Lecture Notes on Interpreting Statistical Results with Marginal Effects

Introduction

• Recorded talk for USR 2024 in Salzburg.
• Discussing the marginal effects package developed over the years.
• Speaker: Professor at the University de moral, Canada, with 15 years of experience publishing packages on CRAN.
• Recently named associate editor of the ART Journal.

Key Problems in Statistics

1. Inconsistency in Software Outputs

   • Example: Different outputs from the predict command in R depending on the type of model (e.g., GLM vs. ordinal logit).
   • Inconsistencies slow down users and complicate data analysis.

2. Difficulty in Interpreting Statistics

   • Example: Logit regression model is hard to interpret due to challenges with probabilities and log-odds ratios.
   • Many people struggle with interpreting probabilities, especially in varying contexts (high and low probabilities).
   • Statistics becomes more complex with interactions and non-linear models.

Proposed Solutions

Post-hoc Transformations

• Quote: "A parameter is just a resting stone on the road to prediction."
• Importance of transforming model parameters into intuitive quantities that stakeholders can understand.

Marginal Effects Package

• Features:
  • Supports 100+ model types (GLM, GAM, mixed effects, machine learning).
  • Provides a consistent workflow across different models.
  • Documented online with 30+ chapters full of case studies.
• Main Quantities:
  1. Predictions: Fitted values for different predictor values.
  2. Counterfactual Comparisons: Risk differences, odds ratios, etc.
  3. Slopes: Partial derivatives or marginal effects.

Key Functions of the Package

1. Hypothesis Testing

   • Flexible hypothesis argument available across all functions.
   • Example: Test if two coefficients are equal or compare treatment effects.

2. Predictions

   • Enhanced predictions function provides richer results (estimates, p-values, confidence intervals).
   • Ability to average predictions by subgroup.
   • Example: Compare average predicted outcomes between different categories.

3. Counterfactual Comparisons

   • Estimate effects when changing predictor values (e.g., effect of increasing a numeric predictor).
   • Supports various comparisons and ratios, allowing customized analysis.

4. Slopes Function

   • Provides easy estimation of marginal effects and enables plotting of predictions versus slopes.

Additional Resources

• Free online book: marginal effects with detailed chapters and illustrations.
• Other packages maintained by the speaker:
  • Tiny Table: Simple, flexible table creation in various formats (HTML, LaTeX, Markdown).
  • Model Summary: For creating regression tables and descriptive statistics.

Conclusion

• Encourages engagement through questions via email or social media.
• Open to issues on GitHub regarding marginal effects or related topics.