# Quantifying the Impact of Student Enrollment Patterns on Academic Success Using a Hidden Markov Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Statement

## 3. Literature Review

## 4. Methodology

## 5. Student Data Records

## 6. Applying HMM to Student Data

## 7. Demographics Clustering Analysis

Key Finding 1: Both FTIC and Transfer Students: Enrollment strategies vary among different demographic groups.

## 8. Academic Performance Clustering Analysis

#### 8.1. GPA Analysis

Key Finding 3: Both FTIC and Transfer Students: FES students have the highest GPA, followed by MES, followed by PES. The higher the student’s engagement, the higher is the student’s GPA.

Key Finding 4: FTIC Students: FES students, when register as full-time, have a higher GPA compared to when they register part-time. There is no difference between the GPA of the full-time and part-time semester for MES and PES students.

Key Finding 5: Transfer Students: FES and PES students, when register as full-time, have a higher GPA compared to when they register part-time. For MES students, there is no difference between the GPA of the full-time and part-time semester.

Key Finding 6: FTIC and Transfer Students: For PES students with full-time and part-time enrollment, transfer students have a higher GPA than FTIC students. More broadly, FTIC students appear to be more sensitive to their enrollment strategy and status.

#### 8.2. DFW Rate Analysis

Key Finding 7: FTIC and Transfer Students: PES students have a higher DFW rate compared to MES and FES groups. As before, the academic performance of FTIC students, as measured by DFW rate, appears more sensitivity to enrollment strategy, then that of transfer students.

#### 8.3. Graduation Rate Analysis

Key Finding 8: FTIC and Transfer Students: FES students have a higher graduation rate than MES and PES groups. While MES students have a substantially improved graduation rate as compared to PES students, especially for transfer students.

Key Finding 9: Transfer Students: Time to graduate for PES students is greater than time to graduate for MES and FES students. When comparing strategies, MES appears to be a suitable strategy as required for transfer students (e.g., for students that must work while in school); while employing MES may extend time-to-graduation, the impact on the graduation rate is limited as compared to PES.

Key Finding 10: FTIC Students: MES and PES students have a longer time to graduate than FES students.

## 9. Discussion

Key Finding 11: All Students: Switching from FES to PES: For students who switch from FES to PES, the probability of halting increases, while their GPA is more likely to decrease.

Key Finding 12: All Students: Switching from MES to FES: For students who switch from FES to MES, the probability of halting decreases, while their GPA is more likely to increase.

## 10. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Dissimilarity % (D) | Cohen’s d | Effect Size |
---|---|---|

D ≤ 9 | 0.0 < d ≤ 0.2 | Small |

9 < D ≤ 20 | 0.2 < d ≤ 0.5 | Medium |

20 < D ≤ 31 | 0.5 < d ≤ 0.8 | Large |

31 < D ≤ 42 | 0.8 < d ≤ 1.2 | Very large |

42 < D | 1.2 < d | Huge |

## Appendix B

Student | #Num. of Courses with DFW | #Num. of All Courses | DFW Rate |
---|---|---|---|

