[R-sig-Geo] INterpretation of AIC

[Roger Bivand]

On Fri, 11 Apr 2014, Bastien Ferland-Raymond wrote:

> Hello,
>
> I'm not familliar with SAR and CAR model, but smaller AIC is better than
> larger AIC.  The important thing here is to have the same Y vector (which
> you have)
>
> See the Burnham and Anderson's book for a full, well explained explanation
> on AIC:
> Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel
> Inference: A Practical Information-Theoretic Approach (2nd ed.),
> Springer-Verlag,

I don't have this reference, but doubt that it covers this case. The 
underlying issue is connected to the way in which the spatial weights 
matrix enters the CAR and SAR models, and whether the underlying model is 
well specified with regard to the spatial processes in Y and X. At face 
value the difference in AIC might seem to point to SAR, but if all the 
models are misspecified, you are still not very much further forward. 
Waller and Gotway link their discussion (2004) to weighted OLS, weighted 
SAR and weighted CAR, where using weights to pick up variability between 
observation units turns out to remove the residual spatial 
autocorrelation.

Roger

>
>
> Bastien
>
>
>
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-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 91 00
e-mail: Roger.Bivand at nhh.no