Model Selection AIC Calculator

Enter Model Inputs

Provide at least two candidate models. Use total estimated parameters and maximized log-likelihood values from the same dataset.

How to Use This Calculator

1. Enter the sample size if you want corrected AIC values for smaller datasets.
2. Add each model name exactly as you want it displayed in the ranking table.
3. Provide the number of estimated parameters for each candidate model.
4. Enter the maximized log-likelihood from fitting each model to the same data.
5. Press Submit to rank models by AIC and review weights, delta AIC, and support labels.
6. Use the CSV or PDF buttons to export the result table for reporting.

Professional Notes

Interpreting Relative Fit Across Candidate Models

AIC compares candidate models by balancing fit and complexity. In the example table, the cubic model has AIC 244.50, the lowest score among four options. It outperforms the quadratic model at 245.82, the spline model at 245.66, and the linear model at 258.88. Lower values indicate better expected information retention when models are fitted to the same response data for predictive use in practical modelling workflows today.

Understanding Delta AIC Thresholds in Practice

Delta AIC makes raw scores easier to interpret. Using the sample values, the cubic model has delta 0.00, spline 1.16, quadratic 1.32, and linear 14.38. Models within 2 units usually remain credible competitors. Values beyond 10 normally indicate weak support. This simple scale helps analysts judge whether a leading model wins narrowly or dominates the candidate set.

Why Parameter Penalties Improve Selection Quality

The penalty term matters because extra parameters can improve likelihood by chasing noise. AIC adds 2k to discourage unnecessary flexibility. In practice, this protects comparisons involving polynomial terms, interaction effects, or nonlinear expansions. If two models fit almost equally well, the one using fewer parameters often ranks higher because it offers a stronger balance between description and parsimony.

When Corrected AIC Becomes More Important

Corrected AIC, or AICc, becomes important when sample size is not large relative to model size. The correction grows as n approaches k plus 1, reducing optimism toward complex specifications. Analysts working with short time series, pilot studies, or restricted experimental samples should inspect AICc carefully. A changed ranking after correction often signals that the richer model demands more information than the data provide.

Using Akaike Weights for Decision Communication

Akaike weights convert score differences into relative support that sums to 1.00. This makes reporting easier. Instead of naming only one winning model, teams can show how support is distributed across alternatives. Evidence ratios go further by indicating how many times less supported a competing model is. These outputs are useful in forecasting, credit analysis, and scientific reporting where uncertainty must be communicated clearly.

Combining Information Criteria with Expert Review

Good selection practice combines information criteria with diagnostics and subject knowledge. The best numerical model may still be unsuitable if residual patterns remain structured or parameters lack meaning. Use this calculator to rank models quickly, then verify assumptions before adoption. That workflow produces choices that are statistically efficient, interpretable, and easier to defend in research, engineering, and business decision settings.

FAQs