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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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Themorefreeparameters a model hasthehigher will be R2.

Themoreparsimonious a model isthelesseristhebiastowardstype I errors.



Theoptimalnumber of model parameters

We have to find a compromisbetweengoodness of fit and bias!



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.