[R-sig-Geo] kriging question

[Edzer Pebesma]

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

-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster,
Weseler Straße 253, 48151 Münster, Germany.  Phone: +49 251
8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de/