An Open-Source Tool Simultaneous Grade Regression and Risk Classification for Education

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This Python package implements methodologies from our research outputs [1] [2] that enable educators to predict student academic outcomes and identify at-risk students efficiently, and integrates regression analysis with binary classification to predict student academic outcomes. Designed for ease of use, this package allows educators to train models, make predictions, and visualize results with just one line of code using their own datasets. This accessibility ensures that sophisticated algorithms are readily available to users with varying levels of IT expertise.

Citation

If you use this package in your research, please cite our paper: Dong, C., et al. (2026). A Data-Analytical Framework for the Early Detection of At-Risk Students in Higher Education. In: Ventura, M.D., Zhan, Z. (eds) Exploring Innovations in Educational Technology: The ICEIT’25 Collection. Lecture Notes in Educational Technology. Springer, Singapore. https://doi.org/10.1007/978-981-95-0872-3_2 📖 Paper Link (Springer) 📊 Presentation Slides (ResearchGate)

Table of Contents

Click to expand

• Package Installation
• 1. Methodology
• 2. The Model Object (Parameters, Methods, and Attributes)
• 3. Quick Start
• References

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Package Installation

This package requires:

• Python (>= 3.9)
• NumPy
• scikit-learn
• Matplotlib
• Seaborn

1. Install dependencies:

pip install numpy scikit-learn matplotlib seaborn

2. Install the package via PyPI or GitHub (Recommended):

pip install dualPredictor

OR

pip install git+https://github.com/098765d/dualPredictor.git

1. Methodology

The package enables educators to predict student academic outcomes and identify at-risk students efficiently. The process involves three key steps:

Fig 1: How does dualPredictor provide dual prediction output?

• Step 1: Grade Prediction Using the Trained Regressor (Fig 1, Step 1) fit the linear model f(x) using the training data, and grade prediction can be generated from the fitted model

  $$y\_pred = f(x) = \sum_{j=1}^{M} w_j x_j + b$$

  Where:

  • y_pred: The predicted grade for a student.
  • x_j: The j-th feature of the student (e.g., previous grades, attendance).
  • w_j: The weight associated with the j-th feature.
  • b: The bias term.
  • M: The total number of features in the model.

• Step 2: Determining the Optimal Cut-off (Fig 1, Step 2)

  The goal is to find the cut-off (c) that has the optimal binary classification performance (evaluated by the metric function g). Firstly, the user specifies the metric type used for the model (e.g., Youden index) and denotes the metric function as g(y_true_label, y_pred_label), where:

  $$\text{optimal\_cut\_off} = \arg\max_c g(y_{\text{true\_label}}, y_{\text{pred\_label}}(c))$$

  Where:

  • c: The tuned cut-off that determines the y_pred_label
  • y_true_label: The true label of the data point based on the default cut-off (e.g., 1 for at-risk, 0 for normal).
  • y_pred_label: The predicted label of the data point based on the tuned cut-off value.
  • g(y_true_label, y_pred_label(c)): The metric value that evaluates the performance of the binary classification (e.g., Youden Index).

  For Instance, if we use Youden Index as the metric for the model performance, the equation would be:

  $$\text{optimal\_cut\_off} = \arg\max_c \left[ \frac{TP}{TP + FN} + \frac{TN}{TN + FP} - 1 \right]$$

  (TP, TN, FP, and FN are calculated based on y_true_label and y_pred_label(c).)

• Step 3: Binary Label Prediction: (Fig 1, Step 3)

  • y_pred_label = 1 (at-risk): if y_pred < optimal_cut_off
  • y_pred_label = 0 (normal): if y_pred >= optimal_cut_off

2. The Model Object (Parameters, Methods, and Attributes)

The dualPredictor package aims to simplify complex models for users of all coding levels. It adheres to the syntax of the scikit-learn library and simplifies model training by allowing you to fit the model with just one line of code. The core part of the package is the model object called DualModel, which can be imported from the dualPredictor library.

