# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 4 Description of the Model to Identify Local Persistence  
Local persistence in this analysis is related to the extent students keep on trying an exercise until they get it right after doing it wrong. This section focuses on identifying how to model local persistence based on students' interactions with exercises. The aim is to define an overall indicator of local persistence, although this indicator can be based on the local persistence of individual exercises. A priori, it is possible to say that student local persistence is minimum if s/he never tries the exercise \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Variable** & **Description** \\ \hline Activity & per\_days & Percentage of days the student has \\ Videos & per\_videos & Percentage of completed videos \\ Exercises & per\_attempt & Percentage of attempted exercises \\  & & over the total available \\  & & Average grade of exercises (only \\ Exercises & avg\_grade & using attempted exercises and all \\  & & the attempts) \\ Persistence & local\_pers & Local persistence (Section 4 gives \\  & & details on how it is computed) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Features used in the predictive analysis. again when s/he gets it wrong (assuming there are no limits in the number of attempts). Similarly, local persistence is maximum if the student always ends up getting the right answer after trying the exercise several times. With this idea of local persistence, it does not matter how the student got the correct answer and/or whether local persistence is good or bad for learning. If a student gets the answers using a trial and error strategy, it will be probably bad for his learning process (learning will be probably superficial), but the student is considered to be persistent because s/he always gets the correct answer (which is our definition of local persistence). Considering the previous ideas, it is easy to determine when a student is fully persistent at the local level or not. However, the difficulty is how to model the overall local persistence of a student who may sometimes be considered as persistent and sometimes not. For the computation of local persistence, the sequence of attempts and the associated results (grades) are considered. For this model, grades of an exercise can only be 0 or 1. This is because 95% of the rows with course-student-exercise in all the SPOCs analyzed here (see Section 3.1) are only graded with 0-1. This can also be generalizable to several learning environments. The remaining 5% (which can include, e.g., checkbox exercises) has been discretized in 0-1 to be consistent with the rest of the exercises by rounding grades down (e.g., 0.8 is converted to 0). Taking this into account, Table 2 shows some examples of sequences (separating grades of attempts by spaces) and the idea of associated local persistence. Table 2 shows that although the outcome of the exercise may be the same, the local persistence the student shows in each case is different because in some cases the student tried to do the exercise more times and showed to be more persistent despite the difficulties. Considering this fact, the following assumptions have been made for the model:  
* If students get the answer right in the first attempt, no local persistence is shown because there is not a situation where an answer is incorrect (i.e., there is not a difficulty the student should address) and the student should decide whether attempting the exercise again or not (to show local persistence). However, this fact does not mean that students are not persistent. Therefore, events where the answer is correct in the first attempt are excluded. Similarly, re-attempts of correct exercises are excluded because the student already got the correct answer. * Students show more local persistence if they need more attempts to solve the exercise, but they should not be penalized if they solve the exercise with few attempts.