Lecture on Logit Model (Logistic Regression)

Introduction

• Presenter: Sava
• Platform: Nettle (Distance learning in business, finance, economics, etc.)
• Topic: Logit Model or Logistic Regression
• Purpose: Estimate regression models with categorical/binary dependent variables (Y)

Key Applications

• Credit Scoring: Predicting borrower defaults (0 = non-default, 1 = default)
• Economic Recessions: Predicting recessions (0 = no recession, 1 = recession)
• Educational Success: Predicting exam success/failure based on study hours

Credit Scoring Example

• Data Sample: 500 applicants
  • Outcome: 0 = Non-default, 1 = Default
  • Defaults in Sample: 127 out of 500 (roughly a quarter)
• Necessary Condition: Sized sample chunks of zeros and ones (not overly dominant by either)
• Variables: Independent/Predictors: Binary (Yes/No)
  • Homeownership (Property as collateral)
  • Full-time employment
• Real numbers: Turned into explanatory variables
  • Income, expenses, assets, debt, loan amount

Transforming Variables

• Expenses/Income Ratio: Indicates thriftiness; expect lower expenses relative to income = higher chances of repayment
• Leverage: Total Debt/Assets after loan; measure of financial vulnerability
• Repayment Time: Loan amount/Income (scaled with natural logarithm)

Logit Model Estimation

• Parameters to Estimate: Constant + Coefficients of explanatory variables
• Odds Ratio: Estimate probability of default using logistic distribution function
  • Logit Value: Exponent of weighted sum of explanatory variables and coefficients
  • Logistic Transformation: Converts logit into an estimated probability (bounded 0 to 1)

Optimization

• Goal: Maximize log likelihood instead of minimizing squared sum of residuals
• Log Likelihood Calculation: Based on actual and estimated probabilities of defaults
  • Sum of products of observed defaults and log of estimated probabilities
• Solver: Optimize coefficients to maximize log likelihood

Result Analysis

• Coefficients Interpretation: Signs and significant relationships
  • Positive Predictors (Reducing Defaults): Homeownership, Full-time employment
  • Negative Predictors (Increasing Defaults): Higher expenses relative to income, Higher leverage, Higher repayment time
• Statistical Significance: P-values to determine significant predictors

Standard Errors and Covariance Matrix

• Matrix Inversion and Multiplication: For variance estimation of coefficients
• Weight Matrix: Accounts for heteroskedasticity in categorical variable estimation

Applying Model for Credit Scoring

• Example Applicant Data: Homeownership, Full-time employment, Income, expenses, assets, debt, loan amount
• Calculation of Probability: Use model coefficients to estimate default probability
  • Decision Making: Compare estimated default probability to average default rate

Conclusion

• Final Outcome: Logit model helps in making informed credit lending decisions
• Further Actions: Invite for suggestions, feedback, and support via Patreon

Thank you for your attention!