Tom Rohmer (INRAE, GenPhySE)
Résumé: In animal genetics, linear mixed models are used to address genetic and environmental effects (referred as G+E model). Variance components are often estimated using the restricted maximum likelihood (REML) approach, using normality assumptions. However, in practice, when dealing with multiple traits, the assumption of multivariate normality for the phenotypes may be violated, particularly due to a non-normal structure between the phenotypes. This is notably caused by a non-Normal copula in the environmental part, i.e. residuals. It is established in a recent paper that using a Gaussian multitrait animal model (G+E) for traits sampled through a non-Normal copula for the residual part can bias the estimated genetic parameters, such as heritability or genetic correlations, especially in population undergoing non-random selection of reproducers. To address this issue, we propose a non-Gaussian inference model that considers not only the genetic and environmental parts, but also a copula on the residual terms, which can be non-Normal. We developed stochastic gradient strategies to maximize the considered log-likelihoods, allowing us to jointly estimate the variance components (genetic and residual) and copula parameters. We will compare the estimations of the genetic and residual parameters obtained from the non-Gaussian inference model with those from classical G+E Gaussian multitrait models, estimated by ‘Average Information’ -REML. This comparison will use simulated data generated from the copula inference model with various copulas, including the Normal one, but also heavy-tailed distributions. Additionally, I will present illustrations using real data from animal farming trait, in which multivariate Gaussian models appear inadequate.