Title:	Statistical Tools for the Analysis of Multi Environment Agronomic Trials
Version:	1.0.1
Description:	Provides tools for the analysis of multi-environment agronomic trials, with a specific focus on plant breeding experiments. Implements the Additive Main effects and Multiplicative Interaction (AMMI) model (Gauch, 1992, ISBN:9780444892409) and the Site Regression (SREG) model (Cornelius, 1996, <doi:10.1201/9780367802226>). To ensure reliable results even with outliers or missing data, it includes robust versions of AMMI (Rodrigues et al., 2016, <doi:10.1093/bioinformatics/btv533>) and SREG (Angelini et al., 2022, <doi:10.1080/15427528.2022.2051217>). Furthermore, the package offers advanced imputation techniques for multi-environment data, covering classical methodologies (Arciniegas-Alarcón et al., 2014, <doi:10.2478/bile-2014-0006>) and recently published imputation methods for MET data (Angelini et al., 2024, <doi:10.1007/s10681-024-03344-z>).
License:	GPL-2
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.3
Imports:	stats, ggforce, ggplot2, scales, MASS, pcaMethods, rrcov, dplyr, missMDA, tidyr, rlang, corpcor
Suggests:	agridat, spelling, knitr, rmarkdown, patchwork, testthat
VignetteBuilder:	knitr
Depends:	R (≥ 2.12.0)
URL:	https://jangelini.github.io/geneticae/, https://github.com/jangelini/geneticae
BugReports:	https://github.com/jangelini/geneticae/issues
Language:	en-US
NeedsCompilation:	no
Packaged:	2026-04-20 22:45:40 UTC; julia
Author:	Julia Angelini [aut, cre], Marcos Prunello [aut], Gerardo Cervigni [aut]
Maintainer:	Julia Angelini <jangelini_93@hotmail.com>
Repository:	CRAN
Date/Publication:	2026-04-21 10:52:14 UTC

Biplot Imputation Method

Description

This function implements the Biplot imputation method as proposed by Yan (2013). It is an iterative algorithm that uses the singular value decomposition (SVD) to impute missing values in a genotype by environment matrix.

Usage

BiplotImputfun(X, precision = 0.01, max.iter = 1000, n_pc = 2)

Arguments

Value

A list containing:

• X_imputed: The final matrix with missing values filled.

• iteration: Total number of iterations performed.

• convergence: Final relative change reached.

• fitted: The fitted values from the AMMI/Biplot model.

References

Yan, W. (2013). Biplot analysis of incomplete two-way data. Crop Science, 53(1), 48-57. doi:10.2135/cropsci2012.05.0301

Arciniegas-Alarcón, S., García-Peña, M., Krzanowski, W., & Dias, C. T. S. (2014b). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects. Biometrical Letters, 51(2), 75-88. doi:10.2478/bile-2014-0006

EM-AMMI imputation method

Description

This function was written by Paderewski (2013) and allow imputing missing values by the EM-AMMI algorithm

Usage

EM.AMMI(
  X,
  PC.nb = 1,
  initial.values = NA,
  precision = 0.01,
  max.iter = 1000,
  change.factor = 1,
  simplified.model = FALSE
)

Arguments

Value

A list containing:

• X: the imputed matrix (filled in with the missing values estimated by the EM-AMMI procedure);

• PC.SS: the sum of squares representing variation explained by the principal components (the squares of eigenvalues of singular value decomposition);

• iteration: the final number of iterations;

• precision.final: the maximum change of the estimated values for missing cells in the last step of iteration (the precision of convergence) . If the algorithm converged, this value is slightly smaller than the argument precision;

• PC.nb.final: a number of principal components that were eventually used by the EM.AMMI() function. The function checks if there are too many missing cells to unambiguously compute the parameters by the SVD decomposition (Gauch and Zobel, 1990). In that case the final number of principal components used is smaller than that which was passed on to the function through the argument PC.nb;

• convergence: the value TRUE means that the algorithm converged in the last iteration.

References

Paderewski, J. (2013). An R function for imputation of missing cells in two-way initial.values), the simplified model can be used to determine a better set of initial values. data sets by EM-AMMI algorithm.. Communications in Biometry and Crop Science 8, 60–69.

EM-SREG Imputation Method

Description

Iterative algorithm to impute missing values in two-way tables using the Sites Regression (SREG) model. It supports several variants including standard SVD and Bayesian PCA.

