metan (version 1.7.0)

mgidi: Genotype-Ideotype Distance Index

Description

Computes the multi-trait genotype-ideotype distance index (MGIDI). MGIDI can be seen as the multi-trait stability index (Olivoto et al., 2019) computed with weight for mean performance equals to 100. The MGIDI indes is computed as follows:

MGIDI_i = _j = 1^f(F_ij - F_j)^2

where MGIDI_i is the multi-trait genotype-ideotype distance index for the ith genotype; F_ij is the score of the ith genotype in the jth factor (i = 1, 2, ..., g; j = 1, 2, ..., f), being g and f the number of genotypes and factors, respectively, and F_j is the jth score of the ideotype. The genotype with the lowest MGIDI is then closer to the ideotype and therefore presents desired values for all the analyzed traits.

Usage

mgidi(
  .data,
  SI = 15,
  mineval = 1,
  ideotype = NULL,
  use = "complete.obs",
  verbose = TRUE
)

Arguments

.data

An object fitted with the function gafem(), gamem() or a two-way table with BLUPs for genotypes in each trait (genotypes in rows and traits in columns). In the last case, row names must contain the genotypes names.

SI

An integer (0-100). The selection intensity in percentage of the total number of genotypes.

mineval

The minimum value so that an eigenvector is retained in the factor analysis.

ideotype

A vector of length nvar where nvar is the number of variables used to plan the ideotype. Use 'h' to indicate the traits in which higher values are desired or 'l' to indicate the variables in which lower values are desired. For example, ideotype = c("h, h, h, h, l") will consider that the ideotype has higher values for the first four traits and lower values for the last trait. If .data is a model fitted with the functions gafem() or gamem(), the order of the traits will be the declared in the argument resp in those functions.

use

The method for computing covariances in the presence of missing values. Defaults to complete.obs, i.e., missing values are handled by casewise deletion.

verbose

If verbose = TRUE (Default) then some results are shown in the console.

Value

An object of class mgidi with the following items:

• data The data used to compute the factor analysis.

• cormat The correlation matrix among the environments.

• PCA The eigenvalues and explained variance.

• FA The factor analysis.

• KMO The result for the Kaiser-Meyer-Olkin test.

• MSA The measure of sampling adequacy for individual variable.

• communalities The communalities.

• communalities_mean The communalities' mean.

• initial_loadings The initial loadings.

• finish_loadings The final loadings after varimax rotation.

• canonical_loadings The canonical loadings.

• scores_gen The scores for genotypes in all retained factors.

• scores_ide The scores for the ideotype in all retained factors.

• gen_ide The distance between the scores of each genotype with the ideotype.|

• MGIDI The multi-trait genotype-ideotype distance index.

• contri_fac The relative contribution of each factor on the MGIDI value. The lower the contribution of a factor, the close of the ideotype the variables in such factor are.

• sel_dif The selection differential for the variables.

• total_gain The selection differential for the variables.

• sel_gen The selected genotypes.

References

Olivoto, T., A.D.C. L\'ucio, J.A.G. da silva, B.G. Sari, and M.I. Diel. 2019. Mean performance and stability in multi-environment trials II: Selection based on multiple traits. Agron. J. 111:2961-2969. doi:10.2134/agronj2019.03.0220

Examples

# NOT RUN {
library(metan)

model <- gamem(data_g,
               gen = GEN,
               rep = REP,
               resp = c(NR, KW, CW, CL, NKE, TKW, PERK, PH))

# Selection for increase all variables
mgidi_model <- mgidi(model)



# plot the contribution of each factor on the MGIDI index
plot(mgidi_model, type = "contribution")

# }