# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 5 Results
### Prediction of Global Persistence and Students' Performance Using Local Persistence  
In the previous section, local persistence was compared to global persistence and students' performance in a descriptive way. However, it is also interesting to analyze whether or not local persistence can enhance predictive models. In order to solve this question, several predictive models are developed to predict the following dependent variables (see Section 3 for definitions): (1) dropout/global persistence related to activity, (2) dropout/global persistence related to completion, and (3) success, defined as obtaining a grade greater than or equal to 5.0 out of 10 (typical passing rate in Spain). For these dependent variables, three models are developed for each algorithm (from those presented in Section 3.3). The first one includes all the interactions except for local persistence (INT), the second one only includes local persistence (PER) and the third one includes all variables (ALL). For the variable of local persistence, as it is not defined for all learners (because some students have only engaged in activities with two attempts at maximum and/or they have got all the exercises right), mean imputation with a dummy has been used ([PERSON], 1999), which is a simple well-known imputation technique (used in many articles, e.g., ([PERSON], 1999; [PERSON], 1999)). This consists of having a dummy variable containing 0 or 1 depending on if the local persistence is available, and a second variable with the value of local persistence. If the dummy variable is 0, the second variable contains the mean of local persistence among students. For the analysis, the 13 SPOCs from the first semester of the academic year 2018/2019 are considered. As the course has 16 weeks (from the beginning of September 2018 to mid-December 2018) and it is desirable to achieve the earliest predictions as possible, the analysis contains the evolution of the predictive powers over the 16 weeks of the course. Figure 7 presents the results of the predictive models. Results are presented using the variables introduced in Section 3.3 and algorithms DT and RF, which are the algorithms that achieve the worse and better predictive power (using all variables), respectively. LR and SVM are omitted to make Figure 7 easier to read, but their predictive power is between the ones achieved by DT and RF when using all variables, and it is similar to the one obtained with these algorithms when only persistence is included. Results from Figure 7 show that it is possible to get accurate predictions (an AUC value over 0.8 can be considered as good [6]) of global persistence/dropout related to completion and success with just five variables (one representing each main category of variables). For these variables, Figure 7 also indicates that it is possible to get very early predictions. It is possible to forecast if students are going to complete 75% of the activities with an AUC over 0.8 (good) from week 3 and an AUC over 0.9 (excellent) from week 6 (Figure 7b). In terms of success, it is possible to predict with AUC over 0.8 from week 1 and over 0.9 from week 5 (Figure 7c). This means that it is possible to obtain early predictions so instructors can identify the problems and try to adapt the contents of the SPOC and/or motivate students to engage with the SPOC more often. In contrast, the predictive power of the global persistence/dropout related to activity is worse (Figure 7a), and AUC is not even 0.8 at the end of the course. A possible reason lies on the course context. As the context of each course is unknown, there is no information about when students should engage with the SPOC. For example, it may be possible that a SPOC is designed for only a specific part of the course. In that case, students do not need to engage all the weeks and that may cause some students are considered dropouts because they do not engage with the course in the weeks when they do not really need to engage with.