Computes the multi-trait stability index proposed by Olivoto et al. (2019)

mtsi(.data, index = "waasby", SI = 15, mineval = 1, verbose = TRUE)

Arguments

.data

An object of class waasb or waas.

index

If index = 'waasby' (default) both stability and mean performance are considered. If index = 'waasb' the multi-trait index will be computed considering the stability of genotypes only. More details can be seen in waasb and waas functions.

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) then some results are shown in the console.

Value

An object of class mtsi 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.

  • MTSI The multi-trait 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.

  • sel.dif The selection differential for the WAASBY or WAASB index.

  • mean.sd The mean for the differential selection.

  • sel.dif.var The selection differential for the variables.

  • Selected 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

Author

Tiago Olivoto tiagoolivoto@gmail.com

Examples

# \donttest{ library(metan) # Based on stability only, for both GY and HM, higher is better mtsi_model <- waasb(data_ge, env = ENV, gen = GEN, rep = REP, resp = c(GY, HM))
#> 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
mtsi_index <- mtsi(mtsi_model, index = 'waasb')
#> #> ------------------------------------------------------------------------------- #> Principal Component Analysis #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 4 #> PC Eigenvalues `Variance (%)` `Cum. variance (%)` #> <chr> <dbl> <dbl> <dbl> #> 1 PC1 1.66 82.8 82.8 #> 2 PC2 0.343 17.2 100 #> ------------------------------------------------------------------------------- #> Factor Analysis - factorial loadings after rotation- #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 4 #> VAR FA1 Communality Uniquenesses #> <chr> <dbl> <dbl> <dbl> #> 1 GY 0.910 0.828 0.172 #> 2 HM 0.910 0.828 0.172 #> ------------------------------------------------------------------------------- #> Comunalit Mean: 0.8283129 #> ------------------------------------------------------------------------------- #> Selection differential for the waasb index #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 6 #> VAR Factor Xo Xs SD SDperc #> <chr> <chr> <dbl> <dbl> <dbl> <dbl> #> 1 GY FA 1 0.250 0.117 -0.134 -53.5 #> 2 HM FA 1 0.614 0.373 -0.241 -39.2 #> ------------------------------------------------------------------------------ #> Mean of selection differential #> ------------------------------------------------------------------------------- #> Xo Xs SD SDperc #> 0.4323231 0.2448764 -0.1874467 -46.3570842 #> ------------------------------------------------------------------------------- #> Selection differential for the mean of the variables #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 8 #> VAR Factor xo Xs SD SDperc sense goal #> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> #> 1 GY FA 1 2.67 2.78 0.105 3.94 increase 100 #> 2 HM FA 1 48.1 47.3 -0.747 -1.55 increase 0 #> ------------------------------------------------------------------------------ #> Selected genotypes #> ------------------------------------------------------------------------------- #> G3 G1 #> -------------------------------------------------------------------------------
# Based on mean performance and stability (using pipe operator %>%) # GY: higher is better # HM: lower is better mtsi_index2 <- data_ge %>% waasb(ENV, GEN, REP, resp = c(GY, HM), mresp = c(100, 0)) %>% mtsi()
#> 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 #> #> ------------------------------------------------------------------------------- #> Principal Component Analysis #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 4 #> PC Eigenvalues `Variance (%)` `Cum. variance (%)` #> <chr> <dbl> <dbl> <dbl> #> 1 PC1 1.58 79.2 79.2 #> 2 PC2 0.415 20.8 100 #> ------------------------------------------------------------------------------- #> Factor Analysis - factorial loadings after rotation- #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 4 #> VAR FA1 Communality Uniquenesses #> <chr> <dbl> <dbl> <dbl> #> 1 GY 0.890 0.792 0.208 #> 2 HM 0.890 0.792 0.208 #> ------------------------------------------------------------------------------- #> Comunalit Mean: 0.7922501 #> ------------------------------------------------------------------------------- #> Selection differential for the waasby index #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 6 #> VAR Factor Xo Xs SD SDperc #> <chr> <chr> <dbl> <dbl> <dbl> <dbl> #> 1 GY FA 1 48.3 76.5 28.2 58.3 #> 2 HM FA 1 54.1 86.2 32.1 59.3 #> ------------------------------------------------------------------------------ #> Mean of selection differential #> ------------------------------------------------------------------------------- #> Xo Xs SD SDperc #> 51.22793 81.37416 30.14624 58.82034 #> ------------------------------------------------------------------------------- #> Selection differential for the mean of the variables #> ------------------------------------------------------------------------------- #> # A tibble: 2 x 8 #> VAR Factor xo Xs SD SDperc sense goal #> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> #> 1 GY FA 1 2.67 2.78 0.105 3.94 increase 100 #> 2 HM FA 1 48.1 47.3 -0.747 -1.55 decrease 100 #> ------------------------------------------------------------------------------ #> Selected genotypes #> ------------------------------------------------------------------------------- #> G3 G1 #> -------------------------------------------------------------------------------
# }