Structural Equation Modelling of Additive Genetic and Residual Covariance Matrices in Beef Cattle

The continuous increase in the number of records collected and the amount of traits available for beef cattle genetic evaluations poses statistical and computational challenges when estimating the genetic and environmental covariance matrices needed to predict breeding values. Structural equation models (SEM) using either factor analysis (FA) or recursive models (REC) can be used to structure genetic and environmental covariance matrices and to obtain more parsimonious and efficient parameterizations. In this article, we use SEM to estimate parameters for growth and ultrasound carcass traits in beef cattle. Data consisted of 2,942 animals, and six traits were analyzed using standard multiple-trait mixed models with either unstructured covariance matrices (SMTM) or structured covariance matrices (SEM). For the latter, we considered FA and REC models implemented with six alternative parameterizations, in which random effects were represented as linear combinations of fewer unobservable random variables. Comparing with SMTM, all heritability estimates from 2-factor SEM for the additive genetic matrix (FA2G) and the model with six recursive effects zeroed out at the residual covariance matrix (REC1) were within one standard error of those obtained by SMTM. The correlations between estimated breeding values (EBV) for all traits and models ranged from 0.94 to 1.00. The most parsimonious model in terms of number of estimated parameters (p_D) was FA2G, with 431.2 p_D, and 25.3 p_D fewer than the traditional model SMTM. The REC1 model showed as a good alternative for this kind of dataset, as it had a smaller p_D (443.6) than the SMTM model (456.5) and a better deviance information criterion than all other models tested (e.g., 37,868.6 for REC1 and 37,874.7 for SMTM). Results from this study indicate that mixed-effects multi-trait models in beef cattle can be successfully analyzed with FA or REC models. These models offer a parsimonious representation of the underlying covariance patterns and offer an interesting option for breeding value prediction.