1 | 0 | 10 | 0/10 = 0 |

2 | 4 | 20 | 4/20 = 0.2 |

3 | 8 | 30 | 8/30 = 0.27 |

## References

- O’toole, D.M.; Stratton, L.S.; Wetzel, J.N. A Longitudinal Analysis of the Frequency of Part-Time Enrollment and the Persistence of Students Who Enroll Part Time. Res. High. Educ.
**2003**, 44, 519–537. [Google Scholar] [CrossRef] - Hearn, J.C. Emerging Variations in Postsecondary Attendance Patterns: An Investigation of Part-Time, Delayed, and Nondegree Enrollment. Res. High. Educ.
**1992**, 33, 657–687. [Google Scholar] [CrossRef] - Cabrera, A.F.; Burkum, K.R.; La Nasa, S.M.; Bibo, E.W. Pathways to a Four-Year Degree; Technical Report ED 482 160; ERIC: Washington, DC, USA, 2003.
- Reardon, S.F.; Baker, R.; Klasik, D. Race, Income, and Enrollment Patterns in Highly Selective Colleges, 1982–2004; Technical Report; Center for Education Policy Analysis, Stanford University: Stanford, CA, USA, 2012. [Google Scholar]
- Hearn, J.C. Attendance at Higher-Cost Colleges: Ascribed, Socioeconomic, and Academic Influences on Student Enrollment Patterns. Econ. Educ. Rev.
**1988**, 7, 65–76. [Google Scholar] [CrossRef] - Center for Community College Student Engagement. Even One Semester: Full-Time Enrollment and Student Success; Center for Community College Student Engagement: Austin, TX, USA, 2017. [Google Scholar]
- Feldman, M.J. Factors associated with one-year retention in a community college. Res. High. Educ.
**1993**, 34, 503–512. [Google Scholar] [CrossRef] - Pelkey, D. Factors Supporting Persistence of Academically Underprepared Community College Students. Ph.D. Thesis, Oregon State University, Corvallis, OR, USA, 2011. [Google Scholar]
- Darolia, R. Working (and studying) day and night: Heterogeneous effects of working on the academic performance of full-time and part-time students. Econ. Educ. Rev.
**2014**, 38, 38–50. [Google Scholar] [CrossRef] - Track, I. National study of non-first-time students shows full-time enrollment may not be appropriate for all. 2015. [Google Scholar]
- Garibaldi, P.; Giavazzi, F.; Ichino, A.; Rettore, E. College cost and time to complete a degree: Evidence from tuition discontinuities. Rev. Econ. Stat.
**2012**, 94, 699–711. [Google Scholar] [CrossRef] - Ryan, C.L.; Bauman, K. Educational Attainment in the United States. Current Population Report P20-578, US Census Bureau. 2016. Available online: https://www.census.gov/content/dam/Census/library/publications/2016/demo/p20-578.pdf (accessed on 12 July 2021).
- Fagioli, L.; Rios-Aguilar, C.; Deil-Amen, R. Changing the context of student engagement: Using Facebook to increase community college student persistence and success. Teach. Coll. Rec.
**2015**, 117, 1–42. [Google Scholar] - Goldrick-Rab, S.; Han, S.W. Accounting for socioeconomic differences in delaying the transition to college. Rev. High. Educ.
**2011**, 34, 423–445. [Google Scholar] [CrossRef] - Cox, R.D. Complicating Conditions: Obstacles and Interruptions to Low-Income Students’ College “Choices”. J. High. Educ.
**2016**, 87, 1–26. [Google Scholar] - Goldrick-Rab, S.; Kelchen, R.; Harris, D.N.; Benson, J. Reducing income inequality in educational attainment: Experimental evidence on the impact of financial aid on college completion. Am. J. Sociol.
**2016**, 121, 1762–1817. [Google Scholar] [CrossRef][Green Version] - Rowan-Kenyon, H.T. Predictors of delayed college enrollment and the impact of socioeconomic status. J. High. Educ.
**2007**, 78, 188–214. [Google Scholar] [CrossRef] - Wells, R.S.; Lynch, C.M. Delayed college entry and the socioeconomic gap: Examining the roles of student plans, family income, parental education, and parental occupation. J. High. Educ.
**2012**, 83, 671–697. [Google Scholar] [CrossRef] - Nguyen, H.; Wu, L.; Fischer, C.; Washington, G.; Warschauer, M. Increasing success in college: Examining the impact of a project-based introductory engineering course. J. Eng. Educ.
**2020**, 109, 384–401. [Google Scholar] [CrossRef] - DesJardins, S.L.; Ahlburg, D.A.; McCall, B.P. The effects of interrupted enrollment on graduation from college: Racial, income, and ability differences. Econ. Educ. Rev.
**2006**, 25, 575–590. [Google Scholar] [CrossRef][Green Version] - Jacobs, J.A.; King, R.B. Age and college completion: A life-history analysis of women aged 15–44. Sociol. Educ.
**2002**, 75, 211–230. [Google Scholar] [CrossRef] - Roksa, J.; Velez, M. A late start: Delayed entry, life course transitions and bachelor’s degree completion. Soc. Forces
**2012**, 90, 769–794. [Google Scholar] [CrossRef] - Taniguchi, H.; Kaufman, G. Degree completion among nontraditional college students. Soc. Sci. Q.
**2005**, 86, 912–927. [Google Scholar] [CrossRef] - Boumi, S.; Vela, A. Application of Hidden Markov Models to Quantify the Impact of Enrollment Patterns on Student Performance. In Proceedings of the International Educational Data Mining Society, Montreal, QC, Canada, 2–5 July 2019. [Google Scholar]
- Milesi, C. Do all roads lead to Rome? Effect of educational trajectories on educational transitions. Res. Soc. Stratif. Mobil.
