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Weighted Estimation of AMMI and GGE Models

Author

Listed:
  • S. Hadasch

    (University of Hohenheim)

  • J. Forkman

    (Swedish University of Agricultural Sciences)

  • W. A. Malik

    (University of Hohenheim)

  • H. P. Piepho

    (University of Hohenheim)

Abstract

The AMMI/GGE model can be used to describe a two-way table of genotype–environment means. When the genotype–environment means are independent and homoscedastic, ordinary least squares (OLS) gives optimal estimates of the model. In plant breeding, the assumption of independence and homoscedasticity of the genotype–environment means is frequently violated, however, such that generalized least squares (GLS) estimation is more appropriate. This paper introduces three different GLS algorithms that use a weighting matrix to take the correlation between the genotype–environment means as well as heteroscedasticity into account. To investigate the effectiveness of the GLS estimation, the proposed algorithms were implemented using three different weighting matrices, including (i) an identity matrix (OLS estimation), (ii) an approximation of the complete inverse covariance matrix of the genotype–environment means, and (iii) the complete inverse covariance matrix of the genotype–environment means. Using simulated data modeled on real experiments, the different weighting methods were compared in terms of the mean-squared error of the genotype–environment means, interaction effects, and singular vectors. The results show that weighted estimation generally outperformed unweighted estimation in terms of the mean-squared error. Furthermore, the effectiveness of the weighted estimation increased when the heterogeneity of the variances of the genotype–environment means increased.

Suggested Citation

  • S. Hadasch & J. Forkman & W. A. Malik & H. P. Piepho, 2018. "Weighted Estimation of AMMI and GGE Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 255-275, June.
    • Handle: RePEc:spr:jagbes:v:23:y:2018:i:2:d:10.1007_s13253-018-0323-z
    DOI: 10.1007/s13253-018-0323-z
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    References listed on IDEAS

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    1. Johannes Forkman & Hans-Peter Piepho, 2014. "Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models," Biometrics, The International Biometric Society, vol. 70(3), pages 639-647, September.
    2. Alison Smith & Brian Cullis & Robin Thompson, 2001. "Analyzing Variety by Environment Data Using Multiplicative Mixed Models and Adjustments for Spatial Field Trend," Biometrics, The International Biometric Society, vol. 57(4), pages 1138-1147, December.
    3. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    4. Bert Green, 1952. "The orthogonal approximation of an oblique structure in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 429-440, December.
    5. 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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