Choice Of Optimal Random Regression Model

Random regression model (RRM) is a mixed model in which the function on time is nested into the random effects for the analysis of test-day records or longitudinal data, which has become common for the analysis of individual repeated records in animal breeding. RRM has already been applied to the genetic evaluation of milk traits, growth traits, survival data, fertility data and genotype by environment interactions. Besides research on the application of RRM, people have been studying on the optimization of RRM and especially focusing on the choice of submodel functions. The purpose of study is to choose the optimal submodel that can fit well all the effects in RRM according to compared with all statistical criteria and behavior of estimated parameter.Data used in this study were from test-day milk production records of Canadian Holsteins from 1998 to 1999 for first parity on 10130 cows. The course of optimization is that firstly 28 submodels were embedded into fixed effects that include the effect of the herd-test date independent of the time scale and functions that account for the phenotypic trajectory of the average observations across all animals in RRM. A Legendre polynomial of 5 orders is chosen as a candidate of optimal submodel for fixed effects according to goodness of fit and F statistic.Secondly, we embedded a Legendre polynomial of 5 orders into fixed effects, additive genetic and permanent environment effects were characterized by using Legendre polynomials with from three to eight orders. A total of 26 RRMs were compared. Variance components of RRMs were estimated using Gibbs sampling. Criteria for model comparison were residual variance estimates, minus two log likelihood function, Akaike's information criterion, Bayesian information criterion, Bayesian factor, information-theoretic measure of model complexity, and percent relative reduction of complexity. Our results showed that Bayesian factor, information-theoretic measure of model complexity, and percent relative reduction of complexity are more sensitive statistical criteria to different RRMs.Based on in comparison of all statistical criteria and behavior of estimated parameter the RRM with a fifth-order Legendre polynomial for both fixed effects and additive genetic effects, a seventh-order Legendre polynomial for permanent environment effects is equally well equipped to model all effects, which is the best model among different RRMs. In addition we also compared the optimal model choosen with other common form of the RRM furthermore confirm the reliability of this choice of optimal method and result.