AIC and BIC Calculator

Estimate AIC and BIC with clear statistical model inputs. Compare candidates, penalties, and fit strength. Export results for simple model selection records and reviews today.

Enter Model Values

Model 1

Model 2

Model 3

Example Data Table

Model Log Likelihood Parameters k Sample Size n Expected AIC Expected BIC
Model A -124.60 4 120 257.20 268.35
Model B -119.40 7 120 252.80 272.31
Model C -122.15 5 120 254.30 268.24

Formula Used

AIC = 2k - 2ln(L)

BIC = kln(n) - 2ln(L)

AICc = AIC + [2k(k + 1) / (n - k - 1)]

Here, k is the number of estimated parameters. L is likelihood. n is sample size. Lower AIC and BIC values usually indicate stronger model support.

How to Use This Calculator

  1. Enter a clear name for each model.
  2. Add the model log likelihood value.
  3. Enter the number of estimated parameters.
  4. Enter the sample size used for fitting.
  5. Press Calculate to compare the models.
  6. Review AIC, BIC, deltas, weights, and ratios.
  7. Download the CSV or PDF report when needed.

Understanding AIC and BIC

AIC and BIC help compare statistical models. They do not prove one model is true. They show which model has stronger support within a chosen set. Lower values usually mean a better balance between fit and complexity.

AIC means Akaike Information Criterion. It rewards fit and penalizes extra parameters. It often works well when prediction is the main goal. It can favor flexible models when the sample is small.

BIC means Bayesian Information Criterion. It uses a stronger penalty as sample size grows. It often favors simpler models. It is useful when you want a compact explanation.

Why This Calculator Helps

Manual model comparison can be very slow. Each model needs a log likelihood, parameter count, and sample size. This calculator applies both formulas instantly. It also finds delta values, evidence ratios, and Akaike weights. These values make the comparison clearer.

Delta values show distance from the best model. A delta near zero means strong support. Larger deltas suggest weaker support. Akaike weights estimate relative support under the AIC set.

Good Inputs Matter

Use the same dataset for every model. Do not compare models fitted on different sample sizes unless the reason is clear. Keep the likelihood method consistent. Mixing methods can make the ranking misleading.

Count every estimated parameter. Include intercepts, variance terms, and shape terms when they are estimated. A wrong parameter count changes the penalty. That can change the final ranking.

Interpreting Results

The smallest AIC model is best by AIC. The smallest BIC model is best by BIC. Sometimes both criteria agree. When they disagree, review the project goal. AIC can suit prediction. BIC can suit parsimony.

Use this tool as a guide. Also inspect residuals, assumptions, diagnostics, and domain knowledge. A model with the lowest score can still be poor. Strong modeling requires both numbers and judgment.

Reporting Tips

Report the model name, log likelihood, k, n, AIC, BIC, and deltas. Include weights when using AIC. Explain why the selected model fits the study goal. Keep the comparison table with your records.

The CSV file is useful for spreadsheets. The PDF file is useful for reports. Both exports save the calculated results. That makes the selection process easier to review later.

FAQs

What is AIC?

AIC is a model comparison score. It balances model fit against the number of parameters. Lower AIC values usually indicate a better supported model within the tested group.

What is BIC?

BIC is another model comparison score. It uses sample size in the penalty term. It often favors simpler models more strongly than AIC.

Should I choose the lowest score?

Usually, yes. The model with the lowest AIC or BIC is preferred under that criterion. Still, you should also check assumptions, diagnostics, and practical meaning.

Why do AIC and BIC disagree?

They penalize complexity differently. AIC often supports predictive flexibility. BIC often supports simpler structure. Choose based on your modeling goal.

What is log likelihood?

Log likelihood measures how well a fitted model explains observed data. Higher log likelihood means better fit before applying complexity penalties.

What is parameter count k?

k is the number of estimated model parameters. Include intercepts, slopes, variance terms, and other estimated values when they apply.

What is AICc?

AICc is a corrected AIC for smaller samples. It adds extra penalty when sample size is limited compared with parameter count.

Can I compare unrelated datasets?

No. AIC and BIC comparisons should use models fitted to the same response data. Different datasets can make the scores misleading.

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