# Analyzing Student Behavioral Patterns in MOOCs Using Hidden Markov Models in Distance Education
## 3 Results
### Baum-Welch
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & \multicolumn{3}{c}{**Most Likely Sequence of Consecutive States**} \\  & \multicolumn{3}{c}{**with Numbers in Ascending Order**} \\ \hline
[13] & forum\_post\_updated & [14] & quiz\_attempt\_started \\ \hline
[15] & quiz\_attempt\_submitted & [16] & wiki\_comment\_created \\ \hline
[17] & wiki\_comments\_viewed & [18] & wiki\_page\_viewed \\ \hline
[19] & forum\_discussion\_viewed & [20] & forum\_post\_created \\ \hline
[21] & forum\_post\_deleted & [22] & forum\_post\_updated \\ \hline
[23] & quiz\_attempt\_started & [24] & quiz\_attempt\_submitted \\ \hline
[25] & wiki\_comment\_created & [26] & wiki\_comments\_viewed \\ \hline
[27] & wiki\_page\_viewed & [28] & forum\_discussion\_viewed \\ \hline
[29] & forum\_post\_created & [30] & forum\_post\_deleted \\ \hline
[31] & forum\_post\_updated & [32] & quiz\_attempt\_started \\ \hline
[33] & quiz\_attempt\_submitted & [34] & wiki\_comment\_created \\ \hline
[35] & wiki\_comments\_viewed & [36] & wiki\_page\_viewed \\ \hline
[37] & forum\_discussion\_viewed & [38] & forum\_post\_created \\ \hline
[39] & forum\_post\_deleted & [40] & forum\_post\_updated \\ \hline
[41] & quiz\_attempt\_started & [42] & quiz\_attempt\_submitted \\ \hline
[43] & wiki\_comment\_created & [44] & wiki\_comments\_viewed \\ \hline
[45] & wiki\_page\_viewed & [46] & forum\_discussion\_viewed \\ \hline
[47] & forum\_post\_created & [48] & forum\_post\_deleted \\ \hline
[49] & forum\_post\_updated & [50] & quiz\_attempt\_started \\ \hline
[51] & quiz\_attempt\_submitted & [52] & wiki\_comment\_created \\ \hline
[53] & wiki\_comments\_viewed & [54] & wiki\_page\_viewed \\ \hline
[55] & forum\_discussion\_viewed & [56] & forum\_post\_created \\ \hline
[57] & forum\_post\_deleted & [58] & forum\_post\_updated \\ \hline
[59] & quiz\_attempt\_started & [60] & quiz\_attempt\_submitted \\ \hline
[61] & wiki\_comment\_created & [62] & wiki\_comments\_viewed \\ \hline
[63] & wiki\_page\_viewed & [64] & forum\_discussion\_viewed \\ \hline
[65] & forum\_post\_created & [66] & forum\_post\_deleted \\ \hline
[67] & forum\_post\_updated & [68] & quiz\_attempt\_started \\ \hline
[69] & quiz\_attempt\_submitted & [70] & wiki\_comment\_created \\ \hline
[71] & wiki\_comments\_viewed & [72] & wiki\_page\_viewed \\ \hline
[73] & forum\_discussion\_viewed & [74] & forum\_post\_created \\ \hline
[75] & forum\_post\_deleted & [76] & forum\_post\_updated \\ \hline
[77] & quiz\_attempt\_started & [78] & quiz\_attempt\_submitted \\ \hline
[79] & wiki\_comment\_created & [80] & wiki\_comments\_viewed \\ \hline
[81] & wiki\_page\_viewed & [82] & forum\_discussion\_viewed \\ \hline
[83] & forum\_post\_created & [84] & forum\_post\_deleted \\ \hline
[85] & forum\_post\_updated & [86] & quiz\_attempt\_started \\ \hline
[87] & quiz\_attempt\_submitted & [88] & wiki\_comment\_created \\ \hline
[89] & wiki\_comments\_viewed & [90] & wiki\_page\_viewed \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._This is the most likely sequence of states generated by the Viterbi algorithm. The numbers indicate the order of each state as produced by Viterbi. The starting state is [1], and the ending state is [90], with transitions occurring sequentially from state [1] to state [90]. We use two columns for presentation purposes, as a single column with 90 elements would not fit on an A4 page. Even though clickstream analysis is widespread in e-commerce [42], to trace the behaviors of the customers, we use it to improve and modify a MOOC course. In e-commerce and learning analytics, visualizations are constructed for this purpose. According to the subject of a course, a sequence of Table 5 can provide different behaviors and styles or characters in the course. Different behavior patterns can be discovered. The identified state transitions, which correspond to particular characters, can help the weak students to perform better and the stronger students to be excellent using personalized learning. The instructors can be aware of probable risks and make a decision.