Modeling relationships between calving traits: a comparison between standard and recursive mixed models

Four models were compared in terms of goodness of fit and predictive ability: 1) standard mixed model (SMM), a model with unstructured (co)variance matrices; 2) recursive mixed model 1 (RMM1), assuming that residual correlations are due to the recursive relationships between phenotypes; 3) RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4) RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes.For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB.Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible.The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the phenotypic recursion may be an important cause of the observed patterns of genetic and environmental correlations.Structural equation models (SEM) are well established and widely used in the social sciences. In quantitative genetics, these models were first suggested by Sewall Wright [1] but were ignored for many years. Recently, Gianola and Sorensen [2] suggested a model in which recursive and simultaneous relationships between phenotypes are considered in the context of a multiple-trait Gaussian model. This stimulated application of SEM in animal breeding and genetics (e.g., de los Campos et al. [3,4], Varona et al. [5], López de Maturana et al. [6], Wu et al. [7]). SEM can be used, for example, to explore potential relations