Predictive ability and covariance parameters of dynamic linear models for analysis of longitudinal traits.

A set of analyses using a multiple-trait model (model 1) and dynamic models for the evaluation of beef cattle growth is presented. All models contained additive direct and maternal environmental effects, as well as contemporary groups as nuisance parameters. The predictive ability of models at different parts of the growth trajectory was compared. Body weight records of 6,856 Nelore animals taken at 6 different ages (birth to 540 d) were used. Different models embedding a Kalman filter (KF) into a mixed model representation were fitted. Model 2 assumed that additive, maternal, and residual effects changed over time according to a linear autoregressive process. Model 3 was similar to model 2, but all regression coefficients were set to 1. In model 4, KF was applied only to direct genetic and maternal environmental effects. A leave-one-out cross-validation check was used to assess the predictive ability of models. Estimates of additive variance were similar in the analysis with models 1, 3, and 4 for all ages. Posterior means of maternal components increased slightly after birth and decreased after 135 d of age. Posterior means of additive rates of change were close to 1 at almost all time points, irrespective of the model. The posterior means of residual rates of change, which varied from 0.096 to 0.529, did not support the restrictions that regression coefficients were equal to 1 imposed by model 3. Estimates of additive and maternal correlations obtained with dynamic models were larger than those from a multivariate model. Model 3 produced different phenotypic correlations. Models 2 and 4 had better predictive ability than the multivariate specification. Model 3 predicted the data very poorly, and errors increased markedly with age. The KF can be a useful tool for structuring (co)variance matrices without reducing dimensionality. This model provided accurate predictions and plausible estimates of (co)variance components. Moreover, KF is a flexible specification, because a multivariate structure can be used for some random effects, whereas a dynamic feature can be incorporated for others.