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A Linear Mixed Model, with Non-stationary Mean and Covariance, for Soil Potassium Based on Gamma Radiometry : Volume 7, Issue 2 (16/03/2010)

By Haskard, K. A.

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Book Id: WPLBN0004005438
Format Type: PDF Article :
File Size: Pages 24
Reproduction Date: 2015

Title: A Linear Mixed Model, with Non-stationary Mean and Covariance, for Soil Potassium Based on Gamma Radiometry : Volume 7, Issue 2 (16/03/2010)  
Author: Haskard, K. A.
Volume: Vol. 7, Issue 2
Language: English
Subject: Science, Biogeosciences, Discussions
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Lark, R. M., Rawlins, B. G., & Haskard, K. A. (2010). A Linear Mixed Model, with Non-stationary Mean and Covariance, for Soil Potassium Based on Gamma Radiometry : Volume 7, Issue 2 (16/03/2010). Retrieved from

Description: Rothamsted Research, Harpenden, Hertfordshire, AL5 2JQ, UK. In this paper we present a linear mixed model for the potassium content of soil across a large region of eastern England in which the mean is modelled as a linear function of the passive gamma-ray emissions of the earth surface in the energy interval commonly associated with potassium decay. Non-stationary models are proposed for the random effect, the variation not captured by this regression. Specifically, we assume that the local spectrum of the standardized random effect can be obtained by tempering a common (stationary) spectrum, that is to say raising its values to a power, the tempering parameter, which is itself modelled as a linear function of the radiometric data. This allows the smoothness of the random effect to vary locally. In addition the local spatially correlated variance and nugget variance (apparently uncorrelated given the resolution of the sampling) can also be modelled as a function of the radiometric data. Using the radiometric signal as a covariate gave some improvement in the precision of predictions of soil potassium at validation sites. In addition, there was evidence that non-stationary models for the random effect fitted the data better than stationary models, and this difference was statistically significant. Non-stationary models also appeared to describe the error variance of predictions at the validation sites better. Further work is needed on selection among alternative non-stationary models, since simple procedures used here, based on comparing log-likelihood ratios of nested models and the Akaike information criterion for non-nested models, did not identify the model which gave the best account of the prediction error variances at validation sites.

A linear mixed model, with non-stationary mean and covariance, for soil potassium based on gamma radiometry


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