Estimation of Factor Analytic Mixed Models for the Analysis of Multi-treatment Multi-environment Trial Data
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An efficient and widely used method of analysis for multi-environment trial (MET) data in plant improvement programs involves a linear mixed model with a factor analytic (FA) model for the variety by environment effects. The variance structure is generally constructed as the kronecker product of two matrices that relate to the variety and environment dimensions, respectively. In many applications, the FA variance structure is assumed for the environment dimension and either an identity matrix or a known matrix, such as the numerator relationship matrix, is used for the variety dimension. The factor analytic linear mixed model can be fitted to large and complex MET datasets using the sparse formulation of the average information algorithm of Thompson et al. (Aust N Z J Stat 45:445–459, 2003) or the extension provided by Kelly et al. (Genet Sel Evo, 41:1186–1297, 2009) for the case of a known non-identity matrix for the variety dimension. In this paper, we present a sparse formulation of the average information algorithm for a more general separable variance structure where all components are parametric and one component has an FA structure. The approach is illustrated using a large and highly unbalanced MET dataset where there is a factorial treatment structure.
Supplementary materials accompanying this paper appear online.
KeywordsAverage information algorithm Factor analytic models Factorial treatment structure Linear mixed model
- Bailey, R. A. (2008), “Design of Comparative Experiments, Cambridge Series in Statistical and Probabilistic Mathematics,” Cambridge University Press, Cambridge.Google Scholar
- Butler, D., Cullis, B., Gilmour, A., and Gogel, B. J. (2009), “ASReml-R Reference Manual, Version 3. Training and Development Series, No. QE02001,” Queensland Department of Primary Industries.Google Scholar
- Butler, D. G., Cullis, B. R., Gilmour, A. R., and Thompson, R. (2018), “ASReml-R Reference Manual, Version 4,” University of Wollongong. Available at https://mmade.org/wp-content/uploads/2019/01/asremlRMfinal.pdf.
- Gelfand, A. E., Diggle, P. J., Fuentes, M., and Guttorp, P. (2010), “Handbook of Spatial Statistics. Handbooks of Modern Statistical Methods”, Chapman and Hall/CRC, Boca Raton.Google Scholar
- Gogel, B., Smith, A., and Cullis, B. (2018), “Comparison of a One- and Two-Stage Mixed Model Analysis of Australia’s National Variety Trial Southern Region wheat data”’ Euphytica, 214, 1–21.Google Scholar
- GRDC. (2017),“ Blackleg Management Guide: 2017 Spring Variety Ratings”, Fact sheet, Grains Research & Development Corporation.Google Scholar
- Sivasithamparam, K., Barbetti, M., and Li, H. (2005), “Recurring Challenges from Necrotrophic Fungal Plant Pathogen: A Case Study with Leptosphaeria maculans (Causal Agent of Blackleg Disease in Brassicas) in Western Australia,” Annals of Botany, 96, 363–377.Google Scholar