Méthodes du maximum de vraisemblance en modèle linéaire mixte

Jean-Louis Foulley; Céline Delmas; Christèle Robert-Granié

Journal de la société française de statistique (2002)

  • Volume: 143, Issue: 1-2, page 5-52
  • ISSN: 1962-5197

How to cite


Foulley, Jean-Louis, Delmas, Céline, and Robert-Granié, Christèle. "Méthodes du maximum de vraisemblance en modèle linéaire mixte." Journal de la société française de statistique 143.1-2 (2002): 5-52. <http://eudml.org/doc/198987>.

author = {Foulley, Jean-Louis, Delmas, Céline, Robert-Granié, Christèle},
journal = {Journal de la société française de statistique},
language = {fre},
number = {1-2},
pages = {5-52},
publisher = {Société française de statistique},
title = {Méthodes du maximum de vraisemblance en modèle linéaire mixte},
url = {http://eudml.org/doc/198987},
volume = {143},
year = {2002},

AU - Foulley, Jean-Louis
AU - Delmas, Céline
AU - Robert-Granié, Christèle
TI - Méthodes du maximum de vraisemblance en modèle linéaire mixte
JO - Journal de la société française de statistique
PY - 2002
PB - Société française de statistique
VL - 143
IS - 1-2
SP - 5
EP - 52
LA - fre
UR - http://eudml.org/doc/198987
ER -