Usage

EM.SREG(
  X,
  PC.nb = 1,
  initial.values = NA,
  precision = 0.01,
  max.iter = 1000,
  change.factor = 1,
  simplified.model = FALSE,
  type = c("EM-SREG", "EM-bSREG")
)

Arguments

Value

A list containing:

• X: The imputed matrix.

• iter: The number of iterations until convergence.

References

Angelini, J., Cervigni, G. D. L., & Quaglino, M. B. (2024). New imputation methodologies for genotype-by-environment data: an extensive study of properties of estimators. Euphytica, 220(6), 92. doi:10.1007/s10681-024-03344-z

Eigenvector Imputation Function (Internal)

Description

Internal function for GxE imputation using the Krzanowski (1988) eigenvector approach with a leave-one-out strategy.

Usage

Eigenvectorfun(X, f)

Arguments

Value

A list with the number of iterations, convergence status, final rank used, and the imputed matrix.

GabrielEigen imputation method

Description

GabrielEigen imputation method

Usage

Gabriel.Calinski(X)

Arguments

Value

A list containing:

• NumeroIterGabriel: final number of iterations;

• CritConvergGabriel: maximum change of the estimated values for missing cells in the last step of iteration (precision of convergence);

• GabrielImput: imputed matrix (filled in with missing values estimated by the GabrielEigein procedure).

References

Arciniegas-Alarcón S., García-Peña M., Dias C.T.S., Krzanowski W.J. (2010). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction. Biometrical Letters 47, 1–14.

Weighted GabrielEigen imputation method

Description

Weighted GabrielEigen imputation method

Usage

WGabriel(DBmiss, Winf, Wsup)

Arguments

Value

A list containing:

• Peso: weight that provides the best predictive difference;

• NumeroIterWGabriel: the final number of iterations;

• CritConvergWGabriel: the maximum change of the estimated values for missing cells in the last step of iteration (the precision of convergence);

• GabrielWImput: the imputed matrix (filled in with the missing values estimated by the Weighted GabrielEigen procedure).

References

Arciniegas-Alarcón S., García-Peña M., Krzanowski W.J., Dias C.T.S. (2014). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects. Biometrical Letters 51, 75-88.

Imputation of missing cells in two-way data sets

Description

Missing values are not allowed by the AMMI, GGE or SREG methods. This function provides several methods to impute missing observations in data from multi-environment trials and to subsequently adjust the mentioned methods.

Usage

imputation(
  Data,
  genotype = "gen",
  environment = "env",
  response = "yield",
  rep = NULL,
  type = "EM-AMMI",
  nPC = 2,
  initial.values = NA,
  precision = 0.01,
  maxiter = 1000,
  change.factor = 1,
  simplified.model = FALSE,
  scale = TRUE,
  method = "EM",
  row.w = NULL,
  coeff.ridge = 1,
  seed = NULL,
  nb.init = 1,
  Winf = 0.8,
  Wsup = 1
)

Arguments

Details

Often, multi-environment experiments are unbalanced because several genotypes are not tested in some environments. Several methodologies have been proposed in order to solve this lack of balance caused by missing values, some of which are included in this function:

• EM-AMMI: an iterative scheme built round the above procedure is used to obtain AMMI imputations from the EM algorithm. The additive parameters are initially set by computing the grand mean, genotype means and environment means obtained from the observed data. The residuals for the observed cells are initialized as the cell mean minus the genotype mean minus the environment mean plus the grand mean, and interactions for the missing positions are initially set to zero. The initial multiplicative parameters are obtained from the SVD of this matrix of residuals, and the missing values are filled by the appropriate AMMI estimates. In subsequent iterations, the usual AMMI procedure is applied to the completed matrix and the missing values are updated by the corresponding AMMI estimates. The arguments used for this method are:initial.values, precision, maxiter, change.factor and simplified.model

• EM-GGE: Iterative SVD-based imputation focusing on G+GE.

• EM-SREG: Iterative algorithm using the Sites Regression model. Supports variants like standard SVD and Bayesian PCA (EM-bSREG).

• Gabriel: combines regression and lower-rank approximation using SVD. This method initially replaces the missing cells by arbitrary values, and subsequently the imputations are refined through an iterative scheme that defines a partition of the matrix for each missing value in turn and uses a linear regression of columns (or rows) to obtain the new imputation. The arguments used for this method is only the dataframe.

• WGabriel: is a a modification of Gabriel method that uses weights chosen by cross-validation. The arguments used for this method are Winf and Wsup.

