Re: [DKIM] Re: Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

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Re: [DKIM] Re: Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

Li Jin
Let try spm and see what we can achieve. All these scripts were directly modified from examples in spm.
> library(spm)
> library(sp)
> library(gstat)
> data(meuse)

> set.seed(999)
> 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$mae
[1] 53.54404 # This much lower than that for KED

> set.seed(999)
> rfcv1 <- rfokcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.22274 # This one further improved the accuracy in comparison with that for RF

> set.seed(999)
> rfcv1 <- rfidwcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.60406 # This one is similar to RFOK

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.

-----Original Message-----
From: R-sig-Geo [mailto:[hidden email]] On Behalf Of Tomislav Hengl
Sent: Thursday, 23 November 2017 8:42 AM
To: Joelle k. Akram; [hidden email]
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
http://gsif.isric.org/lib/exe/detail.php/wiki:xyplot_predicted_vs_observerd_edgeroi.png?id=wiki%3Asoilmapping_using_mla)
gives you graphical idea if there are any problems with your model.

HTH

Tom Hengl



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
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>> 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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Re: [DKIM] Re: Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

Joelle k. Akram
Jin,

Is there any to get the variances of the predictions in spm?



________________________________
From: Li Jin <[hidden email]>
Sent: November 22, 2017 3:28 PM
To: Tomislav Hengl; Joelle k. Akram; [hidden email]
Subject: RE: [DKIM] Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

Let try spm and see what we can achieve. All these scripts were directly modified from examples in spm.
> library(spm)
> library(sp)
> library(gstat)
> data(meuse)

> set.seed(999)
> 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$mae
[1] 53.54404 # This much lower than that for KED

> set.seed(999)
> rfcv1 <- rfokcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.22274 # This one further improved the accuracy in comparison with that for RF

> set.seed(999)
> rfcv1 <- rfidwcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.60406 # This one is similar to RFOK

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.

-----Original Message-----
From: R-sig-Geo [mailto:[hidden email]] On Behalf Of Tomislav Hengl
Sent: Thursday, 23 November 2017 8:42 AM
To: Joelle k. Akram; [hidden email]
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
http://gsif.isric.org/lib/exe/detail.php/wiki:xyplot_predicted_vs_observerd_edgeroi.png?id=wiki%3Asoilmapping_using_mla)
gives you graphical idea if there are any problems with your model.

HTH

Tom Hengl



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> <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.
[[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@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
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>> 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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Re: [DKIM] Re: Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

Li Jin
In reply to this post by Li Jin
That is something I am still working on.

Variances of the predictions by spatial predictive models are not well defined yet, and they are many ways to do this but none of them is satisfactory. Although people may argue that kriging methods can produce such variance, kriging variance in fact does not reflect the uncertainty expected. Please see Goovaerts 1997 'Geostatistics for Natural Resources Evaluation' for details, or simply see my review 'A Review of Spatial Interpolation Methods for Environmental Scientists' for a short explanation.

From: Joelle k. Akram [mailto:[hidden email]]
Sent: Thursday, 23 November 2017 10:01 AM
To: Li Jin; Tomislav Hengl; [hidden email]
Subject: [DKIM] Re: [DKIM] Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]


Jin,

Is there any to get the variances of the predictions in spm?



________________________________
From: Li Jin <[hidden email]<mailto:[hidden email]>>
Sent: November 22, 2017 3:28 PM
To: Tomislav Hengl; Joelle k. Akram; [hidden email]<mailto:[hidden email]>
Subject: RE: [DKIM] Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

Let try spm and see what we can achieve. All these scripts were directly modified from examples in spm.
> library(spm)
> library(sp)
> library(gstat)
> data(meuse)

> set.seed(999)
> 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$mae
[1] 53.54404 # This much lower than that for KED

> set.seed(999)
> rfcv1 <- rfokcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.22274 # This one further improved the accuracy in comparison with that for RF

> set.seed(999)
> rfcv1 <- rfidwcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.60406 # This one is similar to RFOK

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.

-----Original Message-----
From: R-sig-Geo [mailto:[hidden email]] On Behalf Of Tomislav Hengl
Sent: Thursday, 23 November 2017 8:42 AM
To: Joelle k. Akram; [hidden email]<mailto:[hidden email]>
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
http://gsif.isric.org/lib/exe/detail.php/wiki:xyplot_predicted_vs_observerd_edgeroi.png?id=wiki%3Asoilmapping_using_mla)
gives you graphical idea if there are any problems with your model.

