Advanced AIC and BIC Calculator
Enter two or more candidate models. You can use direct log-likelihood values or RSS values for Gaussian linear model estimates.
Example Data Table
| Model | Method | n | k | Log-Likelihood | RSS | Expected Use |
|---|---|---|---|---|---|---|
| Linear Base | Log-likelihood | 120 | 4 | -142.35 | - | Baseline regression model |
| Linear Extended | Log-likelihood | 120 | 6 | -137.90 | - | Regression with added predictors |
| Gaussian RSS Fit | RSS estimate | 120 | 5 | - | 310.75 | Model reported by residual error |
Formula Used
AIC: AIC = 2k - 2 ln(L)
AICc: AICc = AIC + [2k(k + 1)] / [n - k - 1]
BIC: BIC = k ln(n) - 2 ln(L)
RSS to log-likelihood: ln(L) = -n/2 × [ln(2π) + 1 + ln(RSS/n)]
Delta AIC: Delta AIC = AIC - minimum AIC
Akaike weight: wᵢ = exp(-0.5 × Delta AICᵢ) / Σ exp(-0.5 × Delta AIC)
How to Use This Calculator
- Enter a clear name for each candidate model.
- Select whether you have log-likelihood or RSS values.
- Enter the same sample size used to fit each model.
- Enter the number of estimated parameters for every model.
- Use AICc when sample size is small compared with parameters.
- Press the calculate button and review the ranked result table.
- Use the chart to compare AIC, AICc, and BIC visually.
- Export the final table as CSV or PDF for reporting.
AIC and BIC Model Selection Guide
AIC and BIC Basics
AIC and BIC are model selection scores. They help compare several statistical models. Both start from the log likelihood. Then they add a penalty for complexity. Lower values are usually better. AIC means Akaike Information Criterion. BIC means Bayesian Information Criterion. These measures do not prove truth. They only compare the listed choices.
Why These Scores Matter
Many models can fit the same data. A larger model may fit better by chance. AIC and BIC reduce that risk. They reward good fit. They also punish extra parameters. This makes comparison more disciplined. The scores are useful in regression, forecasting, classification, survival analysis, and general likelihood models.
How AIC Works
AIC uses a lighter penalty. It is often preferred for prediction. It can choose a model with more terms. That can be helpful when future accuracy matters. AICc is a small sample correction. It becomes important when sample size is close to the parameter count. It prevents overconfident model choice.
How BIC Works
BIC uses a stronger penalty. The penalty grows with sample size. It often selects simpler models. It is popular when the goal is explanation. It can be stricter than AIC. With large data, BIC may reject small gains in fit. That makes it useful for parsimonious reporting.
Reading Calculator Results
This calculator ranks every model by AIC and BIC. It also shows delta values. Delta means the difference from the best score. A small delta means close support. Akaike weights convert AIC differences into relative evidence. They help show how strongly one model leads.
Good Input Practice
Use the same response variable for every model. Use the same dataset and sample size where possible. Count all estimated parameters. Include intercepts, variance terms, and shape terms when they are estimated. Do not compare models fitted to different rows unless the design allows it. Check residual plots, assumptions, and subject knowledge before making conclusions.
Common Limits
AIC and BIC depend on the likelihood form. Different software may count parameters differently. Always document the method. Treat the final choice as evidence, not certainty. A simple model can still be wrong. A complex model can still be useful.
FAQs
1. What does a lower AIC mean?
A lower AIC means the model has better relative support among the models compared. It balances fit and complexity. It does not prove the model is correct.
2. What does a lower BIC mean?
A lower BIC suggests a better model under a stronger complexity penalty. BIC often favors simpler models, especially when the sample size is large.
3. Can I compare models with different datasets?
Usually, no. AIC and BIC comparisons are safest when models use the same response variable and the same observations. Different datasets can distort rankings.
4. Should I use AIC or AICc?
Use AICc when the sample size is small relative to the number of parameters. AICc reduces small sample bias and becomes close to AIC with larger samples.
5. Why does BIC penalize more than AIC?
BIC uses k times the natural log of sample size. As sample size grows, this penalty becomes larger than the fixed AIC penalty of two per parameter.
6. What is an Akaike weight?
An Akaike weight shows relative support based on AIC differences. Higher weight means stronger support among the tested models, not absolute truth.
7. How should I count parameters?
Count every estimated term. Include slopes, intercepts, variance estimates, dispersion terms, shape terms, and other fitted constants used by the likelihood.
8. Can RSS be used for AIC and BIC?
Yes, for Gaussian error models, RSS can estimate log-likelihood. The calculator uses a common maximum likelihood approximation based on RSS and sample size.