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Annicchiarico's reliability index

Source: R/stab_reliability.R
stab_reliability.Rd

stab_reliability() computes the genotypic reliability index of Annicchiarico (1992): the lower confidence limit of a genotype's yield expressed in percent of the environment means. Like Eskridge's safety-first indices it gives the yield that a genotype exceeds with probability \(1 - \alpha\), but on a relative scale, so that environments of high and low yield weigh alike.

Usage

stab_reliability(
  .data,
  .y,
  .rep,
  .gen,
  .env,
  alpha = 0.25,
  higher_better = TRUE
)

# Default S3 method
stab_reliability(
  .data,
  .y,
  .rep,
  .gen,
  .env,
  alpha = 0.25,
  higher_better = TRUE
)

Arguments

.data

a data frame (or data.table) with one row per plot.

.y

response: a column of .data given by name (.y = Yield or .y = "Yield") or a numeric vector of length nrow(.data).

.rep

replicate: not used (kept for compatibility); may be omitted.

.gen

genotype: a column of .data or a vector, as for .y.

.env

environment: a column of .data or a vector, as for .y.

alpha

probability that the yield falls below the index (default 0.25).

higher_better

TRUE (default) when larger values of the trait are better.

Value

An object of class c("stab_reliability", "stab_result", "list"):

Reliability

data.table sorted by the index: Gen, Mean, Rel.Mean (mean relative performance, percent), Rel.SD, Index, rIndex (1 = best).

Methods: print(), summary(), plot(), stab_interpret().

Details

With \(r_{ij} = 100\,\bar{y}_{ij}/\bar{y}_{\cdot j}\), the mean \(\bar{r}_i\) and standard deviation \(s_i\) of the \(r_{ij}\) over environments, $$I_i = \bar{r}_i - Z_{1-\alpha}\,s_i.$$ \(I_i = 95\) with \(\alpha = 0.25\) means that the genotype yields at least 95 percent of the environment mean in three environments out of four. Annicchiarico used \(\alpha\) from 0.05 to 0.25. For a trait where lower values are better (higher_better = FALSE) the upper limit \(\bar{r}_i + Z\,s_i\) is given, and smaller is better.

References

Annicchiarico, P. (1992). Cultivar adaptation and recommendation from alfalfa trials in Northern Italy. Journal of Genetics and Breeding, 46, 269–278.

See also

stab_eskridge, stab_superiority, stab_interpret

Other stability analyses: add_anova(), ammi(), ammi_biplot(), er_anova(), ge_effects(), ge_means(), gge_biplot(), indiv_anova(), stab_asv(), stab_dist(), stab_eskridge(), stab_fox(), stab_huehn(), stab_kang(), stab_masv(), stab_measures(), stab_par(), stab_reg(), stab_superiority()

Author

Muhammad Yaseen (myaseen208@gmail.com), Kent M. Eskridge (keskridge1@unl.edu)

Examples

data(ge_data)
fit <-
  stab_reliability(
      .data         = ge_data
    , .y            = Yield
    , .rep          = Rep
    , .gen          = Gen
    , .env          = Env
    , alpha         = 0.25
    , higher_better = TRUE
    )
head(fit$Reliability)
#>         Gen     Mean Rel.Mean    Rel.SD    Index rIndex
#>      <char>    <num>    <num>     <num>    <num>  <int>
#> 1:    PR115 4444.273 109.7725  8.936579 103.7449      1
#> 2:   V14154 4364.727 107.9437  6.476023 103.5757      2
#> 3:   V14170 4463.818 109.7141 10.399731 102.6996      3
#> 4:    DN126 4480.864 109.5738 12.062890 101.4375      4
#> 5:   V14168 4342.045 107.0181  9.149658 100.8468      5
#> 6: 12B.2511 4414.409 108.0327 11.363673 100.3680      6