# Analyzing Student Behavioral Patterns in MOOCs Using Hidden Markov Models in Distance Education
## 1 Introduction
Factors influencing this association include the time of the day and the learners' demographic information. An unsupervised clustering algorithm for HMMs is used in [15] to discover students' learning tactics. The outcome data from this algorithm is used to predict learning outcomes. A Markov chain model is used in [16] to predict the students' performance when they perform a science microscopy experiment in a virtual reality environment. Markov chains are used to compare the students' ability to complete the steps in comparison with students who attend traditional training. Markov chains are used instead of HMMs as only the observed students' actions are considered and not any unobserved (hidden) parameters. The authors have tested the efficiency of the Markov chains for the prediction and the modeling of students' actions. HMMs are used in [17] to estimate student engagement. There is an assumption that unobservable states affect the observed actions of the students. For a math tutoring system, a three-level hidden state is considered to be engagement. The action sequences of the students at a certain time point can predict their subsequent actions with HMMs. The authors identify groups of students with equivalent engagement trajectories. The modeling of the learning engagement can enhance intelligent tutoring systems. HMMs are also used in [18] for video face recognition. The authors train the model with video sequences for each subject. They compute and compare the likelihood scores. In addition, HMMs are used [19] to forecast stock prices in interrelated markets for selected airlines. The HMM is initially trained to detect the interest of the behavioral data pattern of the past dataset. Furthermore, HMMs have been widely used in speech recognition [20]. In the study by [21], the authors use the HMMs to model students' actions and predict their performance in an educational game. The dataset relates to a game designed to teach the meaning of a unit in rational numbers. The dynamic analysis enables timely interventions and allows the students to learn at their own pace by progressing through a sequence of concepts. The choice-making behavior of test takers is examined in [22], where the available data are used to explore students' cognitive processes and motivational aspects. These data are complex due to time-related interdependencies, making traditional psychometric models unsuitable. Therefore, HMMs are employed for this purpose. Using HMMs, the authors have revealed the transition probabilities associated with goal orientation states, accumulated score, and accumulated confidence, and the interactions among these factors. The price of crude oil is forecasted in [23], using HMMs and the Forward-Backward algorithm with accuracy. Moreover, HMMs are used in [24] to predict driver behavior and lane changes using natural data from a driving simulator. Some of the data samples are steering wheel angle, steering wheel angular velocity, and yaw acceleration. The lane change is predicted by the Viterbi algorithm, achieving a high accuracy. In [25], HMMs are used to Improve driver awareness and the visibility of pedestrians, especially at crosswalks, to prevent vehicle-pedestrian collisions. Specifically, the researchers use HMMs to analyze the naturalistic brake and jerk data from the Safety Pilot Model Deployment (SPMD). Drivers can slow down and detect pedestrians near crosswalks, regardless of whether the Rectangular Rapid Flashing Beacon (RRFB) is activated. School education during the COVID-19 pandemic was studied in [26] using HMMs with a focus on full-time in-person learning in rural and metropolitan areas. The data are used to evaluate the impact of school policies on COVID-19 transmission, educational achievement, and other related outcomes. Moreover, HMMs are employed to forecast and predict the stock market [27], where predictions for the next day are made using historical data.