Note that (I t - Λ )-1 G0 (I t - Λ )-1 and (I t - Λ )-1 Ψ0 (I t - Λ )-1 are the covariance matrices of additive genetic effects (G 0 * ) and of residuals (R 0 * ) obtained from a standard multiple trait mixed model that accounts for covariance between genetic effects and residuals from different traits, but not for causal relationships between phenotypes [ 13, 25].
A few of the genes in question are part of the architecture of a standard quantitative trait, though certainly examples are present (as discussed earlier).
The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model.
The conditional covariance matrix of y given u can be obtained by fitting a standard multiple trait animal model (MTAM, [ 17]) and obtaining the estimated residual covariance matrix, here represented by R 0 *.
Standard trait correlations may be biased by species relatedness [39].
Currently, Solanaceae breeders' ontology exists, and Rosaceae breeders also developed standard trait descriptors as part of RosBreed project, which are also stored in the cvterm table.
Therefore, Valente et al. [ 12] proposed to use the inferred residual (co variance matrix of a standard multi-trait mixed model (which represents the covariance matrix among traits conditionally on the genetic confounders) as input for the IC algorithm, instead of the observed data, when searching for causal structures in mixed effects settings.
Confirmatory factor analyses were applied to a unidimensional model, to a standard correlate traits model, to second-order representations of a common latent structure, and to a bifactor model.
Fitting a standard multi-trait model for 14 milk fatty acids resulted in convergence issues, but using latent variables to reduce the dimensionality of the data improved convergence of the Bayesian multi-trait mixed model.
Finally, Varona et al. [ 25] have presented an analysis of litter size and average piglet weight at birth in Landrace and Yorkshire using a standard two-trait mixed model (SMM) and a recursive mixed model (RMM).
