Mathematical Modeling and Interpretable Machine Learning for Predicting Academic Performance Based on Latent Dimensions

Source abstract

Accurately predicting academic performance is a major challenge in higher education, particularly in contexts where individualized student support is limited. This study presents a hybrid predictive framework that integrates Exploratory Factor Analysis (EFA), mathematical modeling, and Logistic Regression to predict the academic performance of Master’s students. The analysis is based on a dataset of 400 students described by 24 explanatory variables encompassing academic, cognitive, digital, motivational, socio- family, and contextual dimensions. Academic performance was modeled as a binary outcome, where 0 denotes average performance and 1 indicates high performance. Exploratory Factor Analysis identified four latent dimensions, which were subsequently incorporated as predictors into the logistic regression model. The proposed factor-based model achieved an accuracy of 0.858, an F1-score of 0.855, and an Area Under the Receiver Operating Characteristic Curve (AUC) of 0.907 on the test dataset. Compared with a baseline logistic regression model using all 24 original variables, the proposed approach improved the predictive performance while substantially reducing the model complexity. To facilitate practical implementation, a Streamlit-based web prototype was developed to operationalize the model and provide personalized recommendations for students predicted to belong to the average performance class. These findings demonstrate that combining dimensionality reduction with interpretable statistical learning offers an effective and practical framework for predicting academic performance and supporting students in higher education.