Dear John, Isn't your problem rather a result from the unstable empirical variograms? Mainly due to the very low number of pairs per bin. Furthermore have a look at the weights that each bin gets in the fit.variogram() function. The default is N/h^2. In your case the first bin gets a weight of 2 whereas the other bins have weights ranging from 1e-3 tot 1e-4! Hence no surprise that the nugget is nearly identical to the semivariance of the first bin.
In this case I would not trust the results for fit.variogram(). Not because of bugs in gstat, but because I don't trust empirical variogram with that low number of pairs per bin. HTH, Thierry ---------------------------------------------------------------------------- ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest Cel biometrie, methodologie en kwaliteitszorg / Section biometrics, methodology and quality assurance Gaverstraat 4 9500 Geraardsbergen Belgium tel. + 32 54/436 185 thierry.onkel...@inbo.be www.inbo.be To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data. ~ Roger Brinner The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey -----Oorspronkelijk bericht----- Van: r-sig-geo-boun...@stat.math.ethz.ch [mailto:r-sig-geo-boun...@stat.math.ethz.ch] Namens Carson, John Verzonden: maandag 12 oktober 2009 15:35 Aan: r-sig-geo@stat.math.ethz.ch Onderwerp: [R-sig-Geo] Problem with gstat variogram estimation I have found anomalous behavior in gstat's variogram estimation. I have listed 3 example variograms below for small data sets. In order to better estimate the nugget effect, I slightly perturbed the locations (by 1 foot increments) of duplicate results. The empirical variograms are given below. Before I did this (I averaged duplicate values initially), a Gaussian model with 0 nugget was selected for the second variogram and pure nugget models for the first and third. I am using the candidate model list ('Nug', 'Exp', 'Sph', 'Gau', 'Mat', 'Cir', 'Lin', 'Bes') and selecting the model based on SSErr for preliminary testing purposes. Afterward, the pure nugget models had the lowest SSErr and were selected. Note that the variogram fits are completely controlled by the short range variance, because even the original pure nugget models are substantially different in the estimate of the nugget. The fitted models are listed below. Just by inspection, based on the numbers of pairs in these examples, a pure nugget model should be about halfway between the empirical semivariance of the last lag and the average of the other lags. However, the fitted nuggets are almost identical to the semivariance of the first last (dist = 1.4). It seems to me that this must be due to a bug in the GSTAT code. I pointed this out to Edzer Pebesma, and he asked me to post it here. The variograms are tmp.vgm [[1]] np dist gamma dir.hor dir.ver id 1 4 1.414214 0.14174537 0 0 PC1 2 2 44.742603 6.70989788 0 0 PC1 3 2 57.707880 1.76351594 0 0 PC1 4 4 59.987678 1.52197310 0 0 PC1 5 3 71.512518 1.21348268 0 0 PC1 6 1 84.852877 0.05381849 0 0 PC1 7 1 97.266495 1.21827622 0 0 PC1 8 3 112.237133 5.07947925 0 0 PC1 9 18 121.478856 1.93707676 0 0 PC1 [[2]] np dist gamma dir.hor dir.ver id 1 4 1.414214 0.09725079 0 0 PC2 2 2 44.742603 0.33598072 0 0 PC2 3 2 57.707880 0.39088727 0 0 PC2 4 4 59.987678 0.87315735 0 0 PC2 5 3 71.512518 0.14944845 0 0 PC2 6 1 84.852877 0.19809863 0 0 PC2 7 1 97.266495 0.63557814 0 0 PC2 8 3 112.237133 1.92063948 0 0 PC2 9 18 121.478856 0.65468693 0 0 PC2 [[3]] np dist gamma dir.hor dir.ver id 1 4 1.414214 0.035250817 0 0 PC3 2 2 44.742603 0.105299796 0 0 PC3 3 2 57.707880 0.020245674 0 0 PC3 4 4 59.987678 0.124159836 0 0 PC3 5 3 71.512518 0.008112554 0 0 PC3 6 1 84.852877 0.034337591 0 0 PC3 7 1 97.266495 0.053879459 0 0 PC3 8 3 112.237133 0.021922987 0 0 PC3 9 18 121.478856 0.085270969 0 0 PC3 But the fitted models are: tmp.vgm.fit [[1]] model psill range 1 Nug 0.1483120 0 [[2]] model psill range 1 Nug 0.09849419 0 [[3]] model psill range 1 Nug 0.03535234 0 John H. 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