Computes the multi-trait stability index proposed by Olivoto et al. (2019) considering different parametric and non-parametric stability indexes.

## Usage

mtmps(model, SI = 15, mineval = 1, verbose = TRUE)

## Arguments

model

An object of class mtmps

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.

verbose

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

## Value

An object of class mtmps 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.

• scores_gen The scores for genotypes in all retained factors.

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

• MTSI The multi-trait mean performance and stability index.

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

• contri_fac_rank, contri_fac_rank_sel The rank for the contribution of each factor for all genotypes and selected genotypes, respectively.

• sel_dif_trait, sel_dif_stab, sel_dif_mps A data frame containing the selection differential (gains) for the mean performance, stability index, and mean performance and stability index, respectively. The following variables are shown.

• VAR: the trait's name.

• Factor: The factor that traits where grouped into.

• Xo: The original population mean.

• Xs: The mean of selected genotypes.

• SD and SDperc: The selection differential and selection differential in percentage, respectively.

• h2: The broad-sense heritability.

• SG and SGperc: The selection gains and selection gains in percentage, respectively.

• sense: The desired selection sense.

• goal: selection gains match desired sense? 100 for yes and 0 for no.

• stat_dif_trait, stat_dif_stab, stat_dif_mps A data frame with the descriptive statistic for the selection gains for the mean performance, stability index, and mean performance and stability index, respectively. The following columns are shown by sense.

• sense: The desired selection sense.

• variable: the trait's name.

• min: the minimum value for the selection gain.

• mean: the mean value for the selection gain.

• ci: the confidence interval for the selection gain.

• sd.amo: the standard deviation for the selection gain.

• max: the maximum value for the selection gain.

• sum: the sum of the selection gain.

• 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

mgidi(), mps(), get_model_data()

## Author

Tiago Olivoto tiagoolivoto@gmail.com

## Examples

# \donttest{
library(metan)
# The same approach as mtsi()
# mean performance and stability for GY and HM
# mean performance: The genotype's BLUP
# stability: the WAASB index (lower is better)
# weights: equal for mean performance and stability

model <-
mps(data_ge,
env = ENV,
gen = GEN,
rep = REP,
resp = everything())
#> Evaluating trait GY |======================                      | 50% 00:00:00
Evaluating trait HM |============================================| 100% 00:00:01

#> Method: REML/BLUP
#> Random effects: GEN, GEN:ENV
#> Fixed effects: ENV, REP(ENV)
#> Denominador DF: Satterthwaite's method
#> ---------------------------------------------------------------------------
#> P-values for Likelihood Ratio Test of the analyzed traits
#> ---------------------------------------------------------------------------
#>     model       GY       HM
#>  COMPLETE       NA       NA
#>       GEN 1.11e-05 5.07e-03
#>   GEN:ENV 2.15e-11 2.27e-15
#> ---------------------------------------------------------------------------
#> All variables with significant (p < 0.05) genotype-vs-environment interaction
#> Mean performance: blupg
#> Stability: waasb
selection <- mtmps(model)
#>
#> -------------------------------------------------------------------------------
#> Principal Component Analysis
#> -------------------------------------------------------------------------------
#> # A tibble: 2 × 4
#>   PC    Eigenvalues Variance (%) Cum. variance (%)
#>   <chr>       <dbl>          <dbl>               <dbl>
#> 1 PC1         1.37            68.5                68.5
#> 2 PC2         0.631           31.5               100
#> -------------------------------------------------------------------------------
#> Factor Analysis - factorial loadings after rotation-
#> -------------------------------------------------------------------------------
#> # A tibble: 2 × 4
#>   VAR     FA1 Communality Uniquenesses
#>   <chr> <dbl>       <dbl>        <dbl>
#> 1 GY    0.827       0.685        0.315
#> 2 HM    0.827       0.685        0.315
#> -------------------------------------------------------------------------------
#> Comunalit Mean: 0.6846623
#> -------------------------------------------------------------------------------
#> Selection differential for the mean performance and stability index
#> -------------------------------------------------------------------------------
#> # A tibble: 2 × 6
#>   VAR   Factor    Xo    Xs    SD SDperc
#>   <chr> <chr>  <dbl> <dbl> <dbl>  <dbl>
#> 1 GY    FA 1    48.3  86.4  38.0   78.7
#> 2 HM    FA 1    58.3  79.2  21.0   36.0
#> -------------------------------------------------------------------------------
#> Selection differential for the mean of the variables
#> -------------------------------------------------------------------------------
#> # A tibble: 2 × 11
#>   VAR   Factor    Xo    Xs    SD SDperc    h2    SG SGperc sense     goal
#>   <chr> <chr>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>  <dbl> <chr>    <dbl>
#> 1 GY    FA 1    2.67  2.98 0.305 11.4   0.815 0.249  9.31  increase   100
#> 2 HM    FA 1   48.1  48.4  0.265  0.551 0.686 0.182  0.378 increase   100
#> ------------------------------------------------------------------------------
#> Selected genotypes
#> -------------------------------------------------------------------------------
#> G8 G3
#> -------------------------------------------------------------------------------

# gains for stability
selection$sel_dif_stab #> # A tibble: 2 × 7 #> VAR Xo Xs SD SDperc sense goal #> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> #> 1 GY 0.250 0.182 -0.0686 -27.4 decrease 100 #> 2 HM 0.614 0.400 -0.214 -34.9 decrease 100 # gains for mean performance selection$sel_dif_trait
#> # A tibble: 2 × 11
#>   VAR   Factor    Xo    Xs    SD SDperc    h2    SG SGperc sense     goal
#>   <chr> <chr>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>  <dbl> <chr>    <dbl>
#> 1 GY    FA 1    2.67  2.98 0.305 11.4   0.815 0.249  9.31  increase   100
#> 2 HM    FA 1   48.1  48.4  0.265  0.551 0.686 0.182  0.378 increase   100
# }