waasb  R Documentation 
Compute the Weighted Average of Absolute Scores (Olivoto et al., 2019) for quantifying the stability of g genotypes conducted in e environments using linear mixedeffect models.
The weighted average of absolute scores is computed considering all Interaction Principal Component Axis (IPCA) from the Singular Value Decomposition (SVD) of the matrix of genotypeenvironment interaction (GEI) effects generated by a linear mixedeffect model, as follows: \loadmathjax \mjsdeqnWAASB_i = \sum_k = 1^p IPCA_ik \times EP_k/ \sum_k = 1^pEP_k
where \mjseqnWAASB_i is the weighted average of absolute scores of the ith genotype; \mjseqnIPCA_ik is the score of the ith genotype in the kth Interaction Principal Component Axis (IPCA); and \mjseqnEP_k is the explained variance of the kth IPCA for k = 1,2,..,p, considering \mjseqnp = min(g  1; e  1).
The nature of the effects in the model is
chosen with the argument random
. By default, the experimental design
considered in each environment is a randomized complete block design. If
block
is informed, a resolvable alphalattice design (Patterson and
Williams, 1976) is implemented. The following six models can be fitted
depending on the values of random
and block
arguments.
Model 1: block = NULL
and random = "gen"
(The
default option). This model considers a Randomized Complete Block Design in
each environment assuming genotype and genotypeenvironment interaction as
random effects. Environments and blocks nested within environments are
assumed to fixed factors.
Model 2: block = NULL
and random = "env"
. This
model considers a Randomized Complete Block Design in each environment
treating environment, genotypeenvironment interaction, and blocks nested
within environments as random factors. Genotypes are assumed to be fixed
factors.
Model 3: block = NULL
and random = "all"
. This
model considers a Randomized Complete Block Design in each environment
assuming a randomeffect model, i.e., all effects (genotypes, environments,
genotypevsenvironment interaction and blocks nested within environments)
are assumed to be random factors.
Model 4: block
is not NULL
and random = "gen"
. This model considers an alphalattice design in each environment
assuming genotype, genotypeenvironment interaction, and incomplete blocks
nested within complete replicates as random to make use of interblock
information (Mohring et al., 2015). Complete replicates nested within
environments and environments are assumed to be fixed factors.
Model 5: block
is not NULL
and random = "env"
. This model considers an alphalattice design in each environment
assuming genotype as fixed. All other sources of variation (environment,
genotypeenvironment interaction, complete replicates nested within
environments, and incomplete blocks nested within replicates) are assumed
to be random factors.
Model 6: block
is not NULL
and random = "all"
. This model considers an alphalattice design in each environment
assuming all effects, except the intercept, as random factors.
waasb( .data, env, gen, rep, resp, block = NULL, by = NULL, mresp = NULL, wresp = NULL, random = "gen", prob = 0.05, ind_anova = FALSE, verbose = TRUE, ... )
.data 
The dataset containing the columns related to Environments, Genotypes, replication/block and response variable(s). 
env 
The name of the column that contains the levels of the environments. 
gen 
The name of the column that contains the levels of the genotypes. 
rep 
The name of the column that contains the levels of the replications/blocks. 
resp 
The response variable(s). To analyze multiple variables in a
single procedure a vector of variables may be used. For example 
block 
Defaults to 
by 
One variable (factor) to compute the function by. It is a shortcut
to 
mresp 
The new maximum value after rescaling the response variable. By
default, all variables in 
wresp 
The weight for the response variable(s) for computing the WAASBY
index. By default, all variables in 
random 
The effects of the model assumed to be random. Defaults to

prob 
The probability for estimating confidence interval for BLUP's prediction. 
ind_anova 
Logical argument set to 
verbose 
Logical argument. If 
... 
Arguments passed to the function

An object of class waasb
with the following items for each
variable:
individual A withinenvironments ANOVA considering a fixedeffect model.
fixed Test for fixed effects.
random Variance components for random effects.