Table 1: Model Parameters, Methods, and Attributes

Category	Name	Description
Parameters	model_type	Type of regression model to use. For example: - 'lasso' (Lasso regression)
	metric	Metric optimizes the cut-off value. For example: - 'youden_index' (Youden's Index)
	default_cut_off	Initial cut-off value used for binary classification. For example: 2.50
Methods	fit(X, y)	- X: The input training data, pandas data frame. - y: The target values (predicted grade). - Returns: Fitted DualModel instance
	predict(X)	- X: The input data for predeiction, pandas data frame.
Attributes	alpha_	The value of penalization in Lasso model
	coef_	The coefficients of the model
	intercept_	The intercept value of the model
	feature_names_in_	Names of features during model training
	optimal_cut_off	The optimal cut-off value that maximizes the metric

Demonstration of Model Object Usage

from dualPredictor import DualModel

# Initialize the model and specify the parameters
model = DualModel(model_type='lasso', metric='youden_index', default_cut_off=2.5)

# Using model methods for training and predicting
# Simplify model training by calling fit method with one line of code
model.fit(X_train, y_train)
grade_predictions, class_predictions = model.predict(X_train)

# Accessing model attributes (synthetic result for demo only)
print("Alpha (regularization strength):", model.alpha_)
Alpha (regularization strength): 0.12

print("Model coefficients:", model.coef_)
Model coefficients: [0.2, -0.1, 0.3, 0.4]

print("Model intercept:", model.intercept_)
Model intercept: 2.5

print("Feature names:", model.feature_names_in_)
Feature names: ['feature1', 'feature2', 'feature3', 'feature4']

print("Optimal cut-off value:", model.optimal_cut_off)
Optimal cut-off value: 2.56

3. Quick Start

Note: Results are synthetic and for demonstration purposes only

Step 0. Prepare your Dataset: Prepare the X_train, X_test, y_train, y_test

Step 1. Import the Package: Import the dualPredictor package into your Python environment.

from dualPredictor import DualModel, model_plot

Step 2. Model Initialization: Create a DualModel instance

model = DualModel(model_type='lasso', metric='youden_index', default_cut_off=2.5)

Step 3. Model Training: Fit the model using X_train & y_train

model.fit(X_train, y_train)

Step 4. Model Predictions: Generate predictions on X_test

# example for demo only, model prediction dual output
y_test_pred,y_test_label_pred = model.predict(X_test)

# Example of model's 1st output = predicted scores (regression result)
y_test_pred
array([3.11893389, 3.06013236, 3.05418893, 3.09776197, 3.14898782,
     2.37679417, 2.99367804, 2.77202421, 2.9603209, 3.01052573])

# Example of model's 2nd output = predicted at-risk status (binary label)
y_test_label_pred
array([0, 0, 0, 0, 0, 1, 0, 0, 1, 0])

Step 5.Visualizations: Visualize the model's performance with just one line of code

# Scatter plot for regression analysis 
model_plot.plot_scatter(y_pred, y_true)

# Confusion matrix for binary classification 
model_plot.plot_cm(y_label_true, y_label_pred)

# Model's global explanation: Feature importance plot
model_plot.plot_feature_coefficients(coef=model.coef_, feature_names=model.feature_names_in_)

Fig 2: Visualization Module Sample Outputs

Additional Demonstration

Applied on Kaggle Dataset: Object Oriented Programming Class Student Grades data from Mugla Sitki Kocman University ('19 OOP Class Student Grades).

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References

[1] Dong, C. et al. (2026). A Data-Analytical Framework for the Early Detection of At-Risk Students in Higher Education. In: Ventura, M.D., Zhan, Z. (eds) Exploring Innovations in Educational Technology: The ICEIT’25 Collection. Lecture Notes in Educational Technology. Springer, Singapore. https://doi.org/10.1007/978-981-95-0872-3_2

[2] Yip, J. C., Dong, C., Ling, A. M. H., Kwan, J. L. Y., Yu, P. L. H., Cheng, M. H. M., Lee, J. C. & Li, W. K. "A Data-Analytic Approach to Early Detection of At-Risk Students in Higher Education." 2025 7th International Conference on Computer Science and Technologies in Education (CSTE), Wuhan, China, 2025, pp. 228-232, doi: 10.1109/CSTE64638.2025.11092031.

[3] Fluss, R., Faraggi, D., & Reiser, B. (2005). Estimation of the Youden Index and its associated cutoff point. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 47(4), 458-472.

[4] Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

[5] Lundberg, S. M., & Lee, S. I. (2017). A unified approach to interpreting model predictions. Advances in neural information processing systems, 30.

[6] Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., ... & Duchesnay, É. (2011). Scikit-learn: Machine learning in Python. The Journal of Machine Learning Research, 12, 2825-2830.

[7] Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology, 58(1), 267-288.