• EM-PCA: impute the missing entries of a mixed data using the iterative PCA algorithm. The algorithm first consists imputing missing values with initial values. The second step of the iterative PCA algorithm is to perform PCA on the completed dataset to estimate the parameters. Then, it imputes the missing values with the reconstruction formulae of order nPC (the fitted matrix computed with nPC components for the scores and loadings). These steps of estimation of the parameters via PCA and imputation of the missing values using the fitted matrix are iterate until convergence. The arguments used for this methods are: nPC, scale, method, row.w, coeff.ridge, precision, seed, nb.init and maxiter

Value

A matrix of the imputed data.

References

Paderewski, J. (2013). An R function for imputation of missing cells in two-way data sets by EM-AMMI algorithm. Communications in Biometry and Crop Science 8, 60–69.

Yan, W. (2013). Biplot analysis of incomplete two-way data. Crop Science, 53(1), 48-57. doi:10.2135/cropsci2012.05.0301

Arciniegas-Alarcón, S., García-Peña, M., Krzanowski, W., & Dias, C. T. S. (2014b). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects. Biometrical Letters, 51(2), 75-88. doi:10.2478/bile-2014-0006

Angelini, J., Cervigni, G. D. L., & Quaglino, M. B. (2024). New imputation methodologies for genotype-by-environment data: an extensive study of properties of estimators. Euphytica, 220(6), 92. doi:10.1007/s10681-024-03344-z

Julie Josse, Francois Husson (2016). missMDA: A Package for Handling Missing Values in Multivariate Data Analysis. Journal of Statistical Software 70, 1-31.

Arciniegas-Alarcón S., García-Peña M., Dias C.T.S., Krzanowski W.J. (2010). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction. Biometrical Letters 47, 1–14.

Arciniegas-Alarcón S., García-Peña M., Krzanowski W.J., Dias C.T.S. (2014). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects. Biometrical Letters 51, 75-88.

Examples

library(geneticae)
# Data without replications
library(agridat)
data(yan.winterwheat)

# generating missing values
yan.winterwheat[1,3]<-NA
yan.winterwheat[3,3]<-NA
yan.winterwheat[2,3]<-NA

imputation(yan.winterwheat, genotype = "gen", environment = "env",
           response = "yield", type = "EM-AMMI")

# Data with replications
data(plrv)
head(plrv)
plrv$Yield[plrv$Locality == "Ayac" & plrv$Rep %in% c(1, 2, 3) & plrv$Genotype == '102.18'] <- NA

imputation(plrv, nPC = 2,genotype = "Genotype", environment = "Locality", 
           response = "Yield", rep ='Rep', type = "EM-AMMI")
           
imputation(plrv, genotype = "Genotype", environment = "Locality", 
           response = "Yield", rep ='Rep', type = "EM-SREG")

Clones from the PLRV population

Description

resistance study to PLRV (Patato Leaf Roll Virus) causing leaf curl. 28 genotypes were experimented at 6 locations in Peru. Each clone was evaluated three times in each environment, and yield, plant weight and plot were registered.

Usage

data(plrv)

Format

Data frame with 504 observations and 6 variables (genotype, locality, repetition, weightPlant, weightPlot and yield).

References

Felipe de Mendiburu (2020). agricolae: Statistical Procedures for Agricultural Research. R package version 1.3-2. https://CRAN.R-project.org/package=agricolae

Examples

library(geneticae)
data(plrv)
str(plrv)

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

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:

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")

AMMI Biplots with ggplot2

Description

Generates a high-quality biplot (PC1 vs PC2) for classical or robust AMMI models using the ggplot2 framework.

Usage

rAMMIPlot(
  model_res,
  colGen = "gray47",
  colEnv = "darkred",
  sizeGen = 6,
  sizeEnv = 6,
  titles = TRUE,
  footnote = TRUE,
  axis_expand = 1.2,
  limits = TRUE,
  axes = TRUE,
  axislabels = TRUE
)

Arguments

Details

the biplot is constructed using a scaling factor of 0.5 (symmetric scaling), which allows representing both genotypes and environments in the same algebraic space. Genotypes are displayed as points (text), and environments are represented as vectors from the origin.

Value

A ggplot2 object. This allows further customization using standard ggplot layers (e.g., + theme_bw()).

