Reduction of the number of parameters needed for a polynomial random regression test day model

Legendre polynomials were used to describe the (co)variance matrix within a random regression test day model. The goodness of fit depended on the poly nomial order of fit, i.e., number of parameters to be estimated per animal but is limited by computing capacity. Two aspects: incomplete lactation rec ords and heterogeneous variances were investigated to reduce the order of f it needed. Analysis of the original data set, which contained 50% incomplet e lactation records, required a fifth-order of fit and showed too high vari ances at the end of the lactation. Variance component estimates from only c omplete lactation records improved the goodness of fit. Correlations estima ted were more alike those observed and substantially lower variances st the end of lactation were obtained, such that a fourth-order seemed sufficient . Correction for heterogeneous variances across classes of days in milk imp roved the estimated correlation structure further and the mean square error s of prediction were better, resulting in a third-order of fit being suffic ient. Overall, use of only complete lactation records for parameter estimat ion and correction for heterogeneous variances allowed a reduction of two p arameters that need to be estimated per animal. (C) 2000 Elsevier Science B .V. All rights reserved.