Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?
- PDF / 739,002 Bytes
- 23 Pages / 496.063 x 720 pts Page_size
- 119 Downloads / 167 Views
1. INTRODUCTION Plant-breeding field trials typically show considerable spatial variation. Blocked experimental designs help to capture some of that spatial trend and provide efficient treatment estimates (Edmondson 2005). If the spatial trend is irregular, however, blocking may only be partly successful. In such cases, spatial adjustment using a suitable statistical model can provide an improvement in accuracy. Designs and modelling methods developed for field trials can also be applied with advantage in greenhouses (Hartung et al. 2019), growth
M.P. Boer Biometris, Wageningen University and Research, Wageningen, The Netherlands (E-mail: [email protected]). H.P. Piepho (B),Institute of Crop Science, University of Hohenheim, 70593 Stuttgart, Germany (E-mail: [email protected]). E.R. Williams Statistical Consulting Unit, Australian National University, Canberra, ACT 2601, Australia (E-mail: [email protected]). © 2020 The Author(s) Journal of Agricultural, Biological, and Environmental Statistics, Volume 25, Number 4, Pages 676–698 https://doi.org/10.1007/s13253-020-00412-4
676
Linear Variance, P- splines and Neighbour Differences
677
chambers (Lee and Rawlings 1982) and with phenotyping platforms (Brien et al. 2013; Cabrera-Bosquet et al. 2016; van Eeuwijk et al. 2019). A variety of variance–covariance structures can be used for spatial adjustments, and such structures are readily available in mixed model packages. Most spatial variance–covariance models are nonlinear in the parameters (Stein 1999; Stroup 2002; Schabenberger and Gotway 2004). Our paper is focused on linear models and methods for spatial adjustment. Perhaps the oldest approach of this kind is nearest-neighbour adjustment (NNA) based on differences among neighbouring plots (Papadakis 1937; Wilkinson et al. 1983; Piepho et al. 2008). The first proposals involved one-dimensional adjustment, but extension to two-dimensional spatial models has been subsequently proposed (Green et al. 1985; Kempton et al. 1994). A further option is to employ smoothing splines (Lee et al. 2020). The most recent addition in a field-trial context is the use of P-splines (Eilers and Marx 1996), which has been proposed under the acronym SpATS (Spatial Analysis of field Trials with Splines) (Rodríguez-Álvarez et al. 2018), and is available as R-package on CRAN (https:// cran.r-project.org/package=SpATS). Perhaps the most important common feature of these methods is that they all can be identified with a variance–covariance structure that is linear in the parameters and as such can have computational advantages compared to nonlinear structures. Early work on spatial adjustment using NNA methods focused on second differences (Wilkinson et al. 1983; Green et al. 1985), but it was soon recognized that first differences (Besag and Kempton 1986), and the related linear variance (LV) model (Williams 1986) often provide a good fit. The recently proposed SpATS approach was introduced in terms of second differences. In this paper, we will specifically investigate
Data Loading...
