This function computes the following AMMI-based stability indexes: ASV, AMMI stability value (Purchase et al., 2000); SIPC, sums of the absolute value of the IPCA scores (Sneller et al. 1997); EV, averages of the squared eigenvector values (Sneller et al. 1997); and Za, absolute value of the relative contribution of IPCAs to the interaction (Zali et al. 2012), and WAAS, weighted average of absolute scores (Olivoto et al. 2019).
AMMI_indexes(.data, order.y = NULL, level = 0.95)An object of class waas or performs_ammi
A vector of the same length of x used to order the
response variable. Each element of the vector must be one of the 'h'
or 'l'. If 'h' is used, the response variable will be ordered
from maximum to minimum. If 'l' is used then the response variable
will be ordered from minimum to maximum. Use a comma-separated vector of
names. For example, order.y = c("h, h, l, h, l").
The confidence level. Defaults to 0.95.
A list where each element contains the result AMMI-based stability indexes for one variable.
The ASV index is computed as follows: $$AS{V_i} = {\left[ {{{\left[ {\frac{{r\mathop \lambda \nolimits_1^2 }}{{r\mathop \lambda \nolimits_2^2 }} \times (\mathop \lambda \nolimits_1^{0.5} {a_{i1}}{t_{j1}})} \right]}^2} + {{(\mathop \lambda \nolimits_2^{0.5} {a_{i2}}{t_{j2}})}^2}} \right]^{0.5}}$$
where \(r\) is the number of replications included in the analysis,
The SIPC index is computed as follows: $$SIP{C_i} = \sum\nolimits_{k = 1}^P {\left| {\mathop {|\lambda }\nolimits_k^{0.5} {a_{ik}}} \right|}$$
where \(P\) is the number of IPCA retained via F-tests.
The EV index is computed as follows: $$E{V_i} = \sum\nolimits_{k = 1}^P {\mathop a\nolimits_{ik}^2 } /P$$
The ZA index is computed as follows: $$Z{a_i} = \sum\nolimits_{k = 1}^P {{\theta _k}{a_{ik}}} $$
where \(\theta _k\) is the percentage sum of squares explained by the kth IPCA.
$$ WAAS_i = \sum_{k = 1}^{p} |IPCA_{ik} \times EP_k|/ \sum_{k = 1}^{p}EP_k$$
where \(WAAS_i\) is the weighted average of absolute scores of the ith genotype; \(PCA_{ik}\) is the score of the ith genotype in the kth IPCA; and \(EP_k\) is the explained variance of the *k*th IPCA for k = 1,2,..,p, considering p the number of significant PCAs.
Five simultaneous selection indexes (ssi) are also computed by summation of the ranks of the ASV, SIPC, EV and Za indexes and the ranks of the mean yields (Farshadfar, 2008), which results in ssiASV, ssiSIPC, ssiEV, ssiZa, and ssiWAAS, respectively.
Purchase, J.L., H. Hatting, and C.S. van Deventer. 2000. Genotype vs environment interaction of winter wheat (Triticum aestivum L.) in South Africa: II. Stability analysis of yield performance. South African J. Plant Soil 17:101-107. doi:10.1080/02571862.2000.10634878
Sneller, C.H., L. Kilgore-Norquest, and D. Dombek. 1997. Repeatability of Yield Stability Statistics in Soybean. Crop Sci. 37:383-390. doi:10.2135/cropsci1997.0011183X003700020013x
Zali, H., E. Farshadfar, S.H. Sabaghpour, and R. Karimizadeh. 2012. Evaluation of genotype vs environment interaction in chickpea using measures of stability from AMMI model. Ann. Biol. Res. 3:3126-3136. http://eprints.icrisat.ac.in/id/eprint/7173
Olivoto, T., A.D.C. L\'ucio, J.A.G. da silva, V.S. Marchioro, V.Q. de Souza, and E. Jost. 2019a. Mean performance and stability in multi-environment trials I: Combining features of AMMI and BLUP techniques. Agron. J. 111:2949-2960. doi:10.2134/agronj2019.03.0220
# NOT RUN {
library(metan)
model <- waas(data_ge,
env = ENV,
gen = GEN,
rep = REP,
resp = c(GY, HM),
verbose = FALSE)
model_indexes <- AMMI_indexes(model)
# Alternatively (and more intuitively) using %>%
res_ind <- data_ge %>%
waas(ENV, GEN, REP, c(GY, HM)) %>%
AMMI_indexes()
# }
# NOT RUN {
# }
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