  There has been an increasing interest in residual feed intake (RFI) as a
measure of net feed efficiency in dairy cattle. RFI phenotypes are obtained as
residuals from linear regression encompassing relevant factors (i.e., energy
sinks) to account for body tissue mobilization. However, fitting energy sink
phenotypes as regression variables in standard linear regression was criticized
because phenotypes are subject to measurement errors. Multiple-trait models
have been proposed which derive RFI by follow-up partial regression. By
re-arranging the single-trait linear regression, we showed a causal RFI
interpretation underlying the linear regression for RFI. It postulates
recursive effects in energy allocation from energy sinks on dry matter intake,
but the feedback or simultaneous effects are assumed to be nonexistent. A
Bayesian recursive structural equation model was proposed for directly
predicting RFI and energy sinks and estimating relevant genetic parameters
simultaneously. A simplified Markov chain Monte Carlo algorithm that
implemented the Bayesian recursive model was described. The recursive model is
asymptotically equivalent to one-step linear regression for RFI, yet extends
the analytical capacity to multiple-trait analysis. It is equivalent to
Bayesian-implemented, multiple-trait model reparameterized based on Cholesky
decomposition of phenotypic (co)variance matrix for evaluating RFI, but varied
in assumptions about relationships between energy sinks.
