bayesammi: Bayesian Estimation of the Additive Main Effects and Multiplicative Interaction Model
Source:R/bayesammi-package.R
bayesammi-package.Rdbayesammi estimates the additive main effects and multiplicative interaction (AMMI) model of multi-environment trials in plant breeding by Bayesian methods, with the Gibbs sampler of Crossa et al. (2011). Every parameter has a posterior distribution, so the AMMI biplot gets statistical inference: highest posterior density (HPD) regions show which genotypes and environments interact significantly and which form homogeneous groups. Beyond the article, the package fits unbalanced trials, environment-specific error variances and the GGE (sites regression) model, turns the posterior into decisions (winners, probabilities of superior performance and stability, ranks, stability measures, predictions), compares and checks models, and runs every analysis in a built-in application. It also fits the Finlay-Wilkinson, Eberhart-Russell and Shukla stability models by Gibbs sampling and gives posterior distributions of classical and AMMI-based stability indices. The package is for breeders and agronomists who analyse genotype-by-environment interaction and want uncertainty statements about their conclusions.
Details
Functions, in the order of an analysis:
ge_mean,ge_var,g_eff,e_eff,ge_eff: cell means and variances, main effects, interaction effects and their singular value decomposition.ge_ammi,ge_model: least-squares AMMI and the mixed model of the error variance.bam_priors,bayes_ammi: priors and the Gibbs sampler of the AMMI or GGE model, with a common or environment-specific error variances and missing plots or cells (chains, burn-in, thinning, posterior summaries with HPD intervals, convergence diagnostics, DIC and WAIC).biplots: the biplot with HPD regions.bam_predict,bam_winners,bam_superiority,bam_ranks,bam_stability: decisions for breeders.bam_compare,bam_ppc,bam-draws: model choice, posterior predictive checks, and the draws for posterior, bayesplot and coda.bam_stab_priors,bayes_stability: Bayesian Finlay-Wilkinson, Eberhart-Russell and Shukla stability models;bam_indices,bam_ammi_indices: posterior distributions of classical and AMMI-based stability indices.bam_cite: the references of the methods behind a result (also printed under every result).bam_app: the built-in application.bam_interpret: a plain-language interpretation of a result.matrix_k,orthnorm: orthonormal contrasts and Gram-Schmidt orthonormalisation.
Every analysis returns the named list documented on its help page, with a class and methods (print,
summary, plot, as.data.table); see bam-methods. Utilities:
bam_theme, bam_save, bam_notation, bam_reference.
Data. Maiz: grain yield of 9 maize genotypes in 20 sites with 4 replicates (the example
of Crossa et al. 2011).
Vignettes. Start with vignette("bayesammi_01_getting_started", package = "bayesammi");
browseVignettes("bayesammi") lists all of them, each as HTML and as PDF.
Notation
Scalars are upper-case letters in normal face, indices lower-case italic, vectors lower-case bold and matrices
upper-case bold; Greek letters follow the same rule. The full table is bam_notation().
| \(G\), \(E\), \(B\), \(K\) | numbers of genotypes, environments, replicates, bilinear terms |
| \(\mathbf{Y}\) | \(G \times E\) table of cell means |
| \(\mu\), \(\boldsymbol{\tau}\), \(\boldsymbol{\delta}\) | overall mean, genotype and environment effects |
| \(\lambda_k\), \(\boldsymbol{\alpha}_k\), \(\boldsymbol{\gamma}_k\) | singular value and genotype and environment score vectors of term \(k\) |
| \(\sigma^2\), \(\sigma^2_j\) | common and environment-specific error variance |
| \(\eta_{ij}\) | expected value of genotype \(i\) in environment \(j\) |
| \(g_i\), \(h_j\), \(1 + b_i\) | genotype effect, environmental index and slope of the stability models |
| \(d_{ij}\), \(\sigma^2_{d,i}\) | deviation from the regression and its (genotype-specific) variance |
References
Crossa, J., Perez-Elizalde, S., Jarquin, D., Cotes, J. M., Viele, K., Liu, G. and Cornelius, P. L. (2011). Bayesian estimation of the additive main effects and multiplicative interaction model. Crop Science, 51(4), 1458–1469. doi:10.2135/cropsci2010.06.0343
Perez-Elizalde, S., Jarquin, D. and Crossa, J. (2012). A general Bayesian estimation method of linear-bilinear models applied to plant breeding trials with genotype x environment interaction. Journal of Agricultural, Biological, and Environmental Statistics, 17(1), 15–37. doi:10.1007/s13253-011-0063-9
Viele, K. and Srinivasan, C. (2000). Parsimonious estimation of multiplicative interaction in analysis of variance using Kullback-Leibler information. Journal of Statistical Planning and Inference, 84(1–2), 201–219.
Author
Muhammad Yaseen (myaseen208@gmail.com), ORCID 0000-0002-5923-1714.