Search

International audience; Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.

Cet article traite de l'estimation des parametres genetiques dans un modele individuel a 2 variables. On montre que, dans beaucoup de situations, le temps de calcul peut etre diminue en standardisant les caracteres et en les rendant independants par une transformation, ce qui permet une maximisation sur un espace de parametres de moindre dimension. Un exemple numerique particulier montre que le temps de calcul est divise par 8. Les avantages des differents modeles transformes sont presentes

peer-reviewed Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sampling can be used to calculate approximations of the prediction error variance, which converge to the true values if enough samples are used. However, in practical situations the number of samples, which are computationally feasible, is limited. The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling. Four of these formulations were published, four were corresponding alternative versions, and two were derived as part of this study. The different formulations had different convergence rates and these were shown to depend on the number of samples and on the level of prediction error variance. Four formulations were competitive and these made use of information on either the variance of the estimated breeding value and on the variance of the true breeding value minus the estimated breeding value or on the covariance between the true and estimated breeding values. The authors acknowledge the Irish Cattle Breeding Federation for providing funding and data. Robin Thompson acknowledges the support of the Lawes Agricultural Trust.

A sire evaluation procedure is proposed for situations in which there is uncertainty with respect to the assignment of progeny to sires. The method requires the specification of the prior probabilities Pij that progeny i is out of sire j. Inferences about location parameters (« fixed » environmental and group effects and transmitting abilities of sires) are based on Bayesian statistical procedures. Modal values of the posterior distribution of these parameters are taken as point estimators. Finding this mode entails solving a nonlinear system of equations and several algorithms are suggested. The methodology is described for univariate evaluations obtained from normal or binary traits. Estimation of unknown variances is also addressed. A small numerical example is presented to illustrate the procedure. Potential applications to livestock breeding are discussed., Une méthode d’évaluation des pères est proposée en situation d’incertitude vis-à-vis de l’assignation des descendants à leurs pères. La méthode requiert la spécification des probabilités a priori Pij que le descendant i provienne du père j. L’inférence des paramètres de position (effets « groupe » et de milieu, considérés comme fixes et valeurs génétiques transmises des pères) est basée sur des procédures statistiques bayésiennes. Les valeurs modales de la distribution a posteriori de ces paramètres ont été prises comme estimateurs ponctuels. La recherche du mode nécessite la résolution d’un système d’équations non linéaire pour lequel plusieurs algorithmes sont proposés. La méthodologie est développée dans le cadre univariate pour des caractères normaux et binaires. Le cas de variances inconnues est également abordé. Un petit exemple numérique est présenté à titre d’illustration. Enfin, les applications possibles aux espèces domestiques sont discutées.