[R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging?

Joelle k. Akram chino_tones at hotmail.com
Wed Nov 22 13:11:00 CET 2017 

Thank you Tom. A couple questions.
1) In your code, you used log1p for computing  zinc.vgm. But log1p is not used when defining trend.l for the krige.control 'KC'. Do we need log1p for the zinc response (dependent) variable when defining trend.l?

2) The exponent back-transform is not applied anywhere after applying log1p for computing the  zinc.vgm variable. Do we need exp anywhere or is it done internally?

3) Do we add half the prediction variance to the 'zinc.uk' variable or does geoR do this internally?

4) Is it more advisable to use likfit instead of variofit and why?

5) A value of 800 is used to initialize likfit. Where is value determined?

appreciated,
Chris

________________________________
From: R-sig-Geo <r-sig-geo-bounces at r-project.org> on behalf of Tomislav Hengl <tom.hengl at gmail.com>
Sent: November 22, 2017 3:58 AM
To: r-sig-geo at r-project.org
Subject: Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging?


Hi Chris,

First of all, I think your back-transformation is not correct since you
need to add half the prediction variance to values as indicated in the
Diggle and Ribeiro (2007) P-61
(https://github.com/thengl/GeoMLA/blob/master/RF_vs_kriging/Diggle_Ribeiro_2007_P61.png

).
Otherwise you underpredict the values and hence the cross-validation
error will be high.

I also do not see much point in using lead and copper as covariates
since they are only available at sampling locations.

For log-normal or not-normal variables I advise using geoR package that
does all the transformations for you (it would be interesting to see if
gstat and geoR give exactly the same numbers if the same transformations
and back-transformations are applied):

R> library(geoR)
--------------------------------------------------------------
   Analysis of Geostatistical Data
   For an Introduction to geoR go to http://www.leg.ufpr.br/geoR
The geoR package - LEG-UFPR<http://www.leg.ufpr.br/geoR>
www.leg.ufpr.br
geoR is a free and open-source package for geostatistical analysis to be used as a add-on to the R system



   geoR version 1.7-5.2 (built on 2016-05-02) is now loaded
--------------------------------------------------------------

R> demo(meuse, echo=FALSE)
R> set.seed(999)
R> sel.d = complete.cases(meuse at data[,c("lead","copper","elev", "dist")])
R> meuse = meuse[sel.d,]
R> meuse.geo <- as.geodata(meuse["zinc"])
R> ## add covariates:
R> meuse.geo$covariate = meuse at data[,c("lead","copper","elev", "dist")]
R> trend = ~ lead+copper+elev+dist
R> zinc.vgm <- likfit(meuse.geo, lambda=0, trend = trend,
ini=c(var(log1p(meuse.geo$data)),800), fix.psiA = FALSE, fix.psiR = FALSE)
---------------------------------------------------------------
likfit: likelihood maximisation using the function optim.
likfit: Use control() to pass additional
           arguments for the maximisation function.
          For further details see documentation for optim.
likfit: It is highly advisable to run this function several
          times with different initial values for the parameters.
[[elided Hotmail spam]]
---------------------------------------------------------------
likfit: end of numerical maximisation.
R> zinc.vgm
likfit: estimated model parameters:
       beta0      beta1      beta2      beta3      beta4      tausq
sigmasq        phi       psiA
"  6.0853" "  0.0033" "  0.0053" " -0.0810" " -0.9805" "  0.0210" "
0.0717" "799.9942" "  0.2619"
        psiR
"  3.9731"
Practical Range with cor=0.05 for asymptotic range: 2396.568

likfit: maximised log-likelihood = -883.4
R> locs2 = meuse at coords
R> KC = krige.control(trend.d = trend, trend.l = ~
meuse$lead+meuse$copper+meuse$elev+meuse$dist, obj.model = zinc.vgm)
R> zinc.uk <- krige.conv(meuse.geo, locations=locs2, krige=KC)
krige.conv: model with mean defined by covariates provided by the user
krige.conv: anisotropy correction performed
krige.conv: performing the Box-Cox data transformation
krige.conv: back-transforming the predicted mean and variance
krige.conv: Kriging performed using global neighbourhood