HTH

Tom Hengl



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]<mailto:[hidden email]>>
> *Sent:* November 22, 2017 8:17 AM
> *To:* Joelle k. Akram; [hidden email]<mailto:[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]<mailto:[hidden email]>> on behalf of
>> Tomislav Hengl <[hidden email]<mailto:[hidden email]>>
>> *Sent:* November 22, 2017 3:58 AM
>> *To:* [hidden email]<mailto:[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> <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
<https://stackoverflow.com/questions/47424740/why-is-pre%0b>>>> dictive-error-large-for-universal-kriging#>
>
>>
>> <https://stackoverflow.com/questions/47424740/why-is-predictive-error
<https://stackoverflow.com/questions/47424740/why-is-predictive-error%0b>>> -large-for-universal-kriging#>
>>
>> Why is Predictive error large for Universal Kriging?
>> <https://stackoverflow.com/questions/47424740/why-is-predictive-error
<https://stackoverflow.com/questions/47424740/why-is-predictive-error%0b>>> -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
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>> 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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>> 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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Re: [DKIM] Re: Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]

Joelle k. Akram
Lin,


Your review paper on SIM is very comprehensive and a good read. You touched on Irregular versus Regular System (section 3.1.7  in the paper). I do not have access to the Burrough and McDonnell book but from your experience; are there any tips you can suggest when handling irregular spatial points for kriging and in particular KED (such as in terms of modeling semivariograms, etc) ?


thanks,

Chris



________________________________
From: Li Jin <[hidden email]>
Sent: November 22, 2017 4:30 PM
To: Joelle k. Akram; Tomislav Hengl; [hidden email]
Subject: RE: [DKIM] Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]


That is something I am still working on.



Variances of the predictions by spatial predictive models are not well defined yet, and they are many ways to do this but none of them is satisfactory. Although people may argue that kriging methods can produce such variance, kriging variance in fact does not reflect the uncertainty expected. Please see Goovaerts 1997 �Geostatistics for Natural Resources Evaluation� for details, or simply see my review �A Review of Spatial Interpolation Methods for Environmental Scientists� for a short explanation.



From: Joelle k. Akram [mailto:[hidden email]]
Sent: Thursday, 23 November 2017 10:01 AM
To: Li Jin; Tomislav Hengl; [hidden email]
Subject: [DKIM] Re: [DKIM] Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]



Jin,

Is there any to get the variances of the predictions in spm?





________________________________

From: Li Jin <[hidden email]<mailto:[hidden email]>>
Sent: November 22, 2017 3:28 PM
To: Tomislav Hengl; Joelle k. Akram; [hidden email]<mailto:[hidden email]>
Subject: RE: [DKIM] Re: [R-sig-Geo] Fw: Why is there a large predictive difference for Univ. Kriging? [SEC=UNCLASSIFIED]



Let try spm and see what we can achieve. All these scripts were directly modified from examples in spm.
> library(spm)
> library(sp)
> library(gstat)
> data(meuse)

> set.seed(999)
> 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$mae
[1] 53.54404 # This much lower than that for KED

> set.seed(999)
> rfcv1 <- rfokcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.22274 # This one further improved the accuracy in comparison with that for RF

> set.seed(999)
> rfcv1 <- rfidwcv(meuse[, c(1,2)], meuse[, c(5,4,7,8)], meuse[, 6], predacc = "ALL")
> rfcv1$mae
[1] 42.60406 # This one is similar to RFOK

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.

-----Original Message-----
From: R-sig-Geo [mailto:[hidden email]] On Behalf Of Tomislav Hengl
Sent: Thursday, 23 November 2017 8:42 AM
To: Joelle k. Akram; [hidden email]<mailto:[hidden email]>
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
http://gsif.isric.org/lib/exe/detail.php/wiki:xyplot_predicted_vs_observerd_edgeroi.png?id=wiki%3Asoilmapping_using_mla)
gives you graphical idea if there are any problems with your model.

HTH

Tom Hengl



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]<mailto:[hidden email]>>
> *Sent:* November 22, 2017 8:17 AM
> *To:* Joelle k. Akram; [hidden email]<mailto:[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]<mailto:[hidden email]>> on behalf of
>> Tomislav Hengl <[hidden email]<mailto:[hidden email]>>
>> *Sent:* November 22, 2017 3:58 AM
>> *To:* [hidden email]<mailto:[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> <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.
[[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@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
<https://stackoverflow.com/questions/47424740/why-is-pre%0b>>>> dictive-error-large-for-universal-kriging#>
>
>>
>> <https://stackoverflow.com/questions/47424740/why-is-predictive-error
<https://stackoverflow.com/questions/47424740/why-is-predictive-error%0b>>> -large-for-universal-kriging#>
>>
>> Why is Predictive error large for Universal Kriging?
>> <https://stackoverflow.com/questions/47424740/why-is-predictive-error
<https://stackoverflow.com/questions/47424740/why-is-predictive-error%0b>>> -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]<mailto:[hidden email]>
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>> 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]<mailto:[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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