Random regression (RR) models for longitudinal data often require a considerable number of parameters to describe the associated covariance functions. Estimation of these parameters has proven cumbersome and subject to sampling problems. Moreover, computational restraints have limited analyses of data sets sufficiently large to supply accurate estimates. This holds especially for covariance functions pertaining to early growth of beef cattle, which is subject to both genetic and permanent environmental maternal effects. Analyses so far used restricted maximum likelihood (REML) estimation, and considered less than 4000 animals with records (Albuquerque and Meyer, 2001; Meyer, 2001a). Bayesian analysis provides an alternative which is simpler to implement and requires less computational resources per sample than REML, thus facilitating larger scale analyses. This paper presents a RR analysis of a large set of weight records from commercial beef cattle, considering weights from birth to 820 days of age. A Gibbs sampling algorithm is used to estimate covariance functions for direct and maternal effects

}, author = {Meyer, K.} }