# Structural Equation Modeling of Genetic and Residual Covariance Matrices for Multiple-Trait Evaluation in Beef Cattle

## TL;DR

This paper explores simpler statistical models for evaluating beef cattle traits, showing they can be as accurate as traditional methods while being more efficient.

## Contribution

The study introduces structural equation models as a computationally efficient alternative to traditional methods for estimating genetic covariance in beef cattle.

## Key findings

- FA2G and REC1 models showed comparable accuracy to traditional models in estimating breeding values.
- FA2G reduced the effective number of parameters by 25.3 compared to standard models.
- REC1 had a lower deviance information criterion than traditional models, making it a competitive alternative.

## Abstract

In beef cattle, farmers collect vast amounts of data on many different traits that serve as selection criteria. Therefore, genetic breeding programs must estimate the breeding values by correcting for the relationships that affect the traits throughout the course of causality. For example, a measurement of a particular trait collected at an earlier age may influence another trait that will be collected at a later age. Estimating how these traits are transmitted genetically becomes increasingly complex as the number of traits and records increases. Farmers select animals for multiple traits. Therefore, breeding programs must consider the relationships among these traits. This study aimed to evaluate simpler mathematical methods, known as structural equation models, to assess their accuracy compared to traditional evaluation methods. Data from beef cattle were analyzed, looking at growth and carcass traits. The results showed that some new models are just as accurate as traditional ones in identifying the best animals for breeding. Furthermore, the causal relationships between the various traits could be identified, aiding in the selection and decision-making processes, helping farmers be more efficient and productive for society.

The continuous growth in both the number of phenotypic records and the range of traits included in beef cattle genetic evaluations poses substantial statistical and computational challenges for the estimation of genetic and residual (co)variance matrices required for breeding value estimation. Structural equation models (SEM), implemented using either factor analysis (FA) or recursive model (REC) structures, provide a flexible framework to model genetic and residual (co)variance matrices while yielding more parsimonious and computationally efficient parameterizations. Here, SEM was applied to estimate parameters for growth and ultrasound-measured carcass traits in beef cattle. The dataset comprised 2942 animals, and six traits were evaluated using standard multiple-trait mixed models (SMTM) and SEM. 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. Relative to the SMTM, both the model with two factors in the genetic covariance matrix (FA2G) and the model in which six recursive effects were constrained to zero in the residual covariance matrix (REC1) demonstrated a strong ability to capture genetic variability, as reflected by comparable heritability estimates. Correlations between estimated breeding values (EBV) for the same traits across models were consistently high, ranging from 0.94 to 1.00, indicating strong agreement among model estimates. The FA2G model was the most parsimonious in terms of the effective number of parameters (pD), with 431.2 pD, corresponding to a reduction of 25.3 parameters relative to the SMTM. The REC1 model also emerged as a competitive alternative for this dataset, exhibiting a lower pD (443.6) than the SMTM (456.5) and the most favorable deviance information criterion among all models evaluated (e.g., 37,868.6 for REC1 versus 37,874.7 for SMTM). Overall, these results demonstrate that mixed-effects multi-trait models for beef cattle genetic evaluation can be effectively implemented using FA or REC structures, which provide parsimonious representations of the underlying covariance patterns while maintaining high agreement in EBV.