Genet. Sel. Evol. 36 (2004) 3-27
DOI: 10.1051/gse:2003048

Mixture model for inferring susceptibility to mastitis in dairy cattle: a procedure for likelihood-based inference

Daniel Gianola^{a, b}, Jørgen Ødegård^b, Bjørg Heringstad^b, Gunnar Klemetsdal^b, Daniel Sorensen^c, Per Madsen^c, Just Jensen^c and Johann Detilleux<sup>d

a</sup>  Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA
^b  Department of Animal Science, Agricultural University of Norway, P.O. Box 5025, 1432 Ås, Norway
^c  Department of Animal Breeding and Genetics, Danish Institute of Agricultural Sciences, P.O. Box 50, 8830 Tjele, Denmark
^d  Faculté de Médicine Vétérinaire, Université de Liège, 4000 Liège, Belgium

(Received 20 March 2003; accepted 27 June 2003)

Abstract
A Gaussian mixture model with a finite number of components and correlated random effects is described. The ultimate objective is to model somatic cell count information in dairy cattle and to develop criteria for genetic selection against mastitis, an important udder disease. Parameter estimation is by maximum likelihood or by an extension of restricted maximum likelihood. A Monte Carlo expectation-maximization algorithm is used for this purpose. The expectation step is carried out using Gibbs sampling, whereas the maximization step is deterministic. Ranking rules based on the conditional probability of membership in a putative group of uninfected animals, given the somatic cell information, are discussed. Several extensions of the model are suggested.

Key words: mixture models / maximum likelihood / EM algorithm / mastitis / dairy cattle

Correspondence and reprints: gianola@calshp.cals.wisc.edu

© INRA, EDP Sciences 2004