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

Li Jin Jin.Li at ga.gov.au
Wed Nov 22 23:28:04 CET 2017 

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:r-sig-geo-bounces at r-project.org] On Behalf Of Tomislav Hengl
Sent: Thursday, 23 November 2017 8:42 AM
To: Joelle k. Akram; r-sig-geo at r-project.org
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 at 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$covariate =
> Training_sample at data[,c("lead","copper","elev", "dist")] trend = ~ 
> lead+copper+elev+dist
>   zinc.vgm <- likfit(Training_sample.geo, lambda=0, trend = trend,
>                        
> ini=c(var(log1p(Training_sample.geo$data)),800),
> fix.psiA = FALSE, fix.psiR = FALSE)
> 
> # do prediction for locations in Training set
>   locs2 = Training_sample at 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 at 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 <tom.hengl at gmail.com>
> *Sent:* November 22, 2017 8:17 AM
> *To:* Joelle k. Akram; r-sig-geo at r-project.org
> *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 <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_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 at data[,c("lead","copper","elev", 
>> R> "dist")]) meuse = meuse[sel.d,] meuse.geo <- 
>> R> as.geodata(meuse["zinc"]) ## add covariates:
>> R> meuse.geo$covariate = meuse at data[,c("lead","copper","elev", 
>> R> "dist")] trend = ~ lead+copper+elev+dist zinc.vgm <- 
>> R> likfit(meuse.geo, lambda=0, trend = trend,
>> ini=c(var(log1p(meuse.geo$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 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>
>> 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]]
>>> 
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