Akaike Information Criterion Calculator

Model comparison results

Lower criterion values indicate stronger relative support.

Rank	Model	k	Log-likelihood	AIC	AICc	BIC	Delta	Weight	Cumulative	Evidence ratio	Support

Evidence ratio numerator

Evidence ratio denominator

Selected ratio

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Copy-ready summary

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Calculator inputs

Add models fitted to the same response and observations.

Calculation mode

Ranking criterion

Decimal places

Sort results

Number format

Example set

Competing models

Model name	Model type	Dataset	Response	Observations n	Parameters k	Log-likelihood	Actions

Parameter-count assistant

Choose a model, then estimate its total parameter count.

Preset

Predictors

Variance terms

Covariance terms

Other parameters

Include intercept or drift

Include dispersion parameter

Include residual variance

Include estimated hyperparameters

ARIMA and seasonal terms

Seasonal period

Exogenous regressors

Formula used

Standard AIC
AIC = 2k − 2 ln(L) = 2k − 2LL

Small-sample correction
AICc = AIC + [2k(k + 1)] ÷ (n − k − 1)

Bayesian information criterion
BIC = k ln(n) − 2LL

Regression form
AIC = n ln(RSS ÷ n) + 2k

Delta value
Δi = ICi − ICmin

Akaike weight
wi = exp(−Δi ÷ 2) ÷ Σ exp(−Δr ÷ 2)

How to use

Select the input mode that matches your model output.
Add every model fitted to the same dataset.
Enter observations, parameter counts, and criterion inputs.
Use the parameter assistant when counting estimated terms.
Choose AIC, AICc, or BIC for ranking.
Calculate, review warnings, then export the comparison.

Example data

Model	n	k	Log-likelihood	Purpose
Linear base	120	4	−181.40	Reference model
Linear interaction	120	6	−177.85	Tests extra interaction terms
Linear compact	120	3	−184.10	Tests a simpler specification

Interpretation guide

Delta 0–2

Strong support

The model remains highly competitive.

Delta 4–7

Less support

Evidence declines against the leading model.

Delta above 10

Very little support

The model is usually not competitive.

These bands are practical guidelines. They are not absolute decision rules.

Important comparison rules

Use the same response variable for every model.
Use the same observations and missing-data treatment.
Use comparable likelihood definitions and constants.
Prefer maximum-likelihood estimates for direct AIC comparison.
Count every estimated parameter consistently across models.
Do not treat AIC as absolute goodness-of-fit.

Frequently asked questions

Why is a lower AIC preferred?

A lower value reflects a better fit-complexity tradeoff. It is only meaningful relative to competing models.

When should AICc replace AIC?

AICc is useful when the sample is not large. The correction grows when n approaches k.

Does k include the intercept?

Usually yes when the intercept is estimated. Variance and dispersion terms may also count.

Can AIC values be negative?

Yes. The absolute sign does not matter. Differences between comparable models drive interpretation.

What does an Akaike weight mean?

It measures relative support inside the candidate set. Weights across valid models sum to one.

How is BIC different?

BIC penalizes complexity using ln(n). It often favors simpler models as samples grow.

Can I compare different datasets?

No. Different observations change likelihood scales. Use identical data for a defensible comparison.

Why is AICc sometimes unavailable?

Its denominator requires n greater than k plus one. Otherwise the correction is undefined.

Does the best AIC guarantee good predictions?

No. It ranks candidate models. External validation still matters for predictive performance.