# waas_means: Weighted Average of Absolute Scores In metan: Multi Environment Trials Analysis

## Description

Compute the Weighted Average of Absolute Scores (Olivoto et al., 2019) based on means for genotype-environment data as follows: \loadmathjax \mjsdeqnWAAS_i = \sum_k = 1^p |IPCA_ik \times EP_k|/ \sum_k = 1^pEP_k

where \mjseqnWAAS_i is the weighted average of absolute scores of the ith genotype; \mjseqnPCA_ik is the score of the ith genotype in the kth IPCA; and \mjseqnEP_k is the explained variance of the kth IPCA for k = 1,2,..,p, where p is the number of IPCAs that explain at least an amount of the genotype-interaction variance declared in the argument min_expl_var.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 waas_means( .data, env, gen, resp, mresp = NULL, wresp = NULL, min_expl_var = 85, verbose = TRUE, ... ) 

## Arguments

 .data The dataset containing the columns related to Environments, Genotypes, replication/block and response variable(s). env The name of the column that contains the levels of the environments. gen The name of the column that contains the levels of the genotypes. resp The response variable(s). To analyze multiple variables in a single procedure a vector of variables may be used. For example resp = c(var1, var2, var3). Select helpers are also allowed. mresp The new maximum value after rescaling the response variable. By default, all variables in resp are rescaled so that de maximum value is 100 and the minimum value is 0 (i.e., mresp = NULL). It must be a character vector of the same length of resp if rescaling is assumed to be different across variables, e.g., if for the first variable smaller values are better and for the second one, higher values are better, then mresp = c("l, h") must be used. Character value of length 1 will be recycled with a warning message. wresp The weight for the response variable(s) for computing the WAASBY index. Must be a numeric vector of the same length of resp. Defaults to 50, i.e., equal weights for stability and mean performance. min_expl_var The minimum explained variance. Defaults to 85. Interaction Principal Compoment Axis are iteractively retained up to the explained variance (eigenvalues in the singular value decomposition of the matrix with the interaction effects) be greather than or equal to min_expl_var. For example, if the explained variance (in percentage) in seven possible IPCAs are 56, 21, 9, 6, 4, 3, 1, resulting in a cumulative proportion of 56, 77, 86, 92, 96, 99, 100, then p = 3, i.e., three IPCAs will be used to compute the index WAAS. verbose Logical argument. If verbose = FALSE the code is run silently. ... Arguments passed to the function impute_missing_val() for imputation of missing values in case of unbalanced data.

## Value

An object of class waas_means with the following items for each variable:

• model A data frame with the response variable, the scores of all Principal Components, the estimates of Weighted Average of Absolute Scores, and WAASY (the index that consider the weights for stability and productivity in the genotype ranking.

• ge_means A tbl_df containing the genotype-environment means.

• ge_eff A gxe matrix containing the genotype-environment effects.

• eigenvalues The eigenvalues from the singular value decomposition of the matrix withe the genotype-environment interaction effects.

• proportion The proportion of the variance explained by each IPCA.

• cum_proportion The cumulative proportion of the variance explained.

## Author(s)

Tiago Olivoto tiagoolivoto@gmail.com

## References

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

waas() waasb()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 library(metan) # Data with replicates model <- waas(data_ge, env = ENV, gen = GEN, rep = REP, resp = everything()) # Based on means of genotype-environment data data_means <- means_by(data_ge, ENV, GEN) model2 <- waas_means(data_ge, env = ENV, gen = GEN, resp = everything()) # The index WAAS get_model_data(model, what = "OrWAAS") get_model_data(model2, what = "OrWAAS")