# Analyzing Student Behavioral Patterns in MOOCs Using Hidden Markov Models in Distance Education
## 2 Materials and Methods
We do not test the statistical significance of the output of the Viterbi algorithm because it reliably infers the most likely order of hidden states from events that have been seen, such as the final grades. We aim to uncover meaningful patterns to understand student behaviors rather than make predictions. Future work may focus on prediction. The significance or the accuracy of the output is not tested because no prediction is performed. Moreover, we do not split the sequence because of the two-layer structure, the Markov assumption, and the dependency of each hidden state on the previous hidden state. No time is considered in the methodology. HMMs are generative models, standard splitting may break dependencies data and lead to information leakage. In addition, we define a hypothesis:  
**Hypothesis 3**. : _The output sequence or probabilities are significantly better than a random or baseline model._  
The methodology of [37], for instance, proposed a methodology for electing (gestemes) the number of layers of HMMs, but this methodology regarded speech recognition or motion intention recognition. It emphasized the impact of the number of training samples, noise, and the number of observation symbols. In our findings, the most likely sequence of states is revealed similar to those reported in [38]. In [6], sequence pattern mining is applied to understand students' behavior. As we mentioned above, the R language and specifically the packages \"HMM\" and \"markovchain\" are used in our experiments. Most of the students achieve a good grade (7 to 9), and approximately the same percentages pertain to students who achieve a Grade 0 or a Grade 10. Specifically, the values are given in Table 1 below and Figure 1.  
Therefore, we do not confront differently the students who achieve a Grade 5 to 6 or Grade 4 because the amount is negligible. We consider only the transitions and the corresponding grades rather than considering subsets of students. In addition, in [6], the authors have discovered frequent sequential patterns with various algorithms and they calculate the occurrence of every pattern for each student. They use a binary variable to represent the participation of a student or not in a pattern. The k-means algorithm is also applied to cluster the students according to their post-test scores. We do not explore various sequence patterns to calculate the support of each pattern like the authors do in [6]. Instead of this, a unique pattern is found to be generated by the Viterbi algorithm. In the current work, we propose a methodology for simulating student behavior patterns and we do not apply a performance prediction. This methodology is easily applied to every dataset, which is related to MOOCs. There is no need to apply the same methodology to different MOOCs datasets in order to verify its reliance. The reliance can be applied to the accuracy of a prediction. We have interpreted student behavior with a two-layer HMM. According to [39], we have studied the transition among the states of a MOOC to extract hidden knowledge from a clickstream. One dataset is sufficient to demonstrate the reliance on the proposed method. This method can also be applied to other datasets. It can be applied to any sequence of students with hidden and observed \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Grade 0** & **Grade 4** & **Grade 5** & **Grade 6** & **Grade 7** & **Grade 8** & **Grade 9** & **Grade 10** \\ \hline
439 & 2 & 12 & 93 & 492 & 1102 & 1377 & 516 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Students’ grades. states. The dataset used can range from a large dataset to a smaller one. Using a different dataset would be unrealistic and impractical, as randomized IDs and differing student behaviors would not yield consistency. By considering a sequence of Moodle states in a dataset of student IDs in a MOOC, we apply the Markov property in the sequence, i.e., each Moodle state depends only on the previous Moodle state and the equivalent Moodle states.