**2010**, 28, 23–44. [Google Scholar] [CrossRef] - Zhang, Y.L. STEM Persisters, Switchers, and Leavers: Factors Associated with 6-Year Degree Attainment for STEM Aspiring Community College Transfer Students. Community Coll. J. Res. Pract.
**2021**, 1–16. [Google Scholar] [CrossRef] - Attewell, P.; Heil, S.; Reisel, L. What is academic momentum? Furthermore, does it matter? Educ. Eval. Policy Anal.
**2012**, 34, 27–44. [Google Scholar] [CrossRef][Green Version] - Crosta, P.M. Intensity and attachment: How the chaotic enrollment patterns of community college students relate to educational outcomes. Community Coll. Rev.
**2014**, 42, 118–142. [Google Scholar] [CrossRef][Green Version] - Burley, H.; Butner, B.; Cejda, B. Dropout and stopout patterns among developmental education students in Texas community colleges. Community Coll. J. Res. Pract.
**2001**, 25, 767–782. [Google Scholar] - Kuh, G.D. What student affairs professionals need to know about student engagement. J. Coll. Stud. Dev.
**2009**, 50, 683–706. [Google Scholar] [CrossRef] - McClenney, K.; Marti, C.N.; Adkins, C. Student engagement and student outcomes: Key findings from. Community Coll. Surv. Stud. Engagem.
**2012**. [Google Scholar] - Lee, J.S. The relationship between student engagement and academic performance: Is it a myth or reality? J. Educ. Res.
**2014**, 107, 177–185. [Google Scholar] [CrossRef][Green Version] - Büchele, S. Evaluating the link between attendance and performance in higher education: The role of classroom engagement dimensions. Assess. Eval. High. Educ.
**2021**, 46, 132–150. [Google Scholar] [CrossRef] - Price, D.V.; Tovar, E. Student engagement and institutional graduation rates: Identifying high-impact educational practices for community colleges. Community Coll. J. Res. Pract.
**2014**, 38, 766–782. [Google Scholar] [CrossRef] - Abdi, S.; Khosravi, H.; Sadiq, S. Predicting Student Performance: The Case of Combining Knowledge Tracing and Collaborative Filtering. In Proceedings of the International Conference on Educational Data Mining, Raleigh, NC, USA, 16–20 July 2018. [Google Scholar]
- Beal, C.; Mitra, S.; Cohen, P. Modeling learning patterns of students with a tutoring system using Hidden Markov Model. In Proceedings of the 13th International Conference on Artificial Intelligence in Education (AIED), Los Angeles, CA, USA, 9–13 July 2007. [Google Scholar]
- Boyer, K.E.; Phillips, R.; Ingram, A.; Ha, E.Y.; Wallis, M.; Vouk, M.; Lester, J. Investigating the relationship between dialogue structure and tutoring effectiveness: A hidden Markov modeling approach. Int. J. Artif. Intell. Educ.
**2011**, 21, 65–81. [Google Scholar] - Halpern, D.; Tubridy, S.; Wang, H.Y.; Gasser, C.; Popp, P.O.; Davachi, L.; Gureckis, T.M. Knowledge Tracing Using the Brain. In Proceedings of the 11th International Conference on Educational Data Mining, EDM, Buffalo, NY, USA, 15–18 July 2018. [Google Scholar]
- Hoernle, N.; Gal, K.; Grosz, B.; Protopapas, P.; Rubin, A. Modeling the Effects of Students’ Interactions with Immersive Simulations using Markov Switching Systems. In Proceedings of the Educational Data Mining, Raleigh, NC, USA, 16–20 July 2018. [Google Scholar]
- Falakmasir, M.H.; González-Brenes, J.P.; Gordon, G.J.; DiCerbo, K.E. A data-driven approach for inferring student proficiency from game activity logs. In Proceedings of the Third (2016) ACM Conference on [email protected] Scale, ACM, Edinburgh, UK, 25–26 April 2016; pp. 341–349. [Google Scholar]
- Balakrishnan, G.; Coetzee, D. Predicting student retention in massive open online courses using hidden markov models. Electr. Eng. Comput. Sci. Univ. Calif. Berkeley
**2013**, 53, 57–58. [Google Scholar] - Fergus, M.; Grimes, T.; Kissane, E.; Lydell, L.; Misukanis, M.; Rayburn, J. Enrollment Patterns of Students from Low-Income Families; Minnesota Office of Higher Education: St. Paul, MN, USA, 2008. [Google Scholar]
- Choy, S.P. Access & Persistence: Findings from 10 Years of Longitudinal Research on Students; ERIC: Washington, DC, USA, 2002.
- Long, B.T. The Financial Crisis and College Enrollment: How Have Students and Their Families Responded? University of Chicago Press: Chicago, IL, USA, 2014; pp. 209–234. [Google Scholar]
- Fredrickson, J. Today’s transfer students: Who are they? Community Coll. Rev.
**1998**, 26, 43–54. [Google Scholar] [CrossRef] - Hagedorn, L.S. How to define retention. In College Student Retention Formula for Student Success; ERIC: Washington, DC, USA, 2005; pp. 90–105. [Google Scholar]
- Boumi, S.; Vela, A.E. Improving Graduation Rate Estimates Using Regularly Updating Multi-Level Absorbing Markov Chains. Educ. Sci.
**2020**, 10, 377. [Google Scholar] [CrossRef]

