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## AI-GEOSTATS: Variowin equations and cross-validation

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• Hi, Variowin/equation questions: I have fitted models using variowin and am now trying to plot them in other graphics programs. Vario2D produces a file that I
Message 1 of 4 , Apr 9, 2001
Hi,

Variowin/equation questions:

I have fitted models using variowin and am now trying to plot them in
other graphics programs. Vario2D produces a file that I can use to plot the
experimental variograms, but in the modeling I get an equation like:
gamma(h) = 14.2 + 6.399 Sph. 169.66(h)
I am wondering how to turn the exponential, spherical or power into some
sort of equation that another program can plot. Can anyone point me in the
direction of these equations (other than the manual, which is out of
print)?
While I'm asking, the sill reported in variowin is always about half of
what the sill appears to be from looking at it graphically. What is the
reason for this difference?

Cross-validation:

Any hints for using cross-validation to compare models? What does it
mean if the average error and the square root of the average squared
normalized error are of both models are similar and close to 0 or 1
respectively?
Specifically, I fitted models using Variowin (the file is too large
for Geoeas) and I found a pure nugget model in the same way. Variowin
gives a goodness of fit measure, and the fitted model was in all cases
"better" than the pure nugget model. When I did the cross validation in
Geoeas, the models seemed pretty good (for example, with values raning
from 0-54, average error = -0.093, and the standard deviation of the Zscore
was 1.16. The estimated values were somewhat underestimated, only ranging
from 0-17). However, the pure nugget effect seemed to be pretty good also
and not terribly different from the model (in this example, av. error =
1.665, which is further from 0, but sd of zscore = 1.027, which is closer
to 1. The estimates ranged from 0-14). Several models I looked at didn't
seem to have huge differences between the fitted model and a pure nugget
model.
So, does this mean that there is not a clear spatial effect here?
That there may be a weak spatial effect? That there is definitely not a
spatial effect? Is there some way to test for significance of difference
between the models?. . .

Thank you.

Juliann Aukema
jaukema@...

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• Let me take a stab at the cross-validation part first: Deutch and Journel (GSLib 1998) suggest examining cross-validated residuals keeping in mind that kriging
Message 2 of 4 , Apr 9, 2001
Let me take a stab at the cross-validation part first:

Deutch and Journel (GSLib 1998) suggest examining cross-validated residuals
keeping in mind that kriging estimates should be symmetric around zero with
minimal spread, globally and conditionally unbiased, homoscedastic, and
spatially-independent. I would hesitate on quantitatively evaluating a
model strictly on one error statistic (see Isaaks and Srivastava 1989).

As for the choice of your model, it depends on what makes sense for what you
are studying. If you have a pure nugget effect (no detectable range) but
you think there truly is a dependent effect then you might conclude that the
spatial dependence is occurring at a resolution below the minimum lag
distance. I've seen some folks recommend shortening the x-axis of the
variogram to about 1/6 the total lag distance and concentrate on modeling
the short lags well.

Variowin: I've been using the numerical output file (.var) and importing it
into excel to plot the "data" variograms. Just remember that the values
aren't "standardized" in that file, so for example if you want to plot the
covariance in the form of a variogram you have to subtract the covariance
from the global sample variance, etc. As for the model parameters, the
range, nugget, and sill are given in the Model program. You can plug those
values directly into the equation for the spherical model for plotting in
another program.

Hope this helps.

*************************************************
Sara Kustron
Boston University Department of Geography
675 Commonwealth Avenue Rm 445
Boston, MA 02215

skustron@...
office: (617) 353-8341
**************************************************

----- Original Message -----
From: "Juliann Aukema" <jaukema@...>
To: <ai-geostats@...>
Sent: Monday, April 09, 2001 5:22 PM
Subject: AI-GEOSTATS: Variowin equations and cross-validation

> Hi,
>
> Variowin/equation questions:
>
> I have fitted models using variowin and am now trying to plot them in
> other graphics programs. Vario2D produces a file that I can use to plot
the
> experimental variograms, but in the modeling I get an equation like:
> gamma(h) = 14.2 + 6.399 Sph. 169.66(h)
> I am wondering how to turn the exponential, spherical or power into some
> sort of equation that another program can plot. Can anyone point me in the
> direction of these equations (other than the manual, which is out of
> print)?
> While I'm asking, the sill reported in variowin is always about half of
> what the sill appears to be from looking at it graphically. What is the
> reason for this difference?
>
> Cross-validation:
>
> Any hints for using cross-validation to compare models? What does
it
> mean if the average error and the square root of the average squared
> normalized error are of both models are similar and close to 0 or 1
> respectively?
> Specifically, I fitted models using Variowin (the file is too large
> for Geoeas) and I found a pure nugget model in the same way. Variowin
> gives a goodness of fit measure, and the fitted model was in all cases
> "better" than the pure nugget model. When I did the cross validation in
> Geoeas, the models seemed pretty good (for example, with values raning
> from 0-54, average error = -0.093, and the standard deviation of the
Zscore
> was 1.16. The estimated values were somewhat underestimated, only ranging
> from 0-17). However, the pure nugget effect seemed to be pretty good also
> and not terribly different from the model (in this example, av. error =
> 1.665, which is further from 0, but sd of zscore = 1.027, which is closer
> to 1. The estimates ranged from 0-14). Several models I looked at didn't
> seem to have huge differences between the fitted model and a pure nugget
> model.
> So, does this mean that there is not a clear spatial effect here?
> That there may be a weak spatial effect? That there is definitely not a
> spatial effect? Is there some way to test for significance of difference
> between the models?. . .
>
> Thank you.
>
> Juliann Aukema
> jaukema@...
>
>
>
> --
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> * As a general service to the users, please remember to post a summary of
any useful responses to your questions.
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"unsubscribe ai-geostats" followed by "end" on the next line in the message
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>

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• Juliann Judging the fit of a model cannot be done from the summary statisics. See my 1986 paper The Art of Cross Validation (full reference at
Message 3 of 4 , Apr 10, 2001
Juliann

Judging the fit of a model cannot be done from the
summary statisics. See my 1986 paper "The Art of Cross
Validation" (full reference at
http://uk.geocities.com/drisobelclark/Publications.html)

Better to use something like Noel Cressie's goodness
of fit statistic which tests the semi-variogram fit to
the experimental with a weighted least squares.

Isobel Clark

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• AAgh, sprry people, Mark Burnett just pointed out that I missed a bit in the Web reference: http://uk.geocities.com/drisobelclark/resume/Publications.html Mea
Message 4 of 4 , Apr 10, 2001
AAgh, sprry people, Mark Burnett just pointed out that
I missed a bit in the Web reference:

http://uk.geocities.com/drisobelclark/resume/Publications.html

Mea culpa
Isobel Clark

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