Genotype-by-environment interaction effects

ge_eff() computes the interaction effects (the cell means centred on genotype and environment means) and their singular value decomposition, the least-squares estimate of the multiplicative part of the AMMI model.

Usage

ge_eff(.data, .y, .gen, .env)

# Default S3 method
ge_eff(.data, .y, .gen, .env)

Arguments

.data

a data frame with one row per plot.

.y, .gen, .env

the columns of the response, genotypes and environments: bare names, strings or vectors.

Value

A list (class c("bam_ge_eff", "bam_result", "list")) with ge_effects (the \(G \times E\) matrix \(\mathbf{Z}\)) and ge_svd (svd() of it: d, u, v).

Details

$$\mathbf{Z} = (z_{ij}), \quad z_{ij} = \bar{y}_{ij} - \bar{y}_{i\cdot} - \bar{y}_{\cdot j} + \bar{y}, \qquad \mathbf{Z} = \sum_k \lambda_k\boldsymbol{\alpha}_k\boldsymbol{\gamma}_k^\top,$$ with singular values \(\lambda_1 \ge \lambda_2 \ge \cdots\) and orthonormal singular vectors orthogonal to \(\mathbf{1}\).

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. \emphCrop Science, \strong51(4), 1458–1469. \doi10.2135/cropsci2010.06.0343

Gauch, H. G. (1992). Statistical Analysis of Regional Yield Trials: AMMI Analysis of Factorial Designs. Elsevier, Amsterdam.

See also

ge_ammi

Author

Muhammad Yaseen (myaseen208@gmail.com)

Examples

data(Maiz)
fit <-
  ge_eff(
      .data = Maiz
    , .y    = y
    , .gen  = entry
    , .env  = site
    )
fit$ge_svd$d
#> [1] 5.922891e+03 3.070454e+03 2.552407e+03 2.320222e+03 1.758671e+03
#> [6] 1.313415e+03 7.926324e+02 7.570277e+02 3.268710e-12