[R-sig-Geo] kriging question

[Dave Depew]

Thanks Edzer,

I've requested Cressie's book from our library (just waiting on it).
My main concern was the many 0 counts. I also was not enthusiastic about 
odd transformations which then require appropriate back-transforms (I 
imagine the back transform of the kriging variance gets messy)

I've tried several linear and non-linear combinations....they all do not 
improve on predictions generated by using OK with the untransformed 
data. I am confident that the resultant grid outputs do capture the 
spatial structure quite well. I've also tried a 10 fold cross validation 
of the kriging model - this seems to give reasonable estimates for mean 
error, mean squared prediction error and mean square normalized error. I 
had interpreted this that the variogram model chosen was doing a 
reasonable job.

Edzer Pebesma wrote:
> Hi Dave,
>
> Dave Depew wrote:
>> Hi all,
>> A question for the more experienced geostats users....
>>
>> I have a data set containing 2-3 variables relating to submerged 
>> plant characteristics inferred from acoustic survey.
>> The distribution of the % cover variable is bounded (0-100) and 
>> highly left skewed (many 0's). The transect spacing is quite even, 
>> and I can't seem to notice much difference between a run of ordinary 
>> kriging and a variant of RK using a zeroinflated glm of the %cover 
>> residuals.
>> None of the other co-variates show much correlation with the data 
>> (i.e. bottom depth, x and y). Is this a possible reason why OK and RK 
>> seem to give more or less the same predictions?
> Well, yes, if there's not much of a trend, then RK will essentially 
> simplify to OK.
>>
>> my second question relates to transformation of the target 
>> variable...in this case zero inflated distributions are difficult to 
>> transform. Is it really a requirement of kriging that the data be 
>> transformed? or just that it will generally perform better with a 
>> target variable with a distribution close to normal?
>>
> I believe the argument is along the following lines: kriging is the 
> BLUP in any case, but in case the data are normally distributed 
> (around the trend), the BLUP (or more exactly the BLP, simple kriging) 
> coincides with the conditional expectation, making it the best 
> possible predictor. In other cases, meaning when data are not normally 
> distributed, it is still the best linear predictor, but it may very 
> well be that there are other, better, non-linear predictors that give 
> a result much closer to the best predictor under those circumstances.
>
> If there is a transformation for that data that makes them 
> multivariate Gaussian, then transforming and kriging on that scale is 
> the way to go. A catch that has gotten very little attention is that 
> transformation typically looks at marginal distributions, and not at 
> multivariate distributions, the latter being pretty hard to check with 
> only one realisation of the random field.
>
> Cressie's book is a good source to read this stuff; I've lost my copy 
> when I moved jobs in the spring.
> -- 
> Edzer
>