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Information criteria. What function fits best ?. The more free parameters a model has the higher will be R 2 . The more parsimonious a model is the lesser is the bias towards type I errors. Explained variance. Bias. The optimal number of model parameters.
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Informationcriteria Whatfunctionfitsbest? Themorefreeparameters a model hasthehigher will be R2. Themoreparsimonious a model isthelesseristhebiastowardstype I errors. Explainedvariance Bias Theoptimalnumber of model parameters We have to find a compromisbetweengoodness of fit and bias! many few Model parameters
The Akaike criterion of model choice k: number of model parameters +1 L: maximum likelihood estimate of the model The preferred model is the one with the lowest AIC. If the parameter errors are normal and independent we get n: number data points RSS: residual sums of squares If we fit using R2: If we fit using c2: At small sample size we should use the following correction
We getthesurprisingresultthattheseeminglyworstfitting model appears to be thepreferred one. A single outliermakesthedifference. The single high residualmakestheexponentialfittingworse
Significantdifferencein model fit ApproximatelyDAIC isstatisticalysignificantinfavor of the model withthesmaller AIC atthe 5% errorbenchmarkif |DAIC| > 2. The last model is not significantly (5% level) different from the second model. AIC model selectionserves to find the bestdescriptor of observedstructure. It is a hypothesisgeneratingmethod. It does not test for significance Model selectionusingsignificancelevelsis a hypothesistestingmethod. Significancelevels and AIC must not be usedtogether.