**Figure 3.**Average annually family income for different enrollment strategies, with 5th, 25th, 50th, 75th, and 95th percentiles.

**Figure 4.**Average GPA for different enrollment strategies, with 5th, 25th, 50th, 75th, and 95th percentiles.

**Figure 5.**Average GPA for FTIC and transfer students with different enrollment strategies, with 5th, 25th, 50th, 75th, and 95th percentiles.

**Figure 6.**Average GPA for FTIC students with different enrollment strategies, with 5th, 25th, 50th, 75th, and 95th percentiles.

**Figure 7.**Average GPA for transfer students with different enrollment strategies, with 5th, 25th, 50th, 75th, and 95th percentiles.

**Figure 8.**Average DFW rate for FTIC and transfer students with different enrollment strategies, with 5th, 25th, 50th, 75th, and 95th percentiles.

**Figure 9.**Average D, F, and W rate for FTIC and transfer students with different enrollment strategies.

**Figure 10.**Graduation rate for FTIC and transfer students with junior academic level and different enrollment strategies.

**Figure 11.**Comparing changes in GPA between students who switch from FES to PES and students who stay FES for FTIC and transfer students.

**Figure 12.**Comparing changes in GPA between students who switch from MES to FES and students who stay MES for FTIC and transfer students.

Student Number | Enrollment Status | Enrollment Strategy |
---|---|---|

1 | F,P,F,F,F,F | F,F,F,F,F,F |

2 | F,P,F,P,F,P | M,M,M,M,M,M |

3 | P,F,P,P,F,P,P | P,P,P,P,P,P |

4 | P,F,F,P,P,P,P | M,M,M,P,P,P,P |

Legend | FT = F, PT = P | FES = F, MES = M, PES = P |

Female | Male | |
---|---|---|

Percentage | 56.2% | 43.8% |

White | Hispanic | African-Am. | Other ${}^{1}$ | |
---|---|---|---|---|

Percentage | 55.2% | 23.4% | 11.3% | 10.1% |

First-Time-in-College | Transfer | |
---|---|---|

Percentage | 39.5% | 60.5% |

Semester | Full-Time | Part-Time |
---|---|---|

Fall | 72.4% | 27.6% |

Spring | 70.6% | 29.4% |

Summer | 10.0% | 90.0% |

**Table 6.**Distribution over enrollment status and enrollment strategy for UCF and other universities.

Target | Always FT | Always PT | FES | MES | PES | Other |
---|---|---|---|---|---|---|

