Informationkriterier

Informationkriterier, or information criteria, are statistical measures used to compare and select among competing models by balancing goodness of fit with model complexity. They yield relative scores that help identify models likely to generalize to new data rather than merely fitting the sample at hand.

The best known information criteria include the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). In their common forms, AIC = -2 log-likelihood + 2k and BIC = -2 log-likelihood + k log(n), where k is the number of estimated parameters and n is the sample size. AICc is a small-sample correction of AIC. Other criteria, such as the Hannan–Quinn criterion, provide alternative penalty structures. In Bayesian settings, the Deviance Information Criterion (DIC) is used to compare models.

Interpretation of these criteria is relative: for a given data set, models with lower criterion values are preferred under that criterion, reflecting a better trade-off between fit and complexity. Information criteria do not measure absolute goodness of fit; they depend on the chosen likelihood model and the set of candidate models being compared. They are commonly used in regression, time-series analysis, econometrics, and other areas involving likelihood-based estimation.

Assumptions and limitations include the need for a plausible likelihood specification and comparable models. Criteria can be sensitive to sample size and the penalty scheme, which may lead to different model choices. In small samples, corrected forms like AICc are recommended. Results from information criteria are often complemented by cross-validation or out-of-sample testing to assess predictive performance.