Per\_Videos** & **Avg\_Grade** & **lp\_5\_95** \\ \hline
1 & 307 (12\%) & 0.53 & 0.62 & 0.62 & 0.84 & 0.33–0.77 \\
2 & 594 (23\%) & 0.96 & 0.16 & 0.16 & 0.94 & 0.71–1.00 \\
3 & 578 (23\%) & 0.95 & 0.50 & 0.50 & 0.96 & 0.73–1.00 \\
4 & 604 (24\%) & 0.52 & 0.40 & 0.40 & 0.86 & 0.32–0.71 \\
5 & 461 (18\%) & 0.39 & 0.16 & 0.16 & 0.76 & 0.00–0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Students’ profiles based on their local persistence and interactions with videos/exercises. Figure 2: Boxplot of local persistence for each profile. Figure 3a shows that the local persistence evolves over the time. In fact, the mean of the standard deviation of students' local persistence over time is 0.24, which implies that there are considerable variations over time. Figure 3 also shows that the local persistence was higher at the beginning of the course and around week 10, but there is not a clear trend of the evolution depending on the time. Moreover, Figure 3b indicates that local persistence can be highly course dependent as the evolution of the local persistence was highly affected by the course. This reinforces the idea that the course context is very important to understand students' behaviors, as suggested in [26]. Nevertheless, some patterns were also identified. For example, local persistence decreases in most of the courses after the first week, as it also happens in Figure 3a. Furthermore, there were some courses (e.g., E, F) whose local persistence was 1 (or almost 1) for several weeks. In these cases, it may happen that either the exercises of certain modules had a limited number of options, so students eventually got the correct answer, or part of the SPOC was an important part of the evaluation, so students were extrinsically encouraged to be persistent. Despite the evolution of local persistence seen in Figure 3b, Figure 3c shows that the number of learners interacting with the SPOC (and affecting the computation of local persistence) has significant changes over time. There are some weeks with many students interacting and others where no student interacts (they are represented with \(-\infty\) in logarithmic scale). This fact can be more related to global persistence, as it is shown that many students are not persistent in their use of the SPOC. While this issue would also require further analysis by instructors to ensure that students engage with the SPOC, this fact can also affect the evolution of local persistence over time as the number of students to compute the local persistence each week is different. In addition, the number of exercises involved in the computation of persistence (after filtering) each week is presented in Figure 3d. This figure also shows that there are significant differences on the number of exercises taken each week between the courses (because of the course design); this fact may also affect the computation of local persistence.