Calculator Inputs
Example Data Table
These values show how several stored estimates can be compared after running multiple models.
| Model | Log Likelihood | Parameters | Observations | Approximate BIC | Stata Style Note |
|---|---|---|---|---|---|
| Base predictors | -152.44 | 4 | 180 | 325.65 | Smaller model with fewer terms |
| Expanded predictors | -148.90 | 6 | 180 | 328.96 | Better fit, larger penalty |
| Full interaction model | -147.30 | 8 | 180 | 336.15 | More terms may overfit |
Formula Used
BIC: BIC = -2 × ln(L) + k × ln(N)
AIC: AIC = -2 × ln(L) + 2k
AICc: AICc = AIC + [2k(k + 1)] / [N - k - 1]
HQIC: HQIC = -2 × ln(L) + 2k × ln(ln(N))
CAIC: CAIC = -2 × ln(L) + k × [ln(N) + 1]
Delta BIC: Delta BIC = Model BIC - Lowest BIC
BIC Weight: exp(-0.5 × Delta BIC) / sum of all model likelihood weights
The calculator follows the common information criterion approach used when comparing stored statistical models. Lower BIC usually means the model balances fit and complexity better. The parameter count should include all estimated free parameters. Use the same sample size rule across models whenever possible.
How to Use This Calculator
- Run each model in your statistical workflow.
- Record the model log likelihood, parameter count, and observations.
- Enter each model into a separate card.
- Select log likelihood mode for values like
e(ll). - Select deviance mode if you already have
-2LL. - Press the calculate button.
- Review the model with the lowest BIC.
- Export the result as CSV or PDF.
In Stata, users often store estimates, run several candidate models, and inspect information criteria. This page helps reproduce that comparison when values are copied into a web form.
Article: Comparing Multiple Models With BIC
Why BIC Matters
Bayesian Information Criterion is useful when several statistical models explain the same outcome. It rewards good fit. It also penalizes extra parameters. That balance is important. A complex model can fit sample data very well. Yet it may perform poorly on new data. BIC helps reduce that risk.
Using It With Stored Models
Many analysts estimate a base model first. Then they add predictors, interactions, controls, or nonlinear terms. Each version has a log likelihood. Each version also has a parameter count. BIC combines those values with the sample size. The lowest value is usually preferred. This does not prove the model is true. It only gives a disciplined comparison.
Interpreting Delta Values
Delta BIC shows the distance from the best model. A delta near zero means the model is competitive. A value above six suggests stronger separation. A value above ten often indicates clear support for the lower BIC model. BIC weights convert those differences into relative support. They are helpful when reporting several close candidates.
Good Practice
Compare models fitted to the same dependent variable. Keep the sample consistent when possible. Count parameters carefully. Include intercepts and distribution parameters when they are estimated. Do not choose a model by BIC alone. Check theory, diagnostics, residual patterns, and prediction goals. A smaller BIC is helpful. A meaningful model is still required.
Reporting Results
Reports should list model names, log likelihoods, parameters, observations, and BIC values. Ranking the table makes the comparison easier. Add delta BIC for clarity. Mention the preferred model plainly. If two models are close, explain why the final choice is reasonable. That makes the selection transparent and easier to audit.
FAQs
1. What does BIC compare?
BIC compares candidate models that are fitted to related data. It uses model fit, parameter count, and sample size. The lower value usually indicates the preferred model.
2. Is lower BIC always better?
Lower BIC is preferred within the tested model set. Still, you should also check diagnostics, assumptions, subject knowledge, and whether the model answers the research question.
3. What is k in the formula?
The value k is the number of estimated parameters. It should include free coefficients and other estimated terms that affect model complexity.
4. Can models have different sample sizes?
They can, but comparisons are cleaner when models use the same observations. Different samples may change the meaning of the comparison.
5. What is Delta BIC?
Delta BIC is the difference between one model's BIC and the lowest BIC. Smaller delta values mean stronger competitive support.
6. What are BIC weights?
BIC weights give relative support across the candidate model set. They are based on transformed delta BIC values and sum to one.
7. Should I use AIC or BIC?
AIC often favors prediction and can select larger models. BIC applies a stronger sample-size penalty and often favors simpler models.
8. Can I export the comparison?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for a clean report copy of the calculated model table.