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ANOVA model consists in a separation of a complex variance term into its components [ 25].
However, problems arise in estimation methods for pedigree models combined with a complex variance structure across multiple environments or traits.
21 We then employed multilevel statistical procedures because of their ability to model complex variance structures at multiple levels.
For more complex variance models involving both the factor analytic and pedigree structure, the average information (AI) residual maximum likelihood (REML) methodology requires the formation of both elements of A and A -1 for the score equations and working variables.
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The GBLUP procedure simply requires replacing the numerator relationship matrix with the realized genomic relationship matrix, so it is straightforward to model complex variance-covariance structures, such as genotype by environment interactions in plant breeding.
The Taylor series linearization method (Rust 1985) was used for complex sample variance estimation.
Parameter estimation in subsequent analyses involves maximizing a weighted log-likelihood for clustered data, which means that complex sampling variance estimation methods need to be used to obtain correct statistical tests.
However, in data sets exhibiting complex co-variance patterns (such as W3), joint analysis of all environments using an interaction model imposes inadequate restrictions on co-variance patterns and, consequently, bivariate analysis seems more appropriate.
zero mean unit variance complex Gaussian elements,.
where,, and is zero mean complex Gaussian with variance.
using zero mean and unit variance complex Gaussian distribution.
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