## 3 Methodology
### Data Collection and Description
\[Average_{i}=\frac{\sum_{j=1}^{7}x_{j}}{7}. \tag{2}\]  
Equation (2) represents the average number of interactions in week \(i\), summing up the interactions on each day \(j\), divided by the seven days on the week (to calculate the average, we used the _.mean()_ method contained in Pandas library [52] ([[https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.mean.html](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.mean.html)]([https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.mean.html](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.mean.html)))). \[Median_{i}= \begin{cases}Sample_{n/2},&\text{if $n$ is odd}\\ \frac{Sample_{n/2}+Sample_{(n/2)+1}}{2},&\text{if $n$ is even}.\end{cases}  \tag{3}\]  
Equation (3) represents the _Median_, where \(n\) represents the number of samples in the vector. It is the value in the middle of the crescent ordered vector. If the number of samples is even, the median is the mean of the two middle values of the vector (To calculate the median, we used the _.median()_ method contained in Pandas library ([[http://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.median.html](http://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.median.html)]([http://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.median.html](http://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrameFrame.median.html)))). \[ZeroedWeek_{i}= \begin{cases}ZeroedWeek_{i-1}\,+\,1,&\text{if $Count_{i}=0$}\\ ZeroedWeek_{i-1}\,+\,0,&\text{otherwise}.\end{cases}  \tag{4}\]  
Equation (4) represents the number of weeks that the students had zero interactions, until week \(i\). For example, if he had zero interactions on week \(i\), the result is incremented in one. If the student had at least one interaction on week \(i\), the result stays the same. \[AOD_{i}=\frac{Count_{i}-Count_{i-1}}{2}. \tag{5}\]  
The _Average of the Difference_ represents the average of the difference of interactions between week \(i-1\) and week \(i\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Attribute** & **Description** \\ \hline Cognitive count & Interactions involving content access and visualization: File upload/download, VPL exercise, URL access \\ \hline Teaching count & Interactions with the professor: comments to the files sent \\ \hline Social count & Interactions with other students: forum participation \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Example of interactions classification. \[CF_{i}=\frac{Count_{i}}{\frac{\sum_{j=1}^{i}Count_{i,j}}{n}}. \tag{6}\]  
The _Commitment Factor_ represents the ratio between the interaction count of a student on week \(i\) divided by the average interaction count of the class, where \(j\) represents a student and \(n\) the number of students in the class. Table 4 shows the set of attributes/variables included in each dataset. The idea when creating the datasets was to \"separate\" the derived attributes from each work. For example, in DB3 (dataset 3), we only use the attributes from Swan [23] (together with the interaction count). In DB5, we used attributes similar to Detoni el al. [50]. In DB4, the idea is similar, but with the addition of the average and median. In DB1, there is only the interaction counting, and in DB2, the attributes are derived from the interaction counting only (not using the type of interaction). DB6 contains strictly variables from Swan [23]. In DB7, DB8 and DB9, we created combinations of two variables from the same work [23]. In DB10, DB11 and DB12, the counting of each type of presence were used. DB13 is the datasets that contains all variables shown in Table 2 together. Information from the logs was used together with a socio-demographic-motivational questionnaire that was applied to the students in the first week of the course.