Dear All,
Having fitted common variogram models to experimental semivariogram, I
tried to identify the optimal model that best explain the spatial structure
through Sum of squares error (SSErr) and cross validation method using mean
error (ME) and means square deviation ratio (MSDR) of prediction error with
kriging variance.


Going by the first table,* Exponential *seems to be the best model for
having *lowest value *of sum of squares error. But through the cross
validation of table 2, *Spherical* seems to be the best. I am confused!
Should I based my decision on table 2 by concluding that spherical is
optimal model? I formally concluded that both Spherical and exponential
gave highest prediction accuracy but exponential is optimal for having the
least value of SSerr. Please advise. Should I conclude that spherical model
is optimal based only on table 2? See my R script for obtaining the two
tables below



Table 1.Assessment of goodness fit of each variogram model to experimental
yield variogram across crop-year




*Dataset*



*wheat 2008*

*canola 2009*

*wheat 2010*

*barley 2011*

*Model*

Sum of Squares Error (SSErr)

Spherical

426.87

263.49

124.43

142.12

Gaussian

427.89

347.71

132.29

154.10

Exponential

330.36

163.16

90.45

64.25

Linear

439.93

299.69

138.79

191.26


Table 2. Cross validation diagnostic statistics measured prediction
accuracy of fitted models





*Wheat 2008*

*Canola 2009*

*Wheat 2010*

*Barley 2008*

Model

ME

MSDR

ME

MSDR

ME

MSDR

ME

MSDR

Spherical

-0.00

1.61

-0.00

1.05

-0.00

1.15

-0.00

0.87

Gaussian

-0.00

3.17

-0.00

1.42

-0.00

1.62

-0.00

1.55

Exponential

-0.00

1.91

-0.00

1.14

-0.00

1.25

-0.00

1.00

Linear

-0.42

83.25

-0.00

1.13

-0.00

1.43

-0.00

1.28

### Assess goodness of model fit to empirical semivariogram
SSErr.a<-numeric(4)
names(SSErr.a)<-c("Spherical","Gaussian","Exponential","Linear")
SSErr.a[1]=attr(sph.mod,"SSErr")
SSErr.a[2]=attr(gau.mod,"SSErr")
SSErr.a[3]=attr(exp.mod,"SSErr")
SSErr.a[4]=attr(lin.mod,"SSErr")
print(SSErr.a)


#### Cross validation of the variogram models by ordinary kriging
sph.kcv <- krige.cv(yield ~ 1, canmod.sp, model = sph.var,nmax=100, nfold =
5)
gau.kcv <- krige.cv(yield ~ 1, canmod.sp, model = gau.var,nmax=100, nfold =
5)
exp.kcv <- krige.cv(yield ~ 1, canmod.sp, model = exp.var,nmax=100, nfold=
5)
lin.kcv <- krige.cv(yield ~ 1, canmod.sp, model = lin.var,nmax=100, nfold =
5)


#### Overall measure of precision ME
sph.me <- mean(sph.kcv$residual)
gau.me <- mean(gau.kcv$residual)
exp.me <- mean(exp.kcv$residual)
lin.me <- mean(lin.kcv$residual)

#### Measure of prediction accuracy by Mean Square Deviation Ratio
sph.msdr <- mean(sph.kcv$residual^2/sph.kcv$var1.var)
gau.msdr <- mean(gau.kcv$residual^2/gau.kcv$var1.var)
exp.msdr <- mean(exp.kcv$residual^2/exp.kcv$var1.var)
lin.msdr <- mean(lin.kcv$residual^2/lin.kcv$var1.var)

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