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Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?

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  • Martin P. Boer

    (Wageningen University and Research)

  • Hans-Peter Piepho

    (University of Hohenheim)

  • Emlyn R. Williams

    (Australian National University)

Abstract

Nearest-neighbour methods based on first differences are an approach to spatial analysis of field trials with a long history, going back to the early work by Papadakis first published in 1937. These methods are closely related to a geostatistical model that assumes spatial covariance to be a linear function of distance. Recently, P-splines have been proposed as a flexible alternative to spatial analysis of field trials. On the surface, P-splines may appear like a completely new type of method, but closer scrutiny reveals intimate ties with earlier proposals based on first differences and the linear variance model. This paper studies these relations in detail, first focussing on one-dimensional spatial models and then extending to the two-dimensional case. Two yield trial datasets serve to illustrate the methods and their equivalence relations. Parsimonious linear variance and random walk models are suggested as a good point of departure for exploring possible improvements of model fit via the flexible P-spline framework.

Suggested Citation

  • Martin P. Boer & Hans-Peter Piepho & Emlyn R. Williams, 2020. "Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 676-698, December.
    • Handle: RePEc:spr:jagbes:v:25:y:2020:i:4:d:10.1007_s13253-020-00412-4
    DOI: 10.1007/s13253-020-00412-4
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    1. Brian R. Cullis & Alison B. Smith & Nicole A. Cocks & David G. Butler, 2020. "The Design of Early-Stage Plant Breeding Trials Using Genetic Relatedness," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 553-578, December.
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    3. Arūnas P. Verbyla & Joanne Faveri & John D. Wilkie & Tom Lewis, 2018. "Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 478-508, December.
    4. 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.
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    Cited by:

    1. Hans-Peter Piepho & Robert J. Tempelman & Emlyn R. Williams, 2020. "Guest Editors’ Introduction to the Special Issue on “Recent Advances in Design and Analysis of Experiments and Observational Studies in Agriculture”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 453-456, December.

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