Hello every body
I used Arc Map Geostatistical analyst to interpolate a surface for heavy metals. Before Interpolation I divide my data set to train and test. By training data I interpolate a surface among dataset and now I want to determine residuals for test data to control the precision of interpolation. How can I determine value in an unknown position?
Hello Dear Alexandre
Your Answer really will help me.
Thxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i mostly use these four performance parameters for checking the accuracy of cross validation.
(1) RMSE
(2) AME
(3) coefficient of determination
(4) correlation coefficient
Usman
Thxx dear Muhammad
But I have another question
How do you use correlation coefficient to checking the accuracy of cross validation?
Can you please guide me by introducing a reference e.g. an article?
If you use ArcGIS Geostatistical Analyst module (I guess you are using this one) for generating your interpolated surface, then at the end you will get your observed and interpolated predicted values in a tabular format. You then bring those in MSExcel and simply u can calculate correlation coefficient. However, for cross-validation, you need to use some error criteria which you can find in the ArcGIS Geostatistical Analyst manual.
If you need any help, i can help you.
read documentations about correlation coefficient. Its value vary within 0,1 . Produce predicted points and compare a correlation between predicted and actual point through this formula.
If your CC values of validation are near to 1 (strong correlation), mean good validation.
Check this paper, either it is on missing data but may helpful for you.
Please vote up my answers if these are helpful to you..
http://dspace.unimap.edu.my/dspace/bitstream/123456789/1171/1/ICOSM%202007%20(AZIAN).pdf
A few observations:
1. When you use kriging you are relying on a model for the random function (the data is a non-random sample from one realization of the random function). and that the random function satisfies several crucial assumptions such as intrinsic stationarity and that the data can be used to estimate/model the variogram. There are no statistical tests to determine whether these assumptions are valid..
2. The kriging estimator is "exact" (sometimes also called "perfect"). This means that if you generate an interpolated value at a data location and use the data value in the interpolation the interpolated value will be the data value (the residual is always zero).
3. If you split the data locations into a training set and an interpolation set you are assuming that both are samples from the same realization of the same random function. The method of choosing the two data subsets does not ensure this assumption is satisfied. Hence this technique does not really quantify the accuracy/precision of the interpolation.
4. Cross-valation (leave one out) is really a method to compare one variogram model against another and/or one choice of the variogram parameters against another or possibly to see the effect of the search neighborhood parameters on the interpolated values. It can also be useful for identifying "unusual" data values
5. As an exploratory technique, splitting the data locations into two subsets may be useful but there is no real theory to back it up. A different split might produce very different results and there is no way to determine which set of results is more relevant.
As for cross validation there are multiple statistics that can be computed but no single one is more important or reliable. For a discussion of these see the following
1991, Myers,D.E., On Variogram Estimation in Proceedings of the First Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II, American Sciences Press, 261-281
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