Application of a mixed normal mixture model for the estimation of mastitis-related parameters

Journal of Dairy Science

Volumn 83, Issue 10, 2000, Pages 2341-2349

  Detilleux, J ^a   Leroy, P L ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Expectation conditional maximization; Mixed normal mixture model; SCC

Indexed keywords

ALGORITHM; ANIMAL; ANIMAL DISEASE; ARTICLE; BIOLOGICAL MODEL; BREEDING; CATTLE; CATTLE DISEASE; CELL COUNT; CYTOLOGY; FEMALE; GENETIC PREDISPOSITION; GENETICS; MILK; PREVALENCE; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; BREEDING; CATTLE; CELL COUNT; FEMALE; GENETIC PREDISPOSITION TO DISEASE; LIKELIHOOD FUNCTIONS; MASTITIS, BOVINE; MILK; MODELS, GENETIC; PREVALENCE;

EID: 0034305644     PISSN: 00220302     EISSN: None     Source Type: Journal    
DOI: 10.3168/jds.S0022-0302(00)75122-8     Document Type: Article

References (36)

1. Aitkin, M., and G. T. Wilson. 1980. Mixture models, outliers, and the EM algorithm. Technometrics 22:325-330.
2. Blowey, R., and P. Edmonson, eds. 1995. Mastitis Control in Dairy Herds. An Illustrated and Practical Guide. 1st ed. Farming Press, New York, NY.
3. Boettcher, P. J., L. B Hansen, P. M. VanRaden, and C. A. Ernst. 1992. Genetic evaluation of Holstein bulls for somatic cell in milk of daughters. J. Dairy Sci. 75:1127-1137.
4. Celeux, G., D. Chauveau, and J. Diebolt. 1995. On stochastic versions of the EM algorithm. Rapport de recherche No 2514, INRIA, Rhône-Alpes.
5. Dempster, A., N. Laird, and D. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat Soc B 39:1-38.
6. Detilleux, J., P. Leroy, and D. Volckaert. 1997. Alternative use of somatic cell counts in genetic selection for mastitis resistance. Proc. Intl. Workshop on Genetic Improvement of Functional Traits in Cattle, Uppsala, Sweden.
7. Detilleux, J., J. Arendt, F. Lomba, and P. Leroy. 1999. Methods for estimating areas under receiver-operating characteristic (ROC) curves: Illustration with somatic-cell scores in subclinical intramammary infections. Prev. Vet. Med. 41:75-88.
8. Everitt, B. S., and D. J. Hand. 1981. Finite Mixture Distributions. 1st ed. University Press, Cambridge, England.
9. Foulley, J. L. 1993. A simple argument showing how to derive restricted maximum likelihood. J. Dairy Sci. 76:2320-2324.
10. Fourichon, C., H. Barkema, H. Seegers, T. Lam, and F. Beaudeau. 1997. Fréquence et expression des mammites cliniques en France et aux pays-Bas dans des exploitations classées selon les teneurs en cellules somatiques des laits de tank. Page 284. in Proc. Rencontres Recherche Ruminants, Paris.
11. Genomic Improvement of Functional Traits in Animals Annual Report. 1997. Online. Available: http://www.boku.ac.at/nuwi/ gift/.
12. Harmon, R. J. 1994. Physiology of mastitis and factors affecting somatic cell counts. J. Dairy Sci. 77:2103-2112.
13. Harville, D. A. 1977. Maximum likelihood approaches to variance components estimation and to related problems. J. Am. Stat. Assoc. 72:320-340.
14. Hofer, M. S. 1998. Variance components estimation in animal breeding: a review. J. Anim. Breed. Genet. 115:247-265.
15. Hosmer, D. W. 1973. On MLE of the parameters of the mixtures of 2 normal distributions when the sample size is small. Comm. Stat. 1:217-227.
16. Jamshidan, M., and R. I. Jennrich. 1997. Acceleration of the EM algorithm by using quasi-newton methods. J. R. Stat. Soc. B 59:569-587.
17. Kehrli, M. E., Jr., and D. E. Shuster. 1994. Factors affecting milk somatic cells and their role in health of the bovine mammary gland. J. Dairy Sci. 77:619-627.
