Let try spm and see what we can achieve. All these scripts were directly modified from examples in spm.

> rfcv1 <- RFcv(meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL") # I used the same predictors in the same order as in your model for comparison purpose.

> rfcv1 <- rfokcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")

[1] 42.22274 # This one further improved the accuracy in comparison with that for RF

> rfcv1 <- rfidwcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")

You may try rfcv1$vecv for each method and see how accurate the models are.

I guess the results speak loudly what should be used.

To: Joelle k. Akram;

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

Any type of kriging is a convex predictor which means that predictions at sampling locations will exactly match measured numbers. That is why you get MAE_train = 0.

The actual MAE of your predictions is 85.9. This is not that bad considering that the range of values is: 113-1839. If your repeat the CV process e.g. 10 times you will get a more stable estimate of MAE. Even more interesting is the simple mean error (ME) which tells you whether there are over-estimation or under-estimation problem. Also plotting observed vs predicted (as in

gives you graphical idea if there are any problems with your model.

On 2017-11-22 21:34, Joelle k. Akram wrote:

> Hi Tom,

>

>

> I tried splitting the data into 'training' set and a 'holdout' sample

> set as in my original post. I seem to be getting consistent results,

> i.e., a large predictive difference in terms of MAE between both sets.

> The MAE_train =0.0000000000001165816 and MAE_holdOut = 85.91126. In my

> opinion, this significant difference is an indication of over-fitting

> on the training sample set for the semi-variogram modeling. The code

> is below. Any of your insights are welcome.

>

>

> demo(meuse, echo=FALSE)

> set.seed(999)

> sel.d = complete.cases(meuse@data[,c("lead","copper","elev",

> "dist")])

> meuse = meuse[sel.d,]

> Training_ids <- sample(seq_len(nrow(meuse)), size = (0.7*

> nrow(meuse)))

> Training_sample = meuse[Training_ids,]

> Holdout_sample = meuse[-Training_ids,]

> # Generate VGM using Training set

> Training_sample.geo <- as.geodata(Training_sample["zinc"])

> ## add covariates:

> Training_sample.geo$covariate =

> Training_sample@data[,c("lead","copper","elev", "dist")] trend = ~

> lead+copper+elev+dist

> zinc.vgm <- likfit(Training_sample.geo, lambda=0, trend = trend,

>

> ini=c(var(log1p(Training_sample.geo$data)),800),

> fix.psiA = FALSE, fix.psiR = FALSE)

>

> # do prediction for locations in Training set

> locs2 = Training_sample@coords

> KC = krige.control(trend.d = trend, trend.l = ~

> Training_sample$lead+Training_sample$copper+

> Training_sample$elev+Training_sample$dist,

> obj.model = zinc.vgm)

> zinc_train <- krige.conv(Training_sample.geo, locations=locs2,

> krige=KC)

> # do prediction for new locations in Hold-Out sample set

> newlocs2 = Holdout_sample@coords

> KC2 = krige.control(trend.d = trend, trend.l = ~

> Holdout_sample$lead+Holdout_sample$copper+

> Holdout_sample$elev+Holdout_sample$dist,

> obj.model = zinc.vgm)

> zinc_holdout <- krige.conv(Training_sample.geo, locations=newlocs2,

> krige=KC2)

> # Computing Predictive errors for Training and Hold Out samples

> respectively

> training_prediction_error_term <- Training_sample$zinc -

> zinc_train$predict

> holdout_prediction_error_term <- Holdout_sample$zinc -

> zinc_holdout$predict

>

> # 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

>

>

>

>

> ----------------------------------------------------------------------

> --

> *From:* Tomislav Hengl <

[hidden email]>

> *Sent:* November 22, 2017 8:17 AM

> *To:* Joelle k. Akram;

[hidden email]
> *Subject:* Re: [R-sig-Geo] Fw: Why is there a large predictive

> difference for Univ. Kriging?

>

> On 2017-11-22 13:11, Joelle k. Akram wrote:

>>

>> 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?

>

> Log-transformation in linkfit is defined by setting "lambda=0". I know

> it is a very cryptic package but it has all you need - transformation,

> back-transformation, REML fitting of variograms, trend components etc etc.

>

>>

>> 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?

>

> It is done internally.

>

>>

>> 3) Do we add half the prediction variance to the 'zinc.uk' variable

>> or does geoR do this internally?

>

> It is done internally see:

> "krige.conv: performing the Box-Cox data transformation

> krige.conv: back-transforming the predicted mean and variance"

>

>>

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

>

> likfit has probably more options for variogram modelling (these could

> get quite computational and I think fitting vgms with >>1000 geoR is

> not recommended, while in gstat it is still doable), but it could be a

> matter of taste.

>

>>

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

>

> Arbitrary initial parameter. It does not have to be very accurate.

>

>>

>> appreciated,

>> Chris

>>

>> ---------------------------------------------------------------------

>> ---

>> *From:* R-sig-Geo <

[hidden email]> on behalf of

>> Tomislav Hengl <

[hidden email]>

>> *Sent:* November 22, 2017 3:58 AM

>> *To:*

[hidden email]
>> *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_Ri>> beiro_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 <

http://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@data[,c("lead","copper","elev",

>> R> "dist")]) meuse = meuse[sel.d,] meuse.geo <-

>> R> as.geodata(meuse["zinc"]) ## add covariates:

>> R> meuse.geo$covariate = meuse@data[,c("lead","copper","elev",

>> R> "dist")] trend = ~ lead+copper+elev+dist zinc.vgm <-

>> R> 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.

>> likfit: WARNING: This step can be time demanding!

>> ---------------------------------------------------------------

>> 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@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>

>> orcid.org

>> Your use of the Registry and the results of your search are subject

>> to ORCID's Terms and Conditions of Use

>>

>>

>>

>>

>>

>> On 2017-11-22 01:08, Joelle k. Akram wrote:

>>>

>>>

>>>

>>> down

>>> votefavorite<

https://stackoverflow.com/questions/47424740/why-is-pre>>> dictive-error-large-for-universal-kriging#>

>

>>

>> <

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)

>>>

>>> [[alternative HTML version deleted]]

>>>

>>> _______________________________________________

>>> R-sig-Geo mailing list

>>>

[hidden email]
>>>

https://stat.ethz.ch/mailman/listinfo/r-sig-geo>> R-sig-Geo Info Page - SfS – Seminar for Statistics | ETH ...

>> <

https://stat.ethz.ch/mailman/listinfo/r-sig-geo>

>> stat.ethz.ch

>> A mailing list for discussing the development and use of R functions

>> and packages for handling and analysis of spatial, and particularly

>> geographical, data.

>>

>>

>>

>>>

>>

>> _______________________________________________

>> R-sig-Geo mailing list

>>

[hidden email]
>>

https://stat.ethz.ch/mailman/listinfo/r-sig-geo>> R-sig-Geo Info Page - SfS – Seminar for Statistics | ETH ...

>> <

https://stat.ethz.ch/mailman/listinfo/r-sig-geo>

>> stat.ethz.ch

>> A mailing list for discussing the development and use of R functions

>> and packages for handling and analysis of spatial, and particularly

>> geographical, data.

>>

>>

>>

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