Genet. Sel. Evol. 34 (2002) 423-445
DOI: 10.1051/gse:2002016

Modelling the growth curve of Maine-Anjou beef cattle using heteroskedastic random coefficients models

Christèle Robert-Granié^a, Barbara Heude^b and Jean-Louis Foulley<sup>b

a</sup>  Station d'amélioration génétique des animaux, Institut national de la recherche agronomique, BP 27, 31326 Castanet-Tolosan, France
^b  Station de génétique quantitative et appliquée, Institut national de la recherche agronomique, 78352 Jouy-en-Josas Cedex, France

(Received 6 April 2001; accepted 7 January 2002)

Abstract
A heteroskedastic random coefficients model was described for analyzing weight performances between the 100th and the 650th days of age of Maine-Anjou beef cattle. This model contained both fixed effects, random linear regression and heterogeneous variance components. The objective of this study was to analyze the difference of growth curves between animals born as twin and single bull calves. The method was based on log-linear models for residual and individual variances expressed as functions of explanatory variables. An expectation-maximization (EM) algorithm was proposed for calculating restricted maximum likelihood (REML) estimates of the residual and individual components of variances and covariances. Likelihood ratio tests were used to assess hypotheses about parameters of this model. Growth of Maine-Anjou cattle was described by a third order regression on age for a mean growth curve, two correlated random effects for the individual variability and independent errors. Three sources of heterogeneity of residual variances were detected. The difference of weight performance between bulls born as single and twin bull calves was estimated to be equal to about 15 kg for the growth period considered.

Key words: heteroskedastic random coefficient model / EM-REML / robust estimators / growth curve / Maine-Anjou breed

Correspondence and reprints: Christèle Robert-Granié
    e-mail: robert@germinal.toulouse.inra.fr

© INRA, EDP Sciences 2002