HTH,

Tom Hengl
http://orcid.org/0000-0002-9921-5129
Tomislav Hengl (0000-0002-9921-5129) - ORCID | Connecting ...<http://orcid.org/0000-0002-9921-5129>
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On 2017-11-22 01:08, Joelle k. Akram wrote:
>
>
>
> down votefavorite<https://stackoverflow.com/questions/47424740/why-is-predictive-error-large-for-universal-kriging#>
[https://cdn.sstatic.net/Sites/stackoverflow/img/apple-touch-icon@2.png?v=73d79a89bded]<https://stackoverflow.com/questions/47424740/why-is-predictive-error-large-for-universal-kriging#>

Why is Predictive error large for Universal Kriging?<https://stackoverflow.com/questions/47424740/why-is-predictive-error-large-for-universal-kriging#>
stackoverflow.com
I am using the Meuse dataset for universal kriging (UK) via the gstat library in R. I am following a strategy used in Machine Learning where data is partioned into a Train set and Hold out set. The...



>
>
> I am using the Meuse dataset for universal kriging (UK) via the gstat library in R. I am following a strategy used in Machine Learning where data is partioned into a Train set and Hold out set. The Train set is used for defining the regressive model and defining the semivariogram.
>
> I employ UK to predict on both the Train sample set, as well as the Hold Out sample set. However, there mean absolute error (MAE) from the predictions of the response variable (i.e., zinc for the Meuse dataset) and actual values are very different. I would expect them to be similar or at least closer. So far I have MAE_training_set = 1 and MAE_holdOut_set = 76.5. My code is below and advice is welcome.
>
> library(sp)
> library(gstat)
> data(meuse)
> dataset= meuse
> set.seed(999)
>
> # Split Meuse Dataset into Training and HoldOut Sample datasets
> Training_ids <- sample(seq_len(nrow(dataset)), size = (0.7* nrow(dataset)))
>
> Training_sample = dataset[Training_ids,]
> Holdout_sample_allvars = dataset[-Training_ids,]
>
> holdoutvars_df <-(dataset[,which(names(dataset) %in% c("x","y","lead","copper","elev","dist"))])
> Hold_out_sample = holdoutvars_df[-Training_ids,]
>
> coordinates(Training_sample) <- c('x','y')
> coordinates(Hold_out_sample) <- c('x','y')
>
> # Semivariogram modeling
> m1  <- variogram(log(zinc)~lead+copper+elev+dist, Training_sample)
> m <- vgm("Exp")
> m <- fit.variogram(m1, m)
>
>
> # Apply Univ Krig to Training dataset
> prediction_training_data <- krige(log(zinc)~lead+copper+elev+dist, Training_sample, Training_sample, model = m)
> prediction_training_data <- expm1(prediction_training_data$var1.pred)
>
> # Apply Univ Krig to Hold Out dataset
> prediction_holdout_data <- krige(log(zinc)~lead+copper+elev+dist, Training_sample, Hold_out_sample, model = m)
> prediction_holdout_data <- expm1(prediction_holdout_data$var1.pred)
>
> # Computing Predictive errors for Training and Hold Out samples respectively
> training_prediction_error_term <- Training_sample$zinc - prediction_training_data
> holdout_prediction_error_term <- Holdout_sample_allvars$zinc - prediction_holdout_data
>
>
>
> # Function that returns Mean Absolute Error
> mae <- function(error)
> {
>    mean(abs(error))
> }
>
> # Mean Absolute Error metric :
> # UK Predictive errors for Training sample set , and UK Predictive Errors for HoldOut sample set
> print(mae(training_prediction_error_term)) #Error for Training sample set
> print(mae(holdout_prediction_error_term)) #Error for Hold out sample set
>
>
> cheers,
>
> Kristopher (Chris)
>
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>
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