Credit Scoring with Logistic Regression
Business → Data Analytics Points
RAI Insights | 2025-11-02 19:28:55
RAI Insights | 2025-11-02 19:28:55
Introduction Slide – Credit Scoring with Logistic Regression
Foundations and Importance of Logistic Regression in Credit Scoring
Overview
- Logistic regression models the probability of default and maps credit attributes to default risk.
- It is widely used by lenders and credit rating agencies for assessing creditworthiness.
- The following slides cover model development, predictor importance, scaling, analytics, and practical implementation.
- Key insights include understanding model interpretation, validation, and deployment in risk management.
Key Discussion Points – Credit Scoring with Logistic Regression
Core Concepts and Practical Insights
Main Points
- Logistic regression links score to probability of default using a logistic function, facilitating interpretability.
- Predictor selection is essential to maintain a balance between model simplicity and predictive power.
- Metrics such as p-values and information value guide variable choice and model validation.
- Comparisons to alternative models like decision trees highlight logistic regression's robustness and transparency.
Graphical Analysis – Credit Scoring with Logistic Regression
Visualizing Relationship Between Credit Attributes and Default Risk
Context and Interpretation
- The scatter plot with regression line shows how a key continuous credit attribute correlates positively with default probability.
- The linear trend confirms the relevance and strength of the predictor in logistic regression.
- Variability around the line indicates that other factors also impact default risk.
- This visualization aids in understanding how logistic regression models continuous predictors.
Figure: Linear Relationship of Credit Attribute vs. Default Probability
{
"$schema": "https://vega.github.io/schema/vega-lite/v6.json",
"width": "container",
"height": "container",
"description": "Linear regression example for a credit attribute versus default probability",
"config": {"autosize": {"type": "fit-y", "resize": false, "contains": "content"}},
"data": {"values": [{"Attribute":1,"DefaultProb":0.1},{"Attribute":2,"DefaultProb":0.15},{"Attribute":3,"DefaultProb":0.22},{"Attribute":4,"DefaultProb":0.35},{"Attribute":5,"DefaultProb":0.45},{"Attribute":6,"DefaultProb":0.5},{"Attribute":7,"DefaultProb":0.6}]},
"layer": [
{"mark": {"type": "point", "filled": true}, "encoding": {"x": {"field": "Attribute", "type": "quantitative"}, "y": {"field": "DefaultProb", "type": "quantitative"}}},
{"mark": {"type": "line", "color": "firebrick"}, "transform": [{"regression": "DefaultProb", "on": "Attribute"}], "encoding": {"x": {"field": "Attribute", "type": "quantitative"}, "y": {"field": "DefaultProb", "type": "quantitative"}}}
]
}Graphical Analysis – Credit Scoring with Logistic Regression
Context and Interpretation
- The marginal histogram and heatmap illustrate the distribution and interaction of two important credit scoring variables.
- This visualization helps identify variable distribution skewness and dependence patterns affecting risk prediction.
- Understanding category frequencies and their joint effect provides insights for variable binning and model refinement.
- Such visual tools assist in detecting anomalies and enhancing feature engineering for logistic regression.
Figure: Marginal Histogram and Heatmap of Credit Scoring Variables
{
"$schema": "https://vega.github.io/schema/vega-lite/v6.json",
"width": "container",
"height": "container",
"description": "Marginal histogram and heatmap of two credit scoring variables",
"config": {"autosize": {"type": "fit-y", "resize": false, "contains": "content"}},
"data": {"values": [
{"Income":3,"CreditScore":450},{"Income":5,"CreditScore":550},{"Income":3,"CreditScore":500},{"Income":6,"CreditScore":700},{"Income":7,"CreditScore":600},{"Income":8,"CreditScore":750},{"Income":7,"CreditScore":720},{"Income":2,"CreditScore":430}
]},
"spacing":15,
"vconcat":[
{"mark":"bar","height":60,"encoding":{"x":{"bin":true,"field":"Income","axis":null},"y":{"aggregate":"count","title":"Count"}}},
{"hconcat":[
{"mark":"rect","encoding":{"x":{"bin":true,"field":"Income"},"y":{"bin":true,"field":"CreditScore"},"color":{"aggregate":"count"}}},
{"mark":"bar","width":60,"encoding":{"y":{"bin":true,"field":"CreditScore","axis":null},"x":{"aggregate":"count","title":"Count"}}}
]}
]
}Analytical Summary & Table – Credit Scoring with Logistic Regression
Summary of Model Outcomes and Key Metrics
Key Discussion Points
- The logistic regression model enables probability estimation for credit default based on selected predictors.
