[R] AIC and significance tests
Spencer Graves
spencer.graves at pdf.com
Thu Sep 4 14:42:06 CEST 2003
2*log(likelihood ratio) is approximately chi-square for nested
models. AIC = (-2)*(log(likelihood)-k), where k = number of parameters
in the model.
Thus, del(AIC) = 2*(log(likelihood ratio)-del(k)). If the trend is
strictly linear, then it involves only 1 parameter, so del(k) = 1. Then
log(likelihood ratio) = 1+0.5*(156.7-148.6) = 1+0.5*8.1 = 5.05. From
this, a significance probability (p value) can be obtained as follows:
> pchisq(5.05, 1, lower.tail=FALSE)
[1] 0.02462594
For more information, see, e.g., Burnham and Anderson (2002) Model
Selection and Multi-Model Inference, 2nd ed. (Springer) or Ripley (1996)
Pattern Recognition and Neural Networks (Cambridge U. Pr.). Also,
www.r-project.org -> search -> "R site search" for "Burnham and Anderson".
hope this helps. spencer graves
David Richard John Pleydell wrote:
> Hi
> I have two geostatistical models from geoR. An ordinary kriging model
> with AIC=-148.6 and a universal kriging model with AIC=-156.7, there are
> 345 data points. The improvement shown by the AIC by adding a trend
> component to the model seems quite small given the number of data
> points, is there a test to see if the improvement to the model fit is
> significant?
>
> Thanks
> David
>
>
>
> ************************************************
> David Pleydell
> D 31 Peel Building
> Telford Institute of Environmental Systems
> School of Environment and Life Sciences
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>
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