A set of interpolated values were obtained through ordinary kriging and inverse distance weighting method using gstat library of R. Could anyone guide me on how to cross validate these interpolation methods to obtain diagnostics statistics such as mse, or rmse for identifying the best method?
My R script is as follows:
## Create grid for the interpolation through ordinary kriging and idw
grid
I am not working with gstat or geoR but I use ESRI ArcGIS and the extension "Geostatistical Analyst" for cross validation. This is a nice tool with a graphical interface to play with different interpolation methods and it provides cross validation with a lot of statistics.
Sqrt((round(mean(prok$residual), 5) - 0)^2 + (round(mean(prok$residual),5) - 0)^2 + (round(var(prok$residual), 5) - 1)^2)
you need an independent data set, take a look in the paper attach.
I used GS+ and ArcView at that time
Hi Moshood,
To assess the quality of an interpolation algorithm I use a technique called 'leave one out' cross validation. I am attaching a couple of paragraphs from a paper where I explain the technique. The full paper can be found here: "Sanabria LA., Qin X., Li J., Cechet RP., Lucas C. 2013. Spatial Interpolation of McArthur’s Forest Fires Danger Index across Australia: Observational Study. Environmental Modelling & Software 50, 37-50".
Hope it helps,
Augusto
gstat includes a cross validation function but you do not set up an interpolation grid, you krige the value at each data location but witheout using the data at that location. The output will consist of triples of numbers; the original data value, the kriged value and the kriging std deviation (for each data location). Then you can compute various statistics, e.g. the mean error, the mean square normalized error, fraction of normalized errors greater than 2.5. Since the kriging estimator is unbiased the theoretical value of the mean error is zero, the theoretical value of the mean square normalized error is one and the theoretical probability of normalized errors being less than 2.5 is .05. You also want the correlation between the true value and the kriged value to be close to one and the correlation between the kriged values and the errors to be close to zero, however in the case of Ordinary kriging (as contrasted with Simple kriging) the theoretical values are not one and zero because of the Lagrange multipliers in the kriging equations. It is also often helpful to make a coded plot of the data locations, coded by either the errors or normalized errors, also histograms of th errors or normalized errors
Cross validation has been well known in the geostatistics literature for more than twenty years, certainly well before 2013
In case of kriging we can go through the process of cross-validation, however, for IDW and other interpolation techniques how can we comment on the reliability of the model? For, example if I change the dataset for interpolating some points and select 2/3 data randomly I would expect similar results for a good spatial model.
Islam
IDW is just an intuitive method, it is not based on any theory nor any statistical assumptions. Hence any cross validation statistics you might generate do not provide any basis for interpretation. The suggestion to select 2/3 data randomly is not based on any evidence. You must also distinguish between randomly selecting data values and randomly selecting data locations, those two ideas are not equivalent
Mehmet
Comparing two raster maps is not related nor equivalent to cross validation
For a discussion of cross validation statistics and kriging, see
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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