A Bayesian analysis of an agricultural field trial with three spatial dimensions
Abstract
Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the 'layered CAR model', while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lies in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate conditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.Download Info
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Bibliographic Info
Article provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 55 (2011)
Issue (Month): 12 (December)
Pages: 3320-3332
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Web page: http://www.elsevier.com/locate/csda
Related research
Keywords: Bayesian Conditional autoregressive (CAR) models Cubic radial bases Errors-in-variables Field trial Latent variables Markov Chain Monte Carlo (MCMC) Markov random field (MRF) Orthogonal polynomials Spatial autocorrelation Splines Variance components;References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Chen, Min & Wang, Xinlei, 2011. "Approximate predictive densities and their applications in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1570-1580, April.
- David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
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- J. Besag & D. Higdon, 1999. "Bayesian analysis of agricultural field experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 691-746.
- Long Ngo & Matthew P. Wand, . "Smoothing with Mixed Model Software," Journal of Statistical Software, American Statistical Association, vol. 9(i01).
- Julian Besag & Debashis Mondal, 2005. "First-order intrinsic autoregressions and the de Wijs process," Biometrika, Biometrika Trust, vol. 92(4), pages 909-920, December.
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