rAMMIModel: Robust AMMI Model Fitting

In geneticae: Statistical Tools for the Analysis of Multi Environment Agronomic Trials

Robust AMMI Model Fitting

Description

Fits a classical or robust Additive Main effects and Multiplicative Interaction (AMMI) model for genotype-by-environment data.

Usage

rAMMIModel(
  Data,
  genotype = "gen",
  environment = "env",
  response = "Y",
  rep = NULL,
  Ncomp = 2,
  type = "AMMI"
)

Arguments

Data	a dataframe with genotypes, environments, repetitions (if any) and the phenotypic trait of interest. Other variables that will not be used in the analysis can be included.
genotype	column name containing genotypes. Defaults to '"gen"'.
environment	column name containing environments. Defaults to '"env"'.
response	column name containing the phenotypic trait of interest. Defaults to '"Y"'.
rep	column name containing replications. If this argument is 'NULL' (default), it is assumed that the data already contains means per genotype in each environment. If provided, means are calculated automatically.
Ncomp	number of principal components to retain for the interaction part. Defaults to 2.
type	method for fitting the AMMI model: '"AMMI"' (classical), '"rAMMI"', '"hAMMI"', '"gAMMI"', '"lAMMI"' or '"ppAMMI"' (robust variants). Defaults to '"AMMI"'.

Details

To overcome the problem of data contamination with outlying observations, Rodrigues, Monteiro and Lourenco (2015) propose a robust AMMI model based on the M-Huber estimator and robust SVD/PCA procedures.

The 'type' argument allows choosing between several robust strategies:

• AMMI: Classical AMMI model using Least Squares and standard SVD.

• rAMMI: Uses the L1 norm instead of the L2 norm to compute a robust approximation to the SVD (via pcaMethods).

• hAMMI: Uses the Hubert's approach (PcaHubert) combining projection-pursuit and robust covariance estimation.

• gAMMI: Uses the Grid search algorithm for PCA (PcaGrid).

• lAMMI: Performs PCA on the data projected onto a unit sphere (PcaLocantore).

• ppAMMI: Uses projection-pursuit (PcaProj) to calculate robust eigenvalues and eigenvectors.

Value

A list of class rAMMI containing:

gen_scores	Matrix of genotype scores (U * D).
env_scores	Matrix of environment loadings (V).
eigenvalues	Vector of singular values for the retained components.
gen_labels	Names of the genotypes.
env_labels	Names of the environments.
Ncomp	Number of principal components used.
type	The fitting method used.
vartotal	Total variance explained by the multiplicative terms.

References

Rodrigues P.C., Monteiro A., Lourenco V.M. (2015). A robust AMMI model for the analysis of genotype-by-environment data. Bioinformatics 32, 58-66.

Examples

library(agridat)
data(yan.winterwheat)

# Classical AMMI
mod_ammi <- rAMMIModel(yan.winterwheat, genotype = "gen",
                       environment = "env", response = "yield", type = "AMMI")

# Robust AMMI (using Hubert's method)
mod_rammi <- rAMMIModel(yan.winterwheat, genotype = "gen",
                        environment = "env", response = "yield", type = "hAMMI")

geneticae documentation built on April 21, 2026, 5:10 p.m.