Back-transformation of Beta in geoR

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Back-transformation of Beta in geoR

Ruben Roa
Hi:

I am interested in back-transforming the mle of parameter Beta
and its variance when the Lambda parameter of the Box-Cox
transformation has been estimated and its estimate is not 0 nor
0.5.
Is this back-transformation equivalent to simply averaging over
a fine grid inside the polygon containing the predictions of, say
krige.conv (given that geoR back-transform when kriging=
predicting)?
For example
>alpha<-sum(krig.object$pred)/N
>salpha<-sum(sqrt(krig.object$krige.var))/N
where krig.object has been obtained by using a likfit
object as argument in krige.control, and N is the number of nodes
in the grid (a big number).
The questions are,
1) is alpha aproximately equal to the back-
transformation of the mle of Beta?
2) is salpha aproximately equal to the 'standard
error' of the back-transformation of the mle of Beta?

Ruben



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Back-transformation of Beta in geoR

Ole F. Christensen
Dear Ruben

You don't want to do kriging here.

I think the most simple solution is to this by simulation. Implicitly
you are saying that beta is one-dimensional.
You will find the mean and variance of the beta parameter from the
output from the likfit function.

mean(BCtransform(rnorm(2000, mean=outfromlikfit$beta,
sd=sqrt(outfromlikfit$beta.var)),lambda = 0.72, inverse = TRUE))

gives what you want.

Ole


Ruben Roa wrote:

>Hi:
>
>I am interested in back-transforming the mle of parameter Beta
>and its variance when the Lambda parameter of the Box-Cox
>transformation has been estimated and its estimate is not 0 nor
>0.5.
>Is this back-transformation equivalent to simply averaging over
>a fine grid inside the polygon containing the predictions of, say
>krige.conv (given that geoR back-transform when kriging=
>predicting)?
>For example
>  
>
>>alpha<-sum(krig.object$pred)/N
>>salpha<-sum(sqrt(krig.object$krige.var))/N
>>    
>>
>where krig.object has been obtained by using a likfit
>object as argument in krige.control, and N is the number of nodes
>in the grid (a big number).
>The questions are,
>1) is alpha aproximately equal to the back-
>transformation of the mle of Beta?
>2) is salpha aproximately equal to the 'standard
>error' of the back-transformation of the mle of Beta?
>
>Ruben
>
>_______________________________________________
>R-sig-Geo mailing list
>R-sig-Geo at stat.math.ethz.ch
>https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>
>  
>

--
Ole F. Christensen
BiRC - Bioinformatics Research Center
University of Aarhus