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The unknown parameters in these models, namely, τ2 (the nugget), ν2 (the sill), and φ (the range), can be obtained from a variogram of the data.
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However, a variogram of standardized residuals from the model suggested that residual spatial autocorrelation was appropriately controlled by the village level random effects.
This method was preferred to a kriging because the variogram or expectation of the data is unknown but the data are reliable (Cressie 1993).
In addition, we assume that the variogram of the normal-score transformed data would look very similar to the variogram of the raw data scaled to a unit sill.
The variogram model is defined fitting the experimental variogram of n-scores and provides a description of how the data are spatially correlated.
Experimental variograms show spatial coherence of the data.
We investigated the spatial autocorrelation of the data by a variogram analysis using the Geostatistical Analyst extension of ArcGIS® 9.3 (Environmental Systems Research Institute 2009).
This consists in comparing the observed variogram with variogram 'envelopes' that were computed by simulating 999 permutations of the data values across locations.
The variogram-based approach provides possible spatial anisotropies of the data and range of similarity between measured values of the data.
Simple kriging estimate and variance are computed considering the measured data and those previously simulated during the procedure, according to the variogram model of n-scores and to the statistical distribution of the data.
The vertical variograms can be models for most of the reservoirs in the model, despite the anisotropy and cyclical nature of the data.
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