# Re-Defining, Analyzing and Predicting Persistence Using Student Events in Online Learning +
## 1 Introduction
In this context, the analysis of local persistence is important to know what the distribution of this feature among students is, its relationship with other variables or its predictive power with learning outcomes. Prior research work has mainly identified local persistence through self-reported data (e.g., [7; 14]), but few models have been defined to measure local persistence from students' events in a digital platform. This is important because self-reported data might sometimes not reflect the reality because students might not be aware of their local persistence or they might lie. In these cases, measurements from student' events would be more accurate. In online or blended education, students' interactions with the digital platforms can be used to collect data to measure persistence (global and local). Particularly, local persistence is measured using interactions with individual exercises in an online platform (Open edX). We consider that a student with high local persistence is a student who attempts exercises again and again until the correct solution is obtained. Similarly, we consider that a student with high global persistence is a student who regularly accesses the course and completes all the modules (or at least a minimum required). These considerations are used in this article to analyze different interesting aspects related to persistence. Particularly, there is interest on analyzing the prevalence of local persistence (i.e., how persistence is distributed among learners). This is relevant to understand how local persistence vary among the students in a course, and to identify groups of students based on their local persistence. Moreover, timing considerations are also important, and the evolution of local persistence (i.e., how local persistence varies when it is computed based on the exercises carried out in different time periods, such as weeks) is useful to understand whether or not students' behaviors towards attempting exercisesremain, increase or decrease throughout the course. For example, if local persistence is lower at some stages of the course, it may mean that students engage later in a course or engage more with some activities. In this line, [PERSON] [16] identified that local persistence could vary depending on the domain of expertise of students (e.g., students can be more persistent in tasks they find easier). However, low local persistence does not necessarily mean that exercises are difficult for the students because, according to [PERSON] [17], if exercises are too easy, students may feel bored (and conversely anxious if difficult), and that may also affect local persistence. In addition, local persistence can affect or can be affected by other variables. In online courses, some hypotheses are that local persistence might affect academic achievement and engagement with videos. Moreover, global and local persistence may also be related to each other. The analysis of the relationship between local persistence and other variables serves not only to better understand students' behaviors but can also contribute to the development of predictive models. These models can be useful to anticipate what will happen in the course and early predictions can enable timely interventions. However, for these models, it is important to know which variables influence the variable to be predicted. For example, if global persistence is predicted, it would be relevant to know if variables related to activity, videos, local persistence, etc. influence the predictive models. Considering all the aforementioned issues, the focus of this paper is on the development of a model to determine local persistence, and the analysis of this local persistence with real data to determine if adaptation can make sense (based on the type of students and their evolution over time) and if persistence can be included in early-dropout prediction systems.