About Model Comparison
Model comparison helps you select the best specification for your panel data analysis.
These charts visualize differences in coefficients, model fit, and information criteria
across multiple model specifications.
Available Comparison Charts
- Coefficient Comparison: Compare estimated coefficients across models
- Forest Plot: Visualize coefficient estimates with confidence intervals
- Model Fit Comparison: Compare R-squared and adjusted R-squared
- Information Criteria: Compare AIC and BIC for model selection
{% if models_info %}
Models Being Compared
| Model |
Estimator |
Observations |
R-squared |
AIC |
BIC |
{% for model in models_info %}
| {{ model.name }} |
{{ model.estimator|default('N/A') }} |
{{ model.nobs|default('N/A') }} |
{{ "%.4f"|format(model.r_squared) if model.r_squared else 'N/A' }} |
{{ "%.2f"|format(model.aic) if model.aic else 'N/A' }} |
{{ "%.2f"|format(model.bic) if model.bic else 'N/A' }} |
{% endfor %}
{% endif %}
Model Selection Criteria
- AIC (Akaike Information Criterion): Lower is better. Balances fit and complexity.
- BIC (Bayesian Information Criterion): Lower is better. More conservative penalty for complexity.
- R-squared: Higher is better. Proportion of variance explained.
- Adjusted R-squared: Accounts for number of predictors.
{% if comparison_charts %}
Model Comparison Charts
Interactive comparison charts for comprehensive model evaluation.
Hover over data points for detailed information, zoom to focus on specific areas.
{% if comparison_charts.coefficient_comparison %}
Coefficient Comparison
Compare coefficient estimates across all models. Each variable shows estimates from different models
side-by-side, making it easy to see how specifications affect parameter estimates.
{{ comparison_charts.coefficient_comparison|safe }}
{% endif %}
{% if comparison_charts.forest_plot %}
Forest Plot
Visualize coefficient estimates with 95% confidence intervals. Points represent point estimates,
horizontal lines show confidence intervals. Coefficients that don't overlap zero are statistically significant.
{{ comparison_charts.forest_plot|safe }}
{% endif %}
{% if comparison_charts.fit_comparison %}
Model Fit Comparison
Compare R-squared and adjusted R-squared across models. Higher values indicate better fit,
but beware of overfitting. Adjusted R-squared penalizes model complexity.
{{ comparison_charts.fit_comparison|safe }}
{% endif %}
{% if comparison_charts.ic_comparison %}
Information Criteria Comparison
Compare AIC and BIC across models. Lower values are better. BIC penalizes complexity more heavily than AIC.
Use these criteria for model selection when models are not nested.
{{ comparison_charts.ic_comparison|safe }}
{% endif %}
Chart Interactions
- Hover: Move your mouse over data points to see detailed information
- Zoom: Click and drag to zoom into a region, or use the zoom buttons
- Pan: After zooming, click and drag to pan around
- Reset: Click the "Reset axes" button to restore the original view
- Export: Use the camera icon to download the chart as a PNG image
- Toggle Series: Click on legend items to show/hide specific models
{% else %}
No comparison charts available.
Generate model comparison charts using the visualization system.
{% endif %}
Interpretation Guide
Coefficient Comparison
What to look for: Consistency and magnitude of coefficient estimates across models.
- ✓ Robust coefficients: Similar estimates across different specifications
- ⚠ Sensitivity: Coefficients that change dramatically may indicate specification issues
- ⚠ Sign changes: Coefficient changing sign is a red flag for omitted variable bias
- ✓ Precision improvement: Confidence intervals narrowing with better specification
Forest Plot
What to look for: Confidence intervals and statistical significance across models.
- ✓ Significance: Intervals not crossing zero indicate significance at α=0.05
- ✓ Precision: Narrower intervals = more precise estimates
- ⚠ Inconsistent significance: Variable significant in some models but not others
- ✓ Overlapping intervals: Estimates not significantly different from each other
Model Fit Comparison
What to look for: Balance between fit and complexity.
- ✓ Higher R²: Better fit, but watch for overfitting
- ✓ Adjusted R²: Accounts for number of predictors (use this for comparison)
- ⚠ Marginal improvements: Small R² increases may not justify added complexity
- ⚠ Very high R²: May indicate overfitting or multicollinearity
Note: R² is only comparable across models with the same dependent variable.
Information Criteria (AIC/BIC)
What to look for: Lowest values, considering your research goals.
- ✓ Lower is better: Both AIC and BIC penalize poor fit and complexity
- AIC: Better for prediction, less conservative
- BIC: Better for explanation, more conservative (stronger penalty)
- ⚠ Small differences: ΔIC < 2 suggests models are similar
- ⚠ Moderate differences: 2 < ΔIC < 10 suggests some support for both
- ✓ Large differences: ΔIC > 10 provides strong evidence for better model
Rule of thumb: If BIC and AIC disagree, BIC often selects simpler models.
Model Selection Strategy
- Start simple: Begin with baseline specification
- Add controls: Include theoretically relevant variables
- Test robustness: Check coefficient stability across specifications
- Compare fit: Use AIC/BIC for nested and non-nested models
- Consider theory: Statistical fit is not the only criterion
- Report multiple models: Show robustness of key findings
Common Pitfalls
- ❌ Data mining: Don't just pick the model with highest R²
- ❌ Overfitting: Complex models may not generalize
- ❌ Ignoring theory: Statistical fit doesn't guarantee correct specification
- ❌ Comparing incomparable: Different samples, different dependent variables
- ✓ Best practice: Use multiple criteria and theoretical reasoning
Reporting Recommendations
- Report multiple models showing robustness of key findings
- Explain your model selection criteria clearly
- Discuss sensitivity of key coefficients to specification
- Include both statistical criteria (AIC/BIC) and theoretical justification
- Be transparent about specification searches you conducted