Bayesian inference about parameters of a longitudinal trajectory when selection operates on a correlated trait

A hierarchical model for inferring the parameters of the joint distribution of a trait measured longitudinally and another assessed cross-sectionally, when selection has been applied to the cross-sectional trait, is presented. Distributions and methods for a Bayesian implementation via Markov Chain Monte Carlo procedures are discussed for the case where information about the selection criterion is available for all the individuals, but longitudinal records are available only in the later generations. Alternative specifications of the residual covariance structure are suggested. The procedure is illustrated with an analysis of correlated responses in growth curve parameters in a population of rabbits selected for increased growth rate. Results agree with those obtained in a previous study using both selected and control populations. The high correlation between samples indicates slow mixing, resulting in small effective sample sizes and high Monte Carlo standard errors.