Calculator Inputs
Choose a calculation mode for each model. Add several models for ranking and evidence comparison.
Formula Used
BIC = −2 ln(L̂) + k ln(n)
BIC = n ln(RSS / n) + k ln(n)
The RSS form omits constants shared by models. Use identical observations when comparing candidate models.
How to Use
- Choose log-likelihood, raw likelihood, or regression RSS mode.
- Enter the sample size and base parameter count.
- Add intercept or variance parameters when they are estimated.
- Add competing models fitted to the same observations.
- Calculate, then compare BIC, ΔBIC, evidence, and weights.
Example Data
| Model | Mode | n | Base k | Intercept | Input |
|---|---|---|---|---|---|
| Model A | Log-likelihood | 150 | 4 | Yes | −120.5 |
| Model B | Log-likelihood | 150 | 6 | Yes | −115.2 |
| Regression C | RSS | 200 | 5 | Yes | RSS = 425.8 |
Understanding BIC
BIC balances model fit against model complexity. Better fit lowers the first term. Additional parameters increase the penalty.
The preferred model has the lowest BIC. BIC values have no universal standalone meaning. Compare models fitted to the same response data.
BIC penalises extra parameters more strongly as samples grow. It often favours simpler models than AIC. Selection still requires scientific judgement.
BIC Difference Guide
| ΔBIC | Evidence against the model |
|---|---|
| 0 to 2 | Weak evidence |
| More than 2 to 6 | Positive evidence |
| More than 6 to 10 | Strong evidence |
| Above 10 | Very strong evidence |
Frequently Asked Questions
What does a lower BIC mean?
A lower BIC indicates a better balance between fit and complexity among comparable models.
Can BIC be negative?
Yes. Negative BIC values are possible and remain valid for relative comparison.
Should all models use the same sample?
Yes. Reliable comparison usually requires identical observations and the same response definition.
Does the intercept count as a parameter?
Yes, when the intercept is estimated. Activate the intercept option to include it.
Should error variance count in regression?
It often counts when variance is estimated. Follow the convention used by your software.
How does BIC differ from AIC?
BIC uses a sample-size-dependent penalty. AIC uses a fixed penalty of two per parameter.
Can I compare non-nested models?
Yes, provided the models use the same observations, outcome, and likelihood definition.
What are BIC weights?
They normalise approximate relative evidence across the entered candidate model set.
Why can RSS-based BIC differ across software?
Packages may include constants or count parameters differently. Use one convention consistently.