Overcoming pseudoreplication in experimental designs

Transcription

1 Overcoming pseudoreplication in experimental designs Ky Mathews, Nicole Cocks, David Hughes, Brian Cullis National Institute of Applied Statistics Research Australia University of Wollongong Australasian Applied Statistics Conference 28 Nov-2 Dec, 2016 Ky Mathews pseudo-rep x AASC / 21

2 Real World Problem Experimental design of canola experiments in the NVT Canola (Brassica napus) crop is the 3rd largest crop in Australia with 2000ha in 2016 resulting in 3000t. Herbicide is applied to manage weeds ChemGp: RoundUp, Triazine, Imidazolinone and Conventional (Open Pollinated). Varieties are bred to be tolerant to one ChemGp. The aim of NVT canola trials is to compare ALL Varieties from all ChemGps HOWEVER, there is a REAL agronomic constraint: herbicide needs to be sprayed in blocks to prevent cross-spray of herbicides to dierent chemistry groups Ky Mathews pseudo-rep x AASC / 21

3 Illustrative trial layout:pseudo-replication Each of the 3 Sub-experiments are designed as RCB with 3 reps. ChemGp is allocated to Sub-experiments Varieties within ChemGp are allocated to Plots within Reps within Sub-experiments ChemGp is not replicated, confounded with Sub-experiment (design is disconnected) Example design details 74 rows by 3 columns = 222plots I = 12; R = 30, T = 23 2reps) Ky Mathews pseudo-rep x AASC / 21

4 Illustrative trial layout:agronomic constraint Ky Mathews pseudo-rep x AASC / 21

5 Analysis of current designs Prior to 2014 each Sub-experiment (ChemGp) was analysed separately small numbers of varieties in some ChemGp, e.g. Imidazolinone separate residual variance for each ChemGp identication of optimal spatial model is problematic Co-located analysis in MET datasets, environment is dened to be Year-Location (YrLoc) combination genetic variance varies between YrLoc from a biological and statistical viewpoint it would sensible to constrain non-genetic variance parameters to be the same within in a YrLoc requires the full Experiment layout, including buers BUT... there is no inferential framework to compare across ChemGp Ky Mathews pseudo-rep x AASC / 21

6 How NVT results are presented to growers Breeding companies and agronomists Ky Mathews pseudo-rep x AASC / 21

7 How NVT results are presented to growers Breeding companies and agronomists Ky Mathews pseudo-rep x AASC / 21

8 Real World Problem Skeletal ANOVA Stratum Source df Mean Mean 1 RowMainPlot ChemGp 2 Residual 0 Total 2 RowMainPlot:ColRep RowMainPlot:ColRep 6 RowRep:RowMainPlot:ColRep Variety:ChemGp 62 Residual 126 Total 188 Total 197 ChemGp are completely disconnected, so we CANNOT compare Variety across ChemGp. Ky Mathews pseudo-rep x AASC / 21

9 Real World Solution Parameters Break the disconnectedness between ChemGp Minimse the probability of chemical application mistakes Minimise the addition of resources, both time and plots Ky Mathews pseudo-rep x AASC / 21

10 Real World Solution New Design Ky Mathews pseudo-rep x AASC / 21

11 Real World Solution New Design Blocking Structures Ky Mathews pseudo-rep x AASC / 21

12 Real World Solution New Design Blocking Structures Ky Mathews pseudo-rep x AASC / 21

13 Real World Solution New Design Blocking Structures Ky Mathews pseudo-rep x AASC / 21

14 Real World Solution New Design Blocking Structures Ky Mathews pseudo-rep x AASC / 21

15 Real World Solution Using od() od (Butler, 2015) generates optimal experimental designs under a linear mixed model specied in R formulae objects. Ky Mathews pseudo-rep x AASC / 21

16 Real World Solution Using od() od (Butler, 2015) generates optimal experimental designs under a linear mixed model specied in R formulae objects. des1.od < od(xed= Variety, random= RowRep + RowMainPlot + ColRep + RowRep:ColRep + RowMainPlot:ColRep, data=new.des, permute= Variety, swap= ChemGp, Gstart=des1.init, Rstart=des1.init, search='tabu', maxit=6) Note: we're not tting AR1 AR1 here. Ky Mathews pseudo-rep x AASC / 21

17 Real World Solution Skeletal ANOVA Ky Mathews pseudo-rep x AASC / 21

18 Canonical Eciency Factors Following Dobcsanyi (2003) the cefs, e di, are the ν-1 largest eigenvalues of F d = R 1 C d R 1 where R = diagonal matrix of size ν and values r i, and C d = X V 1 X = information matrix. Φ 1 = (ν 1) (1/e di ) e di Φ 1 Design = 0 < 1 = 1 Current Proposed Ky Mathews pseudo-rep x AASC / 21

19 Real World Solution New Design ChemGp is validly replicated. The constraint of spraying accommodated, slight increase in spraying logistics. There is a slight increase in resources, from 74 rows to 82 (=246 plots) which is the inclusion of 2 more buer strips. Ky Mathews pseudo-rep x AASC / 21

20 Real World Future Adoption of the design by NVT Work with Chris Brien on dae to determine the canonical eciencies for each strata The next real world problem... Ky Mathews pseudo-rep x AASC / 21

21 Acknowledgements co-authors: David Hughes, Nicole Cocks, Brian Cullis Alison Smith, Simon Diey Deborah Bud GRDC for funding Deb's Honours project in 2014 Ky Mathews pseudo-rep x AASC / 21

22 References Bailey R. (2006) Design of Comparative Experiments Dobcsanyi (2003) designtheory.org R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL ASReml-R Butler et al (2015) Asreml: An R package to t the linear mixed model (ASReml-R) David Butler (2016). od: Generate optimal experimantal designs. R package version Butler (2016). pedicure: pedigree tools. R package version ggplot H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, Ky Mathews pseudo-rep x AASC / 21