[R-sig-Geo] regression kriging in gstat with skewed distributions

[G. Allegri]

Thank you Tomislav.
I will try the logit transformation, but an interesting evaluation is
to confront the results reached with a normal score transformation.
Wouldn't this one be better suited for a generic transformation
method?
I know that GSLIB already manages it, but in R I don't know how to do
it. qqnorm(ppoints(my_data)) seems to transform, but
back-transormation is not documented.

Giovanni

2008/1/16, Tomislav Hengl <hengl at science.uva.nl>:
>
> Dear Giovanni,
>
> Logit transformation can be automatically applied to any variables which has a lower and upper
> physical limits (e.g. 0-100%). In R, you can transform a variable to logits by e.g.:
>
> > points = read.dbf("points.dbf")
> > points$SANDt = log((points$SAND/100)/(1-(points$SAND/100)))
>
> After you interpolate your variable, you can back-transform the values by using:
>
> > SAND.rk = krige(fsand$call$formula, points[sel,], SPC, sand.rvgm)
>
> > SAND.rk$pred=exp(SAND.rk$var1.pred)/(1+exp(SAND.rk$var1.pred))*100
>
> The prediction variance can not be back-transformed, but you can use the normalized prediction
> variance by dividing it with the sampled variance. See also section 4.2.1 of my lecture notes
> (http://geostat.pedometrics.org/).
>
> There are many transformations that can be applied to force a normality of your target variable (see
> e.g. http://en.wikipedia.org/wiki/Data_transformation_(statistics) ). The most generic
> transformation is to work with the probability density function values (see e.g.
> http://dx.doi.org/10.1016/j.jneumeth.2006.11.004 ), this way you do not have to think about how the
> histogram looks at all. But then the interpretation of the regression plots becomes rather
> difficult.
>
> In any case, you should apply the transformation already to the target variable because also a
> requirement for linear regression is that the residuals are normally distributed around the
> regression line.
>
>
> see also:
> FITTING DISTRIBUTIONS WITH R (by Vito Ricci)
> http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf
>
>
> Tom Hengl
> http://spatial-analyst.net
>
>
> -----Original Message-----
> From: r-sig-geo-bounces at stat.math.ethz.ch [mailto:r-sig-geo-bounces at stat.math.ethz.ch] On Behalf Of
> G. Allegri
> Sent: dinsdag 15 januari 2008 15:28
> To: r-sig-geo at stat.math.ethz.ch
> Subject: [R-sig-Geo] regression kriging in gstat with skewed distributions
>
> I'm trying to realize e regression kriging with gstat package on my
> soil samples data. The response variable (ECe measuere) and covariates
> appear positvely skewed.
> As Tomislav Hengl suggests in its "framework for RK" [1], a logistic
> transformation is proposed as a generic way to reduce the skeweness by
> using the physical limits of the data.
> Is it really a transformation that can be applied in the generic case
> of skewed datas? I mean,in my case I have non-normal residuals (from
> original data regression), and I'm trying to transform the residuals
> (and not the original values) to do SK on them . Is this approach
> correct?
>
> A related question is how to do normal score transformations (for my
> residuals) in R and gstat. I know gstat doesn't manage transformations
> and back-transformations, so it should be done previously in R... but
> I can't find any package that permit it in a straisghtforward way.
> I've found something with qqnorm(ppoints(data)) and the approx()
> function. Is that all?
>
> Giovanni
>
>
> [1] "A generic framework for spatial prediction of soil variables
> based on regressionkriging" Geoderma 122 (1–2), 75–93.
>
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