LRT The Likelihood Ratio Test for the random effects.
model A tibble with the response variable, the scores of all IPCAs, the estimates of Weighted Average of Absolute Scores, and WAASBY (the index that considers the weights for stability and mean performance in the genotype ranking), and their respective ranks.
BLUPgen The random effects and estimated BLUPS for genotypes (If
random = "gen"
or random = "all"
)
BLUPenv The random effects and estimated BLUPS for environments,
(If random = "env"
or random = "all"
).
BLUPint The random effects and estimated BLUPS of all genotypes in all environments.
PCA The results of Principal Component Analysis with the eigenvalues and explained variance of the matrix of genotypeenvironment effects estimated by the linear fixedeffect model.
MeansGxE The phenotypic means of genotypes in the environments.
Details A list summarizing the results. The following information
are shown: Nenv
, the number of environments in the analysis;
Ngen
the number of genotypes in the analysis; mresp
The value
attributed to the highest value of the response variable after rescaling it;
wresp
The weight of the response variable for estimating the WAASBY
index. Mean
the grand mean; SE
the standard error of the mean;
SD
the standard deviation. CV
the coefficient of variation of
the phenotypic means, estimating WAASB, Min
the minimum value observed
(returning the genotype and environment), Max
the maximum value
observed (returning the genotype and environment); MinENV
the
environment with the lower mean, MaxENV
the environment with the
larger mean observed, MinGEN
the genotype with the lower mean,
MaxGEN
the genotype with the larger.
ESTIMATES A tibble with the genetic parameters (if random = "gen"
or random = "all"
) with the following columns: Phenotypic variance
the phenotypic variance; Heritability
the broadsense
heritability; GEr2
the coefficient of determination of the interaction
effects; h2mg
the heritability on the mean basis;
Accuracy
the selective accuracy; rge
the genotypeenvironment
correlation; CVg
the genotypic coefficient of variation; CVr
the residual coefficient of variation; CV ratio
the ratio between
genotypic and residual coefficient of variation.
residuals The residuals of the model.
formula The formula used to fit the model.
Tiago Olivoto tiagoolivoto@gmail.com
Olivoto, T., A.D.C. L\'ucio, J.A.G. da silva, V.S. Marchioro, V.Q. de Souza, and E. Jost. 2019. Mean performance and stability in multienvironment trials I: Combining features of AMMI and BLUP techniques. Agron. J. 111:29492960. doi: 10.2134/agronj2019.03.0220
Mohring, J., E. Williams, and H.P. Piepho. 2015. Interblock information: to recover or not to recover it? TAG. Theor. Appl. Genet. 128:154154. doi: 10.1007/s0012201525300
Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:8392.
mtsi()
waas()
get_model_data()
plot_scores()
library(metan) #===============================================================# # Example 1: Analyzing all numeric variables assuming genotypes # # as random effects with equal weights for mean performance and # # stability # #===============================================================# model < waasb(data_ge, env = ENV, gen = GEN, rep = REP, resp = everything()) # Genetic parameters get_model_data(model, "genpar") #===============================================================# # Example 2: Analyzing variables that starts with "N" # # assuming environment as random effects with higher weight for # # response variable (65) for the three traits. # #===============================================================# model2 < waasb(data_ge2, env = ENV, gen = GEN, rep = REP, random = "env", resp = starts_with("N"), wresp = 65) # Get the index WAASBY get_model_data(model2, what = "WAASBY") #===============================================================# # Example 3: Analyzing GY and HM assuming a randomeffect model.# # Smaller values for HM and higher values for GY are better. # # To estimate WAASBY, higher weight for the GY (60%) and lower # # weight for HM (40%) are considered for mean performance. # #===============================================================# model3 < waasb(data_ge, env = ENV, gen = GEN, rep = REP, resp = c(GY, HM), random = "all", mresp = c("h, l"), wresp = c(60, 40)) # Plot the scores (response x WAASB) plot_scores(model3, type = 3)
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