bam_stability() gives the posterior distributions of two stability measures of every genotype: the AMMI
stability value (ASV) of Purchase et al. (2000) computed draw by draw, and the variance of the interaction effects
over the environments (Shukla's stability variance of the model), with posterior means, HPD intervals, the
probability of being the most stable genotype and the posterior expected ranks, combined with the mean into a
Bayesian yield stability index.
Arguments
- fit
a result of
bayes_ammi()orbayes_stability()(bam_stability()needsbayes_ammi()).- higher_better
TRUE(default) when larger values of the trait are better.
Value
An object of class c("bam_stability", "bam_result", "list") with stability
(data.table sorted by the index: Gen, mean, ASV, ASV_lower,
ASV_upper, variance, prob_most_stable (smallest ASV), rank_mean, rank_ASV,
YSI).
Methods: print(), plot(), bam_interpret().
Details
With the biplot scores \(u_{ik} = \lambda_k^{1/2}\alpha_{ik}\) and the sums of squares of the terms proportional to \(\lambda_k^2\), $$\mathrm{ASV}_i = \sqrt{\left(\frac{\bar{\lambda}_1^2}{\bar{\lambda}_2^2}u_{i1}\right)^2 + u_{i2}^2}, \qquad V_i = \frac{1}{E - 1}\sum_j ge_{ij}^2,$$ (\(\mathrm{ASV}_i = |u_{i1}|\) with one term), evaluated in every draw. The weight of the first axis uses the posterior means \(\bar{\lambda}_k\) of the singular values: the ratio of the draws themselves has no finite mean when the posterior of \(\lambda_2\) reaches zero. The Bayesian yield stability index is the sum of the posterior expected ranks of the mean and of the ASV.
References
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.
Shukla, G. K. (1972). Some statistical aspects of partitioning genotype-environmental components of variability. Heredity, 29(2), 237–245. doi:10.1038/hdy.1972.87
See also
Other decisions:
bam_predict(),
bam_ranks(),
bam_superiority(),
bam_winners()
Author
Muhammad Yaseen (myaseen208@gmail.com)
Examples
data(Maiz)
fit <-
bayes_ammi(
.data = Maiz
, .y = y
, .gen = entry
, .env = site
, .rep = rep
, .nIter = 1000
, .k = 2
, .burnin = 200
, .thin = 1
, .chains = 1
, .priors = bam_priors(
mu_mean = 0
, mu_var = 1e+8
, tau_mean = 0
, tau_var = 1e+8
, delta_mean = 0
, delta_var = 1e+8
, lambda_mean = 0
, lambda_var = 1e+8
, nu = 1
, s2 = NULL
)
, .level = 0.95
, .seed = 1
, .align = TRUE
, .model = "AMMI"
, .het = FALSE
, .waic = TRUE
)
st <-
bam_stability(
fit = fit
, higher_better = TRUE
)
st$stability
#> Gen mean ASV ASV_lower ASV_upper variance prob_most_stable
#> <char> <num> <num> <num> <num> <num> <num>
#> 1: 6 5331.927 213.0762 107.982997 332.3294 128362.66 0.024
#> 2: 5 5248.385 221.0675 96.155067 335.6657 149841.43 0.021
#> 3: 3 4822.457 129.1675 12.772790 239.9464 57420.18 0.319
#> 4: 7 4665.152 101.0916 5.065334 205.0764 64520.18 0.554
#> 5: 9 4924.780 254.3651 138.100674 378.1377 177020.35 0.008
#> 6: 4 5219.423 405.2636 291.030365 517.2402 410786.63 0.000
#> 7: 2 4606.430 193.0657 75.960309 319.8921 116309.35 0.070
#> 8: 1 4613.857 301.9509 198.330401 434.0974 242789.42 0.004
#> 9: 8 4285.844 379.3936 256.537235 499.2179 404930.79 0.000
#> rank_mean rank_ASV YSI
#> <num> <num> <num>
#> 1: 1.464 4.338 5.802
#> 2: 2.153 4.578 6.731
#> 3: 4.998 2.283 7.281
#> 4: 6.553 1.730 8.283
#> 5: 4.247 5.394 9.641
#> 6: 2.417 8.392 10.809
#> 7: 7.154 3.779 10.933
#> 8: 7.037 6.554 13.591
#> 9: 8.977 7.952 16.929