- Metric evaluation like accuracy and p-values validates model reliability and predictive strength.
- The table below exemplifies scoring and predictor effect estimates, aiding interpretability for risk decisions.
- Considerations include balancing model complexity and predictive performance while ensuring regulatory compliance.
Illustrative Data Table
Example of attribute importance and scoring contributions.
| Attribute | Coefficient | p-value | Score Contribution |
|---|---|---|---|
| Income Level | -0.35 | 0.004 | +150 |
| Credit History Length | -0.22 | 0.012 | +120 |
| Number of Credit Cards | -0.15 | 0.045 | +80 |
| Loan Amount | 0.40 | 0.001 | -200 |
Analytical Explanation & Formula – Credit Scoring with Logistic Regression
Core Mathematical Model Behind Logistic Regression in Credit Scoring
Concept Overview
- Logistic regression models the probability of default via the logistic function applied to a linear combination of predictors.
- The formula estimates the log-odds of default as a weighted sum of credit attributes.
- Key parameters are the model coefficients reflecting each variable's impact on default risk.
- This model supports interpretable, probabilistic risk assessment and decision thresholds.
General Formula Representation
The logistic regression model is expressed as:
$$ P(\text{default}|x) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_n x_n)}} $$
Where:
- \( P(\text{default}|x) \) = Probability of default given predictors.
- \( x_1, x_2, ..., x_n \) = Credit risk attributes (income, loan amount, etc.).
- \( \beta_0 \) = Intercept (baseline log-odds).
- \( \beta_1, ..., \beta_n \) = Model coefficients representing impact of each attribute.
This allows for predicting default probabilities and scoring customer credit risk effectively.
Code Example: Credit Scoring with Logistic Regression
Code Description
This Python example demonstrates building a logistic regression credit scoring model using scikit-learn, including training, predicting default probability, and evaluating performance.
# Python credit scoring with logistic regression example
import numpy as np
import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, roc_auc_score
# Simulated credit data with predictors and default flag
np.random.seed(42)
data_size = 200
X = pd.DataFrame({
'Income': np.random.normal(50000, 15000, data_size),
'CreditHistoryLength': np.random.normal(5, 2, data_size),
'NumCreditCards': np.random.randint(1, 6, data_size),
'LoanAmount': np.random.normal(15000, 5000, data_size)
})
# True model coefficients for simulation
coeffs = np.array([-0.00004, -0.3, -0.1, 0.00007])
intercept = -1.2
# Logistic function to generate default probabilities
log_odds = intercept + np.dot(X, coeffs)
prob_default = 1 / (1 + np.exp(-log_odds))
# Generate binary default labels
y = np.random.binomial(1, prob_default)
# Train-test split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)
# Fit logistic regression model
model = LogisticRegression()
model.fit(X_train, y_train)
# Predict and evaluate
y_pred = model.predict(X_test)
y_prob = model.predict_proba(X_test)[:, 1]
print('Accuracy:', accuracy_score(y_test, y_pred))
print('ROC-AUC:', roc_auc_score(y_test, y_prob))Conclusion
Summary and Next Steps in Credit Scoring
- Logistic regression effectively models and predicts credit risk with clear interpretability.
- Careful predictor selection and model validation optimize performance and regulatory compliance.
- This approach supports informed lending decisions by estimating default probabilities.
- Future work includes integrating alternative models, advanced feature engineering, and continuous monitoring.
