⚠ Official Notice: www.ijisrt.com is the official website of the International Journal of Innovative Science and Research Technology (IJISRT) Journal for research paper submission and publication. Please beware of fake or duplicate websites using the IJISRT name.



A Hybrid Machine Learning and Mathematical Modeling Approach for Predicting Academic Performance Using Latent Dimensions


Authors : Rajoelison Andrianarimalala Abel; Rakotomalala Vololona Harinoro; Rasolomampiandry Gilbert

Volume/Issue : Volume 11 - 2026, Issue 4 - April


Google Scholar : https://tinyurl.com/4f8a45n5

Scribd : https://tinyurl.com/y2c89pa9

DOI : https://doi.org/10.38124/ijisrt/26apr1548

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.


Abstract : Predicting academic performance is a major challenge in higher education, particularly in contexts where student monitoring systems are limited. While machine learning models have demonstrated strong predictive capabilities, their lack of interpretability limits their applicability in educational settings. This study proposes an interpretable model, the Academic Performance Index (API), based on an integrated framework combining mathematical modeling, cognitive sciences, and machine learning. Using real student data, a Random Forest model is employed to identify the most relevant variables and estimate their relative importance. These weights are then used to construct a composite index structured around four latent dimensions : cognitive, motivational, socio-economic, and environmental. The API is subsequently incorporated into a logistic regression model to estimate the probability of academic success. The results show that the proposed model achieves high predictive performance (AUC = 0.897; F1-score = 0.84), comparable to advanced approaches, while providing improved interpretability. The analysis highlights the central role of cognitive factors in academic success.

Keywords : Machine Learning, Mathematical Modeling, Latent Variables, Random Forest, Academic Performance.

References :

  1. Siemens, G. & Baker, R.S. (2012). Learning analytics and educational data mining: towards communication and collaboration. LAK. https://doi.org/10.1145/2330601.2330661
  2. Romero, C. & Ventura, S. (2010). Educational data mining: a review of the state of the art. IEEE Trans. SMC. https://doi.org/10.1109/TSMCC.2010.2053532
  3. Arnold, K.E. & Pistilli, M.D. (2012). Course signals at Purdue: using learning analytics to increase student success. LAK. https://doi.org/10.1145/2330601.2330666
  4. Breiman, L. (2001). Random Forests. Machine Learning. https://doi.org/10.1023/A:1010933404324
  5. Chen, T. & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. KDD. https://doi.org/10.1145/2939672.2939785
  6. Ribeiro, M.T., Singh, S. & Guestrin, C. (2016). “Why Should I Trust You?” Explaining the Predictions of Any Classifier. KDD. https://doi.org/10.1145/2939672.2939778
  7. Pintrich, P.R. (2003). A motivational science perspective on the role of student motivation in learning and teaching contexts. JEP. https://doi.org/10.1037/0022-0663.95.4.667
  8. Lundberg, S.M. & Lee, S.-I. (2017). A Unified Approach to Interpreting Model Predictions. NeurIPS. https://doi.org/10.48550/arXiv.1705.07874
  9. Baker, R.S. & Inventado, P.S. (2014). Educational data mining and learning analytics. In Learning Analytics. https://doi.org/10.1007/978-1-4614-3305-7_1
  10. Liaw, A. & Wiener, M. (2002). Classification and regression by randomForest. R News. https://doi.org/10.32614/RJ-2002-022
  11. Strobl, C. et al. (2007). Bias in random forest variable importance measures. BMC Bioinformatics. https://doi.org/10.1186/1471-2105-8-25
  12. Eccles, J.S. & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology. https://doi.org/10.1146/annurev.psych.53.100901.135153
  13. Han, J., Kamber, M. & Pei, J. (2012). Data Mining: Concepts and Techniques. https://doi.org/10.1016/C2009-0-61819-5
  14. Jolliffe, I.T. & Cadima, J. (2016). Principal component analysis: a review and recent developments. https://doi.org/10.1098/rsta.2015.0202
  15. Breiman, L. (2001). Statistical modeling: The two cultures. https://doi.org/10.1214/ss/1009213726                                            
  16. Hosmer, D.W., Lemeshow, S. & Sturdivant, R.X. (2013). Applied Logistic Regression. https://doi.org/10.1002/9781118548387
  17. Pedregosa, F. et al. (2011). Scikit-learn: Machine Learning in Python. https://doi.org/10.5555/1953048.2078195

Predicting academic performance is a major challenge in higher education, particularly in contexts where student monitoring systems are limited. While machine learning models have demonstrated strong predictive capabilities, their lack of interpretability limits their applicability in educational settings. This study proposes an interpretable model, the Academic Performance Index (API), based on an integrated framework combining mathematical modeling, cognitive sciences, and machine learning. Using real student data, a Random Forest model is employed to identify the most relevant variables and estimate their relative importance. These weights are then used to construct a composite index structured around four latent dimensions : cognitive, motivational, socio-economic, and environmental. The API is subsequently incorporated into a logistic regression model to estimate the probability of academic success. The results show that the proposed model achieves high predictive performance (AUC = 0.897; F1-score = 0.84), comparable to advanced approaches, while providing improved interpretability. The analysis highlights the central role of cognitive factors in academic success.

Keywords : Machine Learning, Mathematical Modeling, Latent Variables, Random Forest, Academic Performance.

Paper Submission Last Date
31 - May - 2026

SUBMIT YOUR PAPER CALL FOR PAPERS
Video Explanation for Published paper

Never miss an update from Papermashup

Get notified about the latest tutorials and downloads.

Subscribe by Email

Get alerts directly into your inbox after each post and stay updated.
Subscribe
OR

Subscribe by RSS

Add our RSS to your feedreader to get regular updates from us.
Subscribe