# Analyzing Student Behavioral Patterns in MOOCs Using Hidden Markov Models in Distance Education
## 3 Results
### Transition and Emission Matrices  
We estimate the transition probabilities among all the viable combinations of resources (9 in total), resulting in a 9 \(\times\) 9 matrix. In addition, we calculated the standard error, the confidence level, the lowerEndpointMatrix, and the upperEndpointMatrix. Using these findings, we have calculated the HMM. It includes an 81 \(\times\) 9 matrix with a 9-element row for each row in the transProbs matrix (transition matrix) and an 81 \(\times\) 9 emissionProbs matrix (emission matrix) after running the hmm function. The emission matrix denotes the dependencies among the resources and the grades achieved. The received grades are the observed states, and the resources are the hidden states, as mentioned above, and it is illustrated in Table 3. Each node in the figures above emits 9 values, which are interpreted by the emission matrix. The sum of the elements  
Figure 4: Transition diagrams representing behavior patterns for some random User IDs. (**a**) Random User ID’s (a) behavior: Moderate number of transitions among quiz_attempt_viewed and forum_discussion_viewed. (**b**) Random User ID’s (b) behavior: Moderate number of transitions among quiz_attempt_submitted and forum_discussion_viewed. (**c**) Random User ID’s (c) behavior: High number of transitions among wiki_page_viewed and forum_discussion_viewed. (**d**) Random User ID’s (d) behavior: Moderate number of transitions from forum_post_deleted and forum_discussion_viewed to wiki_page_viewed and also among forum_post_deleted and forum_discussion_viewed. of each row of both the transition and the emission matrixes is 1. The emission matrix is illustrated in the column chart of Figure 5. It is a column chart of the Emission Matrix showing the percentages of the grades achieved during the course, which appears the Emission Matrix among received grades and hidden states shown in Table 3.  
In Figure 5, we can observe that the emitted values from the resources (hidden variables) to the grades yield the following results. The nine resources are: forum_discussion_viewed, forum_post_created, forum_post_deleted, forum_post_updated, quiz_attempt_started, quiz_attempt_submitted, wiki_comment_created, wiki_comments_viewed, and wiki_page_viewed). We have assigned corresponding numbers 1 to 9 to these resources along the axis:  
* For the first resource, the grades achieved are mainly 8 and 9, with a small percentage also receiving 7 and 10. * For the second resource, the majority of students achieve 8 and 9, with fewer students also receiving 7 and 10. * For the third resource, the majority of students obtain a Grade 7, with fewer students also receiving 8 and 9. * For the fourth resource, the majority achieve Grades 8 and 9, with some students obtaining 7. * For the fifth resource, most students achieve Grades 8 and 9, with some students also receiving 7. * For the sixth resource, some students achieve Grades 6 and 10, while the majority receive 8 and 9. * For the seventh resource, the majority achieve Grades 6, 8, and 10, with some students also receiving 9. * For the eighth resource, most students achieve grades from 8 to 9, while a moderate percentage attain Grade 0, and a small percentage receive grades of 6 and 10. * For the ninth resource, most students achieve Grade 9, with a moderate percentage attaining Grades 8 and 7,10 and a small percentage receiving Grade 6. Students who achieve Grade 0 are associated with resources 1, 2, 3, 4, 5, 6, 8, and 9. The percentage of students achieving this grade is approximately the same (medium) for each resource, except for resource 2, where it is small. We do not discuss the small percentages further, as we consider them negligible. Figure 5: Emission matrix among received grades and hidden states shown in Table 3.  
In Figure 6, we can see a column chart of the transition matrix displaying the percentages of participation in the various resources of the course.