Calculator Inputs
Example Data Table
| Model | Method | n | k | Input Value | BIC | Comment |
|---|---|---|---|---|---|---|
| Segment A | Log-likelihood | 120 | 4 | -58.2 | 135.5500 | Lowest BIC in this comparison. |
| Segment B | Log-likelihood | 120 | 6 | -54.9 | 138.5250 | Better fit, but larger parameter penalty. |
| Segment C | Log-likelihood | 120 | 3 | -63.5 | 141.3625 | Most parsimonious, yet weaker overall fit. |
Formula Used
Direct likelihood form: BIC = k × ln(n) − 2 × ln(L̂)
Log-likelihood form: BIC = k × ln(n) − 2 × logLik
Gaussian RSS approximation: BIC = n × ln(RSS / n) + k × ln(n)
Where:
- n = sample size
- k = number of estimated parameters
- L̂ = maximized likelihood
- RSS = residual sum of squares
Lower BIC values indicate a better trade-off between model fit and complexity. ΔBIC can compare two candidate models directly.
How to Use This Calculator
- Select the method matching your available model output.
- Enter sample size and estimated parameter count.
- Provide log-likelihood, likelihood, or RSS as required.
- Optionally add another model's BIC for comparison.
- Choose decimal precision for reporting.
- Press Calculate BIC to display the result above the form.
- Review BIC, fit term, penalty term, ΔBIC, and model weights.
- Use the CSV or PDF buttons to save the summary.
Frequently Asked Questions
1. What does BIC measure?
BIC measures how well a statistical model balances goodness of fit against complexity. It penalizes extra parameters, so simpler models can outperform overly flexible ones.
2. Is a lower BIC always better?
Yes, lower BIC values are preferred when comparing models fitted to the same dataset. The model with the smallest BIC is usually the best supported.
3. When should I use the RSS method?
Use the RSS method for regression settings where Gaussian error assumptions are reasonable and you have residual sum of squares instead of likelihood output.
4. Can I compare models trained on different datasets?
No. BIC comparisons are meaningful only when models are fitted to the same observations and target variable under comparable assumptions.
5. What does ΔBIC tell me?
ΔBIC shows the gap between two models. Small gaps indicate weak evidence, while larger gaps suggest increasingly stronger preference for the lower BIC model.
6. Why does BIC penalize large parameter counts?
Additional parameters often improve fit mechanically. BIC adds a logarithmic penalty so the model must earn that added complexity through better likelihood.
7. Are BIC weights true probabilities?
They are approximate relative model probabilities under equal priors and comparable candidates. They help rank support, but they are still an approximation.
8. Should I use BIC instead of AIC?
BIC usually favors simpler models more strongly than AIC, especially with large samples. Choose based on your modeling goal and theoretical assumptions.