Open Access

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

  • Daniel Gianola1, 2Email author,
  • Jørgen Øegård2,
  • Bjørg Heringstad2,
  • Gunnar Klemetsdal2,
  • Daniel Sorensen3,
  • Per Madsen3,
  • Just Jensen3 and
  • Johann Detilleux4
Genetics Selection Evolution200436:3

DOI: 10.1186/1297-9686-36-1-3

Received: 20 March 2003

Accepted: 27 June 2003

Published: 15 January 2004


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.


mixture models maximum likelihood EM algorithm mastitis dairy cattle

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Authors’ Affiliations

Department of Animal Sciences, University of Wisconsin-Madison
Department of Animal Science, Agricultural University of Norway
Department of Animal Breeding and Genetics, Danish Institute of Agricultural Sciences
Faculté de Médicine Vétérinaire, Université de Liège


© INRA, EDP Sciences 2004