[R] AIC and significance tests

[Spencer Graves]

	  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
> 
> 
> 
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> David Pleydell
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> Telford Institute of Environmental Systems
> School of Environment and Life Sciences
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