18. Laevens, H., H. Deluyker, Y. H. Schukken, L. De Meulemeester, R. Vandermeersch, E. De Meulenaer, and A. De Kruif. 1997. Influence of parity and stage of lactation on the somatic cell count in bacteriologically negative dairy cow. J. Dairy Sci. 80:3219-3226.
19. Louis, T. A. 1982. Finding the observed information matrix when using the EM algorithm. J. R. Stat. Soc. B 44:226-233.
20. Lund, M. S., Jensen J., and P. H. Petersen. 1999. Estimation of genetic and phenotypic parameters for clinical mastitis, somatic cell production deviance, and protein yield in dairy cattle using Gibbs sampling. J. Dairy Sci. 82:1045-1051.
21. McLachlan, G. J., and T. Khrishnan. 1997. The EM algorithm and extensions. 1st ed. J. Wiley, New York, NY.
22. Miztal, I. 1990. Restricted maximum likelihood estimation of variance components in animal model using sparse matrix inversion and a supercomputer. J. Dairy Sci. 73:163-172.
23. Meng, X.-L., and D. B. Rubin. 1993. Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80:267-278.
24. Meng, X.-L., and D. van Dyk. 1997. The EM algorithm - an old folk song sung to fast new tune (with discussion). J. R. Stat. Soc. B 59:511-567.
25. National Mastitis Council. 1987. Laboratory and Field Handbook on Bovine Mastitis. 1st ed. National Mastitis Council, Madison, WI.
26. Paape, M. J., W. D. Schultze, A. J. Guidry, W. M. Kortum, and B. T. Weinland. 1981. Effect of an intramammary polyethylene device on the concentration of leukocytes and immunoglobulins in milk and on the leukocyte response to Escherichia coli endotoxin and challenge with Staphylococcus aureus. Am. J. Vet. Res. 42:774-783.
27. Redner, R. A., and H. F. Walker. 1984. Mixture, densities, maximum likelihood and the EM algorithm. SIAM Rev. 26:195-239.
28. Reents, R., J.C.M. Dekkers, and L. R. Schaeffer. 1995. Genetic evaluation for SCC with a test day model for multiple lactations. J. Dairy Sci. 78:2871-2876.
29. Schukken, Y. H., B. A. Mallard, J.C.M. Dekkers, K. E. Leslie, and M. J. Stear. 1994. Genetic impact of the risk of intramammary infection following Staphylococcus aureus challenge. J. Dairy Sci. 77:639-647.
30. Schutz, M. M., P. M. VanRaden, and G. R. Wiggans. 1994. Genetic variation in lactation means of SCC for six breeds of dairy cattle. J. Dairy Sci. 77:284-293.
31. Shook, G. E., and M. M. Schutz. 1994. Selection on SCC to improve resistance to mastitis in the United States. J. Dairy Sci. 77:648-658.
32. Titterington, D. M., A.F.M. Smith, and U. E. Makov. 1985. Statistical analysis of finite mixture distribution. 1st ed. Wiley, New-York, NY.
33. Van Werven, T., E. N. Noordhuizen-Stassen, A.J.J.M. Daemen, Y. H. Schukken, A. Brand, and C. Burvenich. 1997. Preinfection in vitro chemotaxis, phagocytosis, oxidative burst, and expression of CD11/CD18 receptors and their predictive capacity on the outcome of mastitis induced in dairy cows with Escherichia coli. J. Dairy Sci. 80:67-74.
34. Vecht, U., H. J. Wisselink, and P. R. Defize. 1989. Dutch national mastitis survey. The effect of herd and animal factors on SCC. Neth. Milk Dairy J. 43:425-429.
35. Welper, R. D., and A. E. Freeman. 1992. Genetic parameters for yield traits of Holsteins, including lactose and SCC. J. Dairy Sci. 75:1342-1348.
36. Wilson, D. J., R. N. Gonzalez, and H. H. Das. 1997. Bovine mastitis pathogens in New York and Pennsylvania: prevalence and effects on somatic cell count and milk production. J. Dairy Sci. 80:2592-2598.