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
_______________________________________________
R-sig-Geo mailing list
R-sig-Geo@stat.math.ethz.ch
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