Examples

library(agridat)
data(yan.winterwheat)

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

rAMMIPlot(mod_ammi,sizeGen=4,sizeEnv=4)

data(plrv)
mod_ammi_rep <- rAMMIModel(plrv, genotype="Genotype", environment="Locality", 
                        response="Yield", rep="Rep", type="AMMI")
rAMMIPlot(mod_ammi_rep,sizeGen=4,sizeEnv=4)

Site Regression model

Description

The Site Regression model (also called genotype + genotype-by-environment (GGE) model) is a powerful tool for effective analysis and interpretation of data from multi-environment trials in breeding programs. There are different functions in R to fit the SREG model, however, this function has the following improvements:

• Includes recently published robust versions of the SREG model (Angelini et al., 2022).

• It can be used for data from trials with repetitions (there is no need to calculate means beforehand).

• Other variables not used in the analysis can be present in the dataset.

Usage

rSREGModel(
  Data,
  genotype = "gen",
  environment = "env",
  response = "yield",
  rep = NULL,
  model = "SREG",
  SVP = "symmetrical"
)

Arguments

Details

A linear model by robust regression using an M estimator proposed by Huber (1964, 1973) fitted by iterated re-weighted least squares, in combination with three robust SVD/PCA procedures, resulted in a total of three robust SREG alternatives. The robust SVD/PCA considered were:

• CovSREG: robust PCA that is obtained by replacing the classical estimates of location and covariance by their robust analogues using Minimum Regularized Covariance Determinant (MRCD) approach;

• hSREG: robust PCA method that tries to combine the advantages of both approaches, PCA based on a robust covariance matrix and based on projection pursuit;

• ppSREG: robust PCA that uses the projection pursuit and directly calculates the robust estimates of the eigenvalues and eigenvectors without going through robust covariance estimation. It is a very attractive method for bigdata situations, which are very common in METs (a few genotypes tested in a large number of environments), as the principal components can be calculated sequentially.

Value

A list of class GGE_Model containing:

A biplot of class ggplot

References

Julia Angelini, Gabriela Faviere, Eugenia Bortolotto, Gerardo Domingo Lucio Cervigni & Marta Beatriz Quaglino (2022) Handling outliers in multi-environment trial data analysis: in the direction of robust SREG model, Journal of Crop Improvement, doi:10.1080/15427528.2022.2051217

Examples

 library(geneticae)

 # Data without replication
 library(agridat)
 data(yan.winterwheat)
 GGE1 <- rSREGModel(yan.winterwheat, genotype="gen", environment="env", response="yield")

 # Data with replication
 data(plrv)
 GGE2 <- rSREGModel(plrv, genotype = "Genotype", environment = "Locality",
                  response = "Yield", rep = "Rep")

GGE biplots with ggplot2

Description

GGE biplots are used for visual examination of the relationships between test environments, genotypes, and genotype-by-environment interactions. ‘rSREGPlot()' produces a biplot as an object of class ’ggplot', using the output of the rSREGModel function. Several types of biplots are offered which focus on different aspects of the analysis. Customization options are also included. This function is a modification of the 'rSREGPlot' function from the GGEBiplots package.

Usage

rSREGPlot(
  rSREGModel,
  type = "Biplot",
  d1 = 1,
  d2 = 2,
  selectedE = NA,
  selectedG = NA,
  selectedG1 = NA,
  selectedG2 = NA,
  colGen = "gray47",
  colEnv = "darkred",
  colSegment = "gray30",
  colHull = "gray30",
  sizeGen = 6,
  sizeEnv = 6,
  largeSize = 4.5,
  axis_expand = 1.2,
  axislabels = TRUE,
  axes = TRUE,
  limits = TRUE,
  titles = TRUE,
  footnote = TRUE
)

Arguments

Value

A biplot of class ggplot

References

Yan W, Kang M (2003). GGE Biplot Analysis: A Graphical Tool for Breeders, Geneticists, and Agronomists. CRC Press.

Sam Dumble (2017). GGEBiplots: GGE Biplots with 'ggplot2'. R package version 0.1.1. https://CRAN.R-project.org/package=GGEBiplots

Examples

 library(geneticae)

 # Data without replication
 library(agridat)
 data(yan.winterwheat)
 GGE1 <- rSREGModel(yan.winterwheat)
 rSREGPlot(GGE1, sizeGen=4, sizeEnv=4)

 # Data with replication
 data(plrv)
 GGE2 <- rSREGModel(plrv, genotype = "Genotype", environment = "Locality",
                  response = "Yield", rep = "Rep")
 rSREGPlot(GGE2, sizeGen=4, sizeEnv=4)