Title:	Statistical Tools for the Analysis of Multi Environment Agronomic Trials
Version:	0.4.0
Description:	Data from multi environment agronomic trials, which are often carried out by plant breeders, can be analyzed with the tools offered by this package such as the Additive Main effects and Multiplicative Interaction model or 'AMMI' ('Gauch' 1992, ISBN:9780444892409) and the Site Regression model or 'SREG' ('Cornelius' 1996, <doi:10.1201/9780367802226>). Since these methods present a poor performance under the presence of outliers and missing values, this package includes robust versions of the 'AMMI' model ('Rodrigues' 2016, <doi:10.1093/bioinformatics/btv533>), and also imputation techniques specifically developed for this kind of data ('Arciniegas-Alarcón' 2014, <doi:10.2478/bile-2014-0006>).
License:	GPL-2
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.1.2
Imports:	stats, GGEBiplots, ggforce, ggplot2, scales, MASS, pcaMethods, rrcov, dplyr, missMDA, calibrate, graphics, reshape2, matrixStats, tidyr, prettydoc, rlang
Suggests:	agridat, spelling, knitr, rmarkdown, testthat
VignetteBuilder:	knitr
Depends:	R (≥ 2.12.0)
URL:	https://jangelini.github.io/geneticae/
BugReports:	https://github.com/jangelini/geneticae/issues
Language:	en-US
NeedsCompilation:	no
Packaged:	2022-07-20 12:32:08 UTC; julia-fedora
Author:	Julia Angelini [aut, cre], Marcos Prunello [aut], Gerardo Cervigni [aut]
Maintainer:	Julia Angelini <jangelini_93@hotmail.com>
Repository:	CRAN
Date/Publication:	2022-07-20 15:40:06 UTC

EM-AMMI imputation method

Description

This function was writted 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.

GGE biplots with ggplot2

Description

GGE biplots are used for visual examination of the relationships between test environments, genotypes, and genotype-by-environment interactions. ‘GGEPlot()' produces a biplot as an object of class ’ggplot', using the output of the GGEmodel 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 GGEPlot from the GGEBiplots package.

Usage

GGEPlot(
  GGEModel,
  type = "Biplot",
  d1 = 1,
  d2 = 2,
  selectedE = NA,
  selectedG = NA,
  selectedG1 = NA,
  selectedG2 = NA,
  colGen = "gray47",
  colEnv = "darkred",
  colSegment = "gray30",
  colHull = "gray30",
  sizeGen = 4,
  sizeEnv = 4,
  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 <- GGEmodel(yan.winterwheat)
 GGEPlot(GGE1)

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

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, such as the GGEModel from the GGEBiplots package. 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

GGEmodel(
  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 <- GGEmodel(yan.winterwheat, genotype="gen", environment="env", response="yield")

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

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

agregar descripcion.

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-byenvironment 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 or GGE 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

• 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

imputed data matrix

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.

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-byenvironment 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)
plrv[1,3] <- NA
plrv[3,3] <- NA
plrv[2,3] <- NA
imputation(plrv, genotype = "Genotype", environment = "Locality",
           response = "Yield", rep = "Rep", type = "EM-AMMI")

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)

AMMI biplots with ggplot2

Description

Produces classical or robust AMMI biplot as an object of class 'ggplot', with options for customization.

Usage

rAMMI(
  Data,
  genotype = "gen",
  environment = "env",
  response = "Y",
  rep = NULL,
  Ncomp = 2,
  type = "AMMI",
  colGen = "gray47",
  colEnv = "darkred",
  sizeGen = 4,
  sizeEnv = 4,
  titles = TRUE,
  footnote = TRUE,
  axis_expand = 1.2,
  limits = TRUE,
  axes = TRUE,
  axislabels = TRUE
)

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 in robusts SVD/PCA procedures. Several SVD/PC methods were considered, briefly described below, thus conveying a total of five robust AMMI candidate models:

• R-AMMI: uses the L1 norm instead of the more usual least squares L2 norm, to compute a robust approximation to the SVD of a rectangular matrix.

• H-AMMI: Combines projection-pursuit and robust covariance estimation techniques to compute the robust loadings. It is most adequate for high-dimensional data.

• G-AMMI: Uses projection-pursuit to compute PCA estimators. The optimization is done via the grid search algorithm in the plane instead of the p-dimensional space.

• L-AMMI: The idea behind this approach is to perform classical PCA on the data but projected onto a unit sphere. When the data are elliptically distributed the estimates of the eigenvectors are consistent

• PP-AMMI: Uses projection-pursuit calculating the robust eigenvalues and eigenvectors without going through robust covariance estimation. The principal components can be sequentially computed and thus this method is very appealing when few genotypes are evaluated under a wide range of environmental and/or experimental conditions.

Value

A biplot of class ggplot

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(geneticae)
# Data without replication
library(agridat)
data(yan.winterwheat)
BIP_AMMI <- rAMMI(yan.winterwheat, genotype = "gen", environment = "env",
                  response = "yield", type = "AMMI")
BIP_AMMI

# Data with replication
data(plrv)
BIP_AMMI2 <- rAMMI(plrv, genotype = "Genotype", environment = "Locality",
                   response="Yield", rep = "Rep", type = "AMMI")
BIP_AMMI2