UCF | 35% | 7% | 53% | 3% | 17% | 27% |

Prior research | 29% | 18% | − | − | − | − |

Gender | FES | MES | PES | Other | Population Size |
---|---|---|---|---|---|

Male | 52.9% | 3.9% | 14.5% | 28.7% | 62,157 |

Female | 56.4% | 4.0% | 15.5% | 24.1% | 68,135 |

Gender | FES | MES | PES | Other | Population Size |
---|---|---|---|---|---|

Male | 70.8% | 1.1% | 1.2% | 27.0% | 26,376 |

Female | 77.6% | 1.1% | 1.1% | 20.2% | 26,748 |

Gender | FES | MES | PES | Other | Population Size |
---|---|---|---|---|---|

Male | 39.9% | 5.9% | 24.1% | 30.1% | 35,431 |

Female | 42.9% | 5.9% | 24.5% | 26.7% | 41,043 |

Ethnicity | FES | MES | PES | Other | Population Size |
---|---|---|---|---|---|

White | 56.5% | 3.5% | 13.6% | 26.4% | 71,852 |

Hispanic | 52.0% | 4.5% | 17.4% | 26.1% | 30,843 |

Black | 52.9% | 4.4% | 17.8% | 24.9% | 14,545 |

Other race | 53.8% | 4.1% | 14.5% | 27.6% | 13,210 |

Ethnicity | FES | MES | PES | Other | Population Size |
---|---|---|---|---|---|

White | 74.1% | 1.0% | 1.0% | 23.9% | 31,208 |

Hispanic | 74.8% | 1.1% | 1.4% | 22.7% | 11,322 |

Black | 74.9% | 1.5% | 1.1% | 22.5% | 4963 |

Other race | 72.4% | 1.5% | 1.5% | 24.6% | 5632 |

Ethnicity | FES | MES | PES | Other | Population Size |
---|---|---|---|---|---|

White | 43.0% | 5.6% | 23.0% | 28.4% | 40,139 |

Hispanic | 38.9% | 6.5% | 26.4% | 28.2% | 1939 |

Black | 41.6% | 5.9% | 26.3% | 26.2% | 9514 |

Other race | 40.3% | 6.1% | 23.5% | 30.1% | 7424 |

**Table 13.**Effect size and distribution dissimilarity percentage between full-time and part-time semester GPA for FTIC students with different enrollment strategies.

Pairs | Semester | Dissimilarity % | Effect Size |
---|---|---|---|

FES vs. MES | Full-time | 19% | Medium |

Part-time | 5% | Small | |

FES vs. PES | Full-time | 36% | Very Large |

Part-time | 17% | Medium | |

MES vs. PES | Full-time | 22% | Large |

Part-time | 15% | Medium |

**Table 14.**Effect size and distribution dissimilarity percentage between full-time and part-time semester GPA for transfer students with different enrollment strategies.

Pairs | Semester | Dissimilarity % | Effect Size |
---|---|---|---|

FES vs. MES | Full-time | 10% | Medium |

Part-time | 6% | Small | |

FES vs. PES | Full-time | 9% | Small |

Part-time | 14% | Medium | |

MES vs. PES | Full-time | 6% | Small |

Part-time | 11% | Medium |

**Table 15.**Six-year graduation and halt rate for FTIC students who start in Fall 2008, 2009, and 2010.

Strategy | Graduation Rate | Halt Rate |
---|---|---|

FES | 69% | 30% |

MES | 41% | 51% |

PES | 16% | 81% |

Other | 82% | 17% |

**Table 16.**Graduation rate and time (semesters) to finish school for FTIC students with different enrollment strategies.

Strategy | States | G. Rate | Time to Graduate | Time to Halt |
---|---|---|---|---|

FES | Start | 66% | 11.56 | 4.75 |

Freshman | 63% | 11.09 | 3.82 | |

Sophomore | 78% | 8.78 | 3.29 | |

Junior | 90% | 6.27 | 3.16 | |

Senior | 97% | 3.64 | 2.78 | |

MES | Start | 49% | 12.57 | 5.52 |

Freshman | 43% | 12.74 | 4.70 | |

Sophomore | 64% | 10.20 | 4.18 | |

Junior | 77% | 7.44 | 2.97 | |

Senior | 93% | 4.58 | 3.3 | |

PES | Start | 12% | 12.10 | 4.00 |

Freshman | 6% | 13.26 | 3.15 | |

Sophomore | 15% | 11.17 | 2.65 | |

Junior | 38% | 8.48 | 2.58 | |

Senior | 82% | 5.33 | 2.44 | |

Other | Start | 80% | 13.17 | 8.32 |

Freshman | 79% | 12.65 | 7.58 | |

Sophomore | 82% | 10.27 | 5.97 | |

Junior | 88% | 7.61 | 4.79 | |

Senior | 94% | 4.8 | 4.23 |

**Table 17.**Graduation rate and time (semesters) to finish school for transfer students with different enrollment strategies.

