2026-11-05
Source:vignettes/stability_09_validation.qmd
\[ \newcommand{\mY}{\mathbf{Y}} \newcommand{\mZ}{\mathbf{Z}} \newcommand{\mX}{\mathbf{X}} \newcommand{\mU}{\mathbf{U}} \newcommand{\mV}{\mathbf{V}} \newcommand{\mD}{\mathbf{D}} \newcommand{\vg}{\boldsymbol{\gamma}} \newcommand{\vd}{\boldsymbol{\delta}} \newcommand{\ybar}{\bar{y}} \newcommand{\vgs}{\mathbf{g}} \newcommand{\ves}{\mathbf{e}} \newcommand{\va}{\mathbf{a}} \newcommand{\vx}{\mathbf{x}} \]
Every result is checked against an independent computation. This vignette shows the main checks and lists the corrections of the earlier version, each with its effect on ge_data.
reg <-
stab_reg(
.data = ge_data
, .y = Yield
, .rep = Rep
, .gen = Gen
, .env = Env
)
M <- with(data = ge_data, expr = tapply(X = Yield, INDEX = list(Gen, Env), FUN = mean))
b <-
vapply(
X = reg$StabIndvReg$Gen
, FUN = function(g) coef(lm(M[g, ] ~ colMeans(M)))[[2]]
, FUN.VALUE = 0
)
all.equal(target = reg$StabIndvReg$Slope, current = unname(b))[1] TRUEEskridge’s Table 4 gives the four safety-first indices of 12 CIMMYT entries at \(\alpha = 0.05\), computed from the summaries of his Table 3 (means, variances, slopes, Shukla’s variances, deviation mean squares, with \(S^2_y = 1.87\), \(\hat{\sigma}^2_E = 1.80\) and \(E = 15\)). The package’s core recomputes all 48 values from the same summaries:
ref <-
stab_reference(
source = "Eskridge"
, evaluate = TRUE
, level = 1
)
tab <- ref[, list(
quantity = sub(pattern = " \\(alpha.*", replacement = "", x = quantity)
, published = value
, computed = round(x = computed, digits = 3)
, agrees
)]
tab quantity published computed agrees
<char> <num> <num> <lgcl>
1: EV of entry 1 2.24 2.239 TRUE
2: EV of entry 2 2.04 2.045 TRUE
3: EV of entry 3 1.72 1.717 TRUE
4: EV of entry 4 2.14 2.139 TRUE
5: EV of entry 5 1.46 1.462 TRUE
6: EV of entry 6 1.90 1.903 TRUE
7: EV of entry 7 1.67 1.668 TRUE
8: EV of entry 8 1.74 1.740 TRUE
9: EV of entry 9 2.83 2.826 TRUE
10: EV of entry 10 2.36 2.360 TRUE
11: EV of entry 11 2.26 2.265 FALSE
12: EV of entry 12 2.49 2.487 TRUE
13: FW of entry 1 4.52 4.516 TRUE
14: FW of entry 2 4.38 4.381 TRUE
15: FW of entry 3 3.76 3.756 TRUE
16: FW of entry 4 3.81 3.812 TRUE
17: FW of entry 5 3.87 3.874 TRUE
18: FW of entry 6 4.28 4.279 TRUE
19: FW of entry 7 4.03 4.033 TRUE
20: FW of entry 8 4.17 4.063 FALSE
21: FW of entry 9 4.16 4.158 TRUE
22: FW of entry 10 4.33 4.334 TRUE
23: FW of entry 11 3.10 3.099 TRUE
24: FW of entry 12 4.60 4.600 TRUE
25: SH of entry 1 2.47 2.471 TRUE
26: SH of entry 2 2.20 2.199 TRUE
27: SH of entry 3 1.58 1.581 TRUE
28: SH of entry 4 1.81 1.811 TRUE
29: SH of entry 5 1.75 1.755 TRUE
30: SH of entry 6 2.18 2.179 TRUE
31: SH of entry 7 2.20 2.197 TRUE
32: SH of entry 8 2.17 2.166 TRUE
33: SH of entry 9 2.28 2.279 TRUE
34: SH of entry 10 2.19 2.192 TRUE
35: SH of entry 11 1.41 1.409 TRUE
36: SH of entry 12 2.24 2.239 TRUE
37: ER of entry 1 4.34 4.356 FALSE
38: ER of entry 2 3.85 3.844 FALSE
39: ER of entry 3 3.12 3.122 TRUE
40: ER of entry 4 3.35 3.363 FALSE
41: ER of entry 5 3.18 3.174 FALSE
42: ER of entry 6 3.70 3.709 FALSE
