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

Martin P. Boer, Hans Peter Piepho*, Emlyn R. Williams

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)676-698
JournalJournal of Agricultural, Biological, and Environmental Statistics
Volume25
Early online date18 Sep 2020
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Geostatistics
  • Linear mixed model
  • Random walk
  • Spatial correlation
  • Sweep operator

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