## 3 Materials and Methods
### Data  
All of the anonymized data in this study were provided by three online higher-education entities. The data came from student interaction data with Moodle courses. As Figure 10 shows, the student interaction data were sequentially grouped by week. It is also important to note that a student could start and drop out a course in any week during the course. Thus, for each student, there was a sequence of weeks or rows in the data file where their interaction activity with the course was stored. The length of the sequence (number of rows) for each learner was variable depending on the number of weeks where each learner presented interaction information. The final status of each student: dropout (value 1) or nondropout (value 0), was added as a class to predict. A dropout student in our context referred to a student who enrolled in an online course but did not complete it.  
Figure 8: Federated learning approach.  
Figure 9: Experimental design scheme.  
The data used in this paper came from three different LMS (learning management system) Moodle servers representing three educational entities with diverse students and courses (see Figure 11):  
* The first entity's dataset comprised 224,136 students and 7706 courses of which 174,556 students completed their courses (78%), and 49,580 dropped out before finishing the course (22%). This was a large dataset.
* The second entity's dataset comprised 98,829 students and 5871 courses of which 74,048 students completed their courses (75%), and 24,781 dropped out before finishing the course (25%). This was a medium dataset.
* The third entity's dataset comprised 15,023 students and 517 courses of which 10,552 students completed their courses (77%), and 4382 dropped out before finishing the course (23%). This was a small dataset.  
Figure 11 shows that the distribution of classes was unbalanced, but there was a similar percentage of dropout in the three entities' data (between 22% and 25%).  
We used the same attributes to predict student dropout for the three entities. We used only attributes related to students' activity on their courses in the LMS Moodle system, avoiding any bias in the data and trying to achieve homogeneous entity datasets. The specific attributes are shown in Table 1. We only selected summarization attributes or features that could be directly obtained from students' interaction with the online courses. Our objective was to be able to generate prediction models that could be directly applied or transferred to any learning management systems (LMS), massive online open courses (MOOCs), etc. These summarization variables can be easily obtained from any type of online educational environment. In our case, the 11 specifically used variables were provided by the online course provider, and we only had to preprocess them.  
Figure 10: Data approach by weeks.  
The values of these attributes were preprocessed as follows:  
* Data cleaning: if a null or unknown value was found in any attribute, it was replaced with a value of 0.
* Data normalization/scaling: to bring all numerical values into the same range, they were rescaled to the range [0-1] using the standard min-max scaler normalization, as shown in Equation (1): \[Xscaled=\frac{(X-Xmin)}{(Xmax-Xmin)},\] (1)