Strategy | States | G. Rate | Time to Graduate | Time to Halt |
---|---|---|---|---|

FES | Start | 74% | 7.08 | 3.68 |

Freshman | 58% | 8.28 | 3.01 | |

Sophomore | 62% | 7.88 | 2.74 | |

Junior | 73% | 6.27 | 2.69 | |

Senior | 89% | 3.82 | 2.51 | |

MES | Start | 72% | 8.15 | 4.74 |

Freshman | 67% | 8.41 | 4.19 | |

Sophomore | 64% | 8.85 | 4.05 | |

Junior | 71% | 7.51 | 3.78 | |

Senior | 85% | 4.78 | 3.41 | |

PES | Start | 36% | 9.5 | 3.73 |

Freshman | 26% | 9.36 | 2.76 | |

Sophomore | 17% | 10.25 | 2.36 | |

Junior | 29% | 9.3 | 2.73 | |

Senior | 61% | 6.13 | 2.79 | |

Other | Start | 82% | 8.74 | 5.94 |

Freshman | 79% | 9.59 | 6.14 | |

Sophomore | 78% | 9.49 | 5.55 | |

Junior | 81% | 8.05 | 5.01 | |

Senior | 88% | 5.36 | 4.21 |

**Table 18.**Halting ratio comparison between students who remain FES and students who switch from FES to PES for different colleges.

College | FES to PES Students | Staying FES Students |
---|---|---|

Science | 10 out of 62 [16.1%] | 21 out of 3246 [0.6%] |

Engr & Comp Sci | 3 out of 26 [11.5%] | 13 out of 1789 [0.7%] |

Medicine | 1 out of 4 [25.0%] | 5 out of 651 [0.8%] |

Business | 2 out of 35 [5.7%] | 11 out of 1506 [0.7%] |

**Table 19.**Analysis of variance for the linear regression model for FTIC students switching from FES to PES.

Source | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

College | 7 | 6.388 | 0.9125 | 1.11 | 0.367 |

Switching | 1 | 19.995 | 19.9952 | 24.41 | 0.000 |

College × Switching | 7 | 9.219 | 1.317 | 1.61 | 0.152 |

Error | 56 | 45.875 | 0.8192 | ||

Total | 71 | 82.442 |

**Table 20.**Analysis of variance for the linear regression model for transfer students switching from FES to PES.

Source | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

College | 7 | 3.548 | 0.5068 | 0.55 | 0.797 |

Switching | 1 | 9.485 | 9.4854 | 10.2 | 0.002 |

College × Switching | 7 | 1.747 | 0.2496 | 0.27 | 0.964 |

Error | 62 | 57.639 | 0.9297 | ||

Total | 77 | 72.420 |

**Table 21.**Analysis of variance for the linear regression model for FTIC students switching from MES to FES.

Source | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

College | 4 | 1.442 | 0.36049 | 0.43 | 0.789 |

Switching | 1 | 4.9863 | 4.98631 | 5.89 | 0.019 |

College × Switching | 4 | 0.2207 | 0.05518 | 0.07 | 0.992 |

Error | 54 | 45.6819 | 0.84596 | ||

Total | 63 | 52.6965 |

**Table 22.**Analysis of variance for the linear regression model for transfer students switching from MES to FES.

Source | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

College | 5 | 0.7707 | 0.1541 | 0.24 | 0.941 |

Switching | 1 | 6.1566 | 6.1566 | 9.76 | 0.003 |

College × Switching | 5 | 2.8658 | 0.5732 | 0.91 | 0.481 |

Error | 66 | 41.6462 | 0.6310 | ||

Total | 77 | 50.5700 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Boumi, S.; Vela, A.E. Quantifying the Impact of Student Enrollment Patterns on Academic Success Using a Hidden Markov Model. *Appl. Sci.* **2021**, *11*, 6453.
https://doi.org/10.3390/app11146453

**AMA Style**

Boumi S, Vela AE. Quantifying the Impact of Student Enrollment Patterns on Academic Success Using a Hidden Markov Model. *Applied Sciences*. 2021; 11(14):6453.
https://doi.org/10.3390/app11146453

**Chicago/Turabian Style**

Boumi, Shahab, and Adan Ernesto Vela. 2021. "Quantifying the Impact of Student Enrollment Patterns on Academic Success Using a Hidden Markov Model" *Applied Sciences* 11, no. 14: 6453.
https://doi.org/10.3390/app11146453