# 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 |

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**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 |

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## 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