# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 5 Results
### Prediction of Global Persistence and Students' Performance Using Local Persistence
This fact entails that the definition of global persistence/dropout needs to be adapted to each context and in this case, a definition related to completion can be better as students should eventually do the activities even when the time framing can differ. Nevertheless, this definition may not be perfect if e.g., some exercises are optional and not all students should engage with them. With regard to the local persistence, its predictive power by itself (i.e., using only this variable) for the three variables (dropout related to activity, dropout related to completion, and success) is low. It can add some information as the AUC is higher than 0.5 (except for the dropout related to completion)  
Figure 7: Evolution of the predictive power when predicting (**a: left**) dropout related to activity, (**b: middle**) dropout related to completion and (**c right**) success. but local persistence is not a strong predictor. When comparing the model with and without local persistence, results show that local persistence only slightly improves the model in some cases (e.g., RF in dropout related to activity), but the improvement is low. However, it is possible that local persistence does not significantly enhance the models because other variables capture most of the information. In order to analyze this issue, several models have been developed using local persistence with other single variables. These models have been developed using the Random Forest (RF) algorithm, as it the best and most consistent algorithm among the four algorithms when predicting the three dependent variables (according to the previous analysis) and it also outperforms other algorithms in other related papers (e.g., [29; 47]). The variables used in each model are presented in Table 5. There is one model for each single variable plus local persistence (and the dummy variable used, as explained before), and a model including all variables. Models have been developed using the data until half of the course (week 8) since the predictive power is good enough at that moment and these models can be used for early predictions. Taking this into account, the importance of variables has been evaluated using the Mean Decrease Gini, which is often used to evaluate importance in RF [48]. The relative importance of each variable in each model for the three dependent variables is presented in Figure 8.  
Results show that when predictive models are developed with local persistence plus another variable, local persistence has an important weight in the relative importance, which means that local persistence can be used to improve the predictive models with respect to models with single variables. The only exception is in the case of the models with local persistence and per_attempt (ATT), and particularly when predicting dropout related to completing and success. In these cases, it can be observed that local persistence has little importance (less than 13%, including the dummy variable) on  
Figure 8: Relative importance of variables when predicting **(a: left)** dropout related to activity, **(b: middle)** dropout related to completion and **(c: right)** success using different combinations of variables. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Variables** \\ \hline ALL & per\_days/per\_videos/avg\_grade/per\_attempt/local\_pers \\  & (+dummy variable) \\ DAY & per\_days/local\_pers (+dummy variable) \\ ATT & per\_attempt/local\_pers (+dummy variable) \\ VID & per\_videos/local\_pers (+dummy variable) \\ AVG & avg\_grade/local\_pers (+dummy variable) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Models used in the predictive analysis. the model. The percentage of attempted exercises is also the best predictor in all the models where it is used, and it has a high relative importance when predicting dropout related to completion and success. This means that completing activities is very important to be successful.