43: ER of entry 7 3.67 3.679 FALSE
44: ER of entry 8 3.55 3.502 FALSE
45: ER of entry 9 3.78 3.763 FALSE
46: ER of entry 10 3.76 3.751 FALSE
47: ER of entry 11 2.86 2.854 FALSE
48: ER of entry 12 3.73 3.730 TRUE
quantity published computed agrees
<char> <num> <num> <lgcl>
sum(ref$agrees)[1] 36[1] 0.01660005Of the 48 values, 36 agree to the two printed decimals. The remaining ones differ by at most 0.02, because the summaries of Table 3 are printed to two decimals, with one exception. For entry 8, Table 3 prints the slope \(b = 1.27\), the same as for entry 7; the published FW (4.17) and ER (3.55) of entry 8 both fit \(b = 1.22\), so the printed slope appears to be a misprint. stab_reference() gives the reason for every difference in the column note.
The earlier version attached stability statistics to the wrong genotypes when the data were not sorted by genotype. The results no longer depend on the order of the rows:
| Function | Earlier version | Now |
|---|---|---|
stab_kang, stab_asv, stab_masv, stab_dist, stab_reg, AMMI1 plot |
statistics attached to other genotypes unless the data were sorted by genotype | each statistic on its genotype |
indiv_anova |
genotypes only in each environment | randomized complete blocks (replicates in the model) |
er_anova |
Total and Gen from the replicate line; deviations divided by \(B\); error df \(EG(B-1)\) | Eberhart and Russell’s lines; error df \(E(G-1)(B-1)\) |
stab_reg |
Delta = deviation SS divided by \(B\)
|
Delta = \(S^2_{d_i}\) with its test |
stab_par |
parameters divided by \(B\); error df \((G-1)^2E\); rating +2 at alpha; one-sided LSD; covariate per plot |
scale of the means; error df \(E(G-1)(B-1)\); rating \(-2\); two-sided LSD; covariate per environment |
stab_fox |
plots ranked and counted (up to 12 of 11 environments) | genotype means ranked in each environment |
stab_asv |
\(\lambda_1/\lambda_2\) on the squared score | \(SS_1/SS_2\) on the score |
stab_masv |
ratios of singular values | ratios of sums of squares |
ammi |
an axis with a zero singular value | the axes that exist |
The analyses of variance and the regressions agree with lm(); the stability statistics follow their published formulas and no longer depend on the order of the data.
Eskridge, K. M. (1990). Selection of stable cultivars using a safety-first rule. Crop Science, 30(2), 369–374.
Eberhart, S. A. and Russell, W. A. (1966). Stability parameters for comparing varieties. Crop Science, 6(1), 36–40.
Purchase, J. L., Hatting, H. and van Deventer, C. S. (2000). Genotype x environment interaction of winter wheat in South Africa: II. Stability analysis of yield performance. South African Journal of Plant and Soil, 17(3), 101–107.
Zali, H., Farshadfar, E., Sabaghpour, S. H. and Karimizadeh, R. (2012). Evaluation of genotype x environment interaction in chickpea using measures of stability from AMMI model. Annals of Biological Research, 3(7), 3126–3136.
Fox, P. N., Skovmand, B., Thompson, B. K., Braun, H. J. and Cormier, R. (1990). Yield and adaptation of hexaploid spring triticale. Euphytica, 47(1), 57–64.