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Structural equation models (SEQM) can be used to model causal relationships between multiple variables in multivariate systems. Among the strengths of SEQM is its ability to consider causal links between latent variables. The use of latent variables allows modeling complex phenomena while reducing at the same time the dimensionality of the data. One relevant aspect in the quantitative genetics context is the possibility of correlated genetic effects influencing sets of variables under study. Under this scenario, if one aims at inferring causality among latent variables, genetic covariances act as confounders if ignored. Here we describe a methodology for assessing causal networks involving latent variables underlying complex phenotypic traits. The first step of the method consists of the construction of latent variables defined on the basis of prior knowledge and biological interest. These latent variables are jointly evaluated using confirmatory factor analysis. The estimated factor scores are then used as phenotypes for fitting a multivariate mixed model to obtain the covariance matrix of latent variables conditional on the genetic effects. Finally, causal relationships between the adjusted latent variables are evaluated using different SEQM with alternative causal specifications. We have applied this method to a data set with pigs for which several phenotypes were recorded over time. Five different latent variables were evaluated to explore causal links between growth, carcass, and meat quality traits. The measurement model, which included 5 latent variables capturing the information conveyed by 19 different phenotypic traits, showed an acceptable fit to data (e.g., χ/df = 1.3, root-mean-square error of approximation = 0.028, standardized root-mean-square residual = 0.041). Causal links between latent variables were explored after removing genetic confounders. Interestingly, we found that both growth (-0.160) and carcass traits (-0.500) have a significant negative causal effect on quality traits (-value ≤ 0.001). This result may have important implications for strategies for pig production improvement. More generally, the proposed method allows further learning regarding phenotypic causal structures underlying complex traits in farm species.

Searching for causal networks involving latent variables in complex traits: Application to growth, carcass, and meat quality traits in pigs1