  1. ANDERSON R.L., BANCROFT T.A. (1952), Statistical theory in research. Mc Graw-Hill, New-York. Zbl0049.09803
  2. BERGER J.O., LISEO B., WOLPERT R.L. (1999), Integrated Likelihood methods for eliminating nuisance parameters, Statistical Science, 14, 1-28. Zbl1059.62521MR1702200
  3. COX D.R., REID N. (1987), Parameter orthogonality and approximate conditional inference, Journal of the Royal Statistical Society B, 49, 1-39. Zbl0616.62006MR893334
  4. COX D.R., HINKLEY D.V. (1974), Theoretical statistics, Chapman & Hall, London. Zbl0334.62003MR370837
  5. CRESSIE N., LAHIRI S.N. (1993), The asymptotic distribution of REML estimators, Journal of Multivariate Analysis, 45, 217-233. Zbl0772.62008MR1221918
  6. CRUMP S.L. (1947), The estimation of components of variance in multiple classifications, PhD thesis, Iowa State University, Ames. 
  7. DAVIDIAN M., GILTINIAN D.M. (1995), Nonlinear Models for Repeated Measurement Data, Chapman and Hall, London. 
  8. DAWID A.P. (1980), A Bayesian look at nuisance parameters, Proceedings of the first international meeting held in Valencia (Bernardo J.M., DeGroot M.H., Lindley D.V., Smith A.F.M., eds), University Press, Valencia, Spain, 167-184. Zbl0455.62004MR638877
  9. DELMAS C., FOULLEY J.L., ROBERT-GRANIÉ C. (2002), Further insights into tests of variance components and model selection, Proceedings of the 7th World Congress of Genetics applied to Livestock Production, Montpellier, France, 19-23 August 2002. 
  10. DEMPSTER A., LAIRD N., RUBIN R. (1977), Maximum likelihood estimation from incomplete data via the EM algorithm, Journal of the Royal Statistical Society B, 39,1-20. Zbl0364.62022
  11. DIGGLE P.J., LIANG K.Y., ZEGER S.L. (1994), Analysis of longitudinal data, Oxford Science Publications, Clarendon Press, Oxford Zbl1031.62002
  12. EDWARDS A.W.F. (1972), Likelihood, Cambridge University Press, Cambridge Zbl0578.62001MR1191161
  13. EISENHART C. (1947), The assumptions underlying the analysis of variance, Biometrics, 3, 1-21. MR20761
  14. FISHER R.A. (1922), On the mathematical foundations of theoretical statistics, Philosophical Transactions of the Royal Society of London, Séries A 222, 309-368. Zbl48.1280.02JFM48.1280.02
  15. FISHER R.A. (1925), Statistical methods for research workers, Oliver and Boyd. Edinburgh and London. Zbl51.0414.08JFM54.0573.07
  16. FOULLEY J. (1993), A simple argument showing how to derive restricted maximum likelihood, Journal of Dairy Science, 76, 2320-2324. 
  17. FOULLEY J.L., QUAAS R.L. (1995), Heterogeneous variances in Gaussian linear mixed models, Genetics Selection Evolution, 27, 211-228. 
  18. FOULLEY J.L., VAN DYK D.A. (2000), The PX EM algorithm for fast fitting of Henderson's mixed model, Genetics Selection Evolution, 32, 143-163. 
  19. FOULLEY J., JAFFREZIC F., ROBERT-GRANIÉ C. (2000), EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis, Genetics Selection Evolution, 32, 129-141. 
  20. GIANOLA D., FOULLEY J., FERNANDO R. (1986), Prediction of breeding values when variances are not known, Genetics Selection Evolution, 18, 485-498. 
  21. GILMOUR A.R., THOMPSON R., CULLIS B.R. (1995), An efficient algorithm for REML estimation in linear mixed models, Biometrics, 51, 1440-1450. Zbl0875.62314
  22. GOFFINET B. (1983), Risque quadratique et sélection : quelques résultats appliqués à la sélection animale et végétale, Thèse de Docteur Ingénieur, Université Paul Sabatier, Toulouse. 
  23. GOURIEROUX C. , MONTFORT A. (1989), Statistique et modèles économétriques, Economica, France. 
  24. HARTLEY H.O., RAO J.N.K. (1967), Maximum likelihood estimation for the mixed analysis of variance model, Biometrika, 54, 93-108. Zbl0178.22001MR216684
  25. HARVEY W.R. (1970), Estimation of variance and covariance components in the mixed model, Biometrics, 61, 485-504. 
  26. HARVILLE D.A. (1974), Bayesian inference for variance components using only error contrasts, Biometrika, 61, 383-385. Zbl0281.62072MR368279
  27. HARVILLE D.A. (1977), Maximum likelihood approaches to variance component estimation and to related problems, Journal of the American Statistical Association, 72, 320-340. Zbl0373.62040MR451550
  28. HARVILLE D.A. (1997), Matrix algebra from a statistician's perspective, Springer, Berlin. Zbl1142.15001MR1467237
  29. HARVILLE D.A., CALLANAN T.P. (1990), Computational aspects of likelihood based inference for variance components, Advances in Statistical Methods for Genetic Improvement of Livestock (Gianola D, Hammond K, eds), Springer Verlag, 136-176. 
  30. HENDERSON C.R. (1953), Estimation of variance and covariance components, Biometrics, 9, 226-252. MR55650
  31. HENDERSON C.R. (1973), Sire evaluation and genetic trends, In : Proceedings of the animal breeding and genetics symposium in honor of Dr J Lush, American Society Animal Science-American Dairy Science Association, 10-41, Champaign, IL. 
  32. HENDERSON C.R. (1984), Applications of linear models in animal breeding, University of Guelph, Guelph. 
  33. HENDERSON C.R., KEMPTHORNE O., SEARLE S.R., VON KROSIGK C.N. (1959), Estimation of environmental and genetic trends from records subject to culling, Biometrics, 13, 192-218. Zbl0128.40301
  34. KACKAR A.N., HARVILLE D.A. (1984), Approximation for standard errors of estimators of fixed and random effects in mixed linear models, Journal of the American Statistical Association, 79, 853-862. Zbl0557.62066MR770278
  35. KALBFLEISCH J.D., SPROTT D.A. (1970), Application of the likelihood methods to models involving large numbers of parameters, Journal of the Royal Statistical Society B, 32, 175-208. Zbl0205.45903MR270474
  36. KENWARD M.G., ROGER J.H. (1997), Small sample inference for fixed effects from restricted maximum likelihood, Biometrics, 53, 983-997. Zbl0890.62042
  37. LAIRD N.M., WARE J.H. (1982), Random effects models for longitudinal data, Biometrics, 38 963-974. Zbl0512.62107
  38. LAMOTTE L.R. (1970), A class of estimators of variance components, Technical report 10, Department of Statistics, University of Kentucky, Lexington, KE. 
  39. LAMOTTE L.R. (1973), Quadratic estimation of variance components, Biometrics, 29, 311-330. MR329142
  40. LEONARD T., HSU J.S.J. (1999), Bayesian methods, an analysis for statisticians and interdisciplinary researchers, Cambridge University Press, Cambridge, UK. Zbl0983.62012MR1693571
  41. LIANG K.Y., ZEGER S.L. (1986), Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. Zbl0595.62110MR836430
  42. LINDLEY D.V., SMITH A.F.M. (1972), Bayes Estimates for the Linear Model, Journal of the Royal Statistical Society B, 34, 1-41. Zbl0246.62050MR415861
  43. LIU C. , RUBIN D.B., WU Y.N. (1998), Parameter expansion to accelerate EM : the PX- EM algorithm, Biometrika, 85, 755-770. Zbl0921.62071MR1666758
  44. LIU C., WU Y.N. (1999), Parameter expansion scheme for data augmentation, Journal of the American Statistical Association, 94, 1264-1274. Zbl1069.62514MR1731488
  45. MARDIA K.V., MARSHALL R.J. (1985), Maximum likelihood estimation of models for residual covariance in spatial regression, Biometrika, 71, 135-146. Zbl0542.62079MR738334
  46. McCULLAGH P., NELDER J. (1989), Generalized linear models, 2nd edition, Chapman and Hall, London. Zbl0588.62104MR727836
  47. McLACHLAN G.J., KRISHNAN T. (1997), The EM algorithm and extensions, John Wiley & Sons, New York. Zbl0882.62012MR1417721
  48. MENG X.L., VAN DYK D.A. (1998), Fast EM-type implementations for mixed effects models, Journal of the Royal Statistical Society B, 60, 559-578. Zbl0909.62073MR1625942
  49. MONOD H. (2000), On the efficiency of generally balanced designs analysed by restricted maximum likelihood, Proceedings of Optimum Design, Cardiff, 12-14 april 2000, Kluwer Academic. MR1829421
  50. MOOD A.M., GRAYBILL F.A., BOES D.C. (1974), Introduction to the theory of statistics, Third edition, International student edition. Zbl0277.62002
  51. MORRELL C.H. (1998), Likelihood ratio of variance components in the linear mixed-effects model using restricted maximum likelihood, Biometrics, 54, 1560-1568. Zbl1058.62541
  52. PATTERSON H.D., THOMPSON R. (1971), Recovery of inter-block information when block sizes are unequal, Biometrika, 58, 545-554. Zbl0228.62046MR319325
  53. QUAAS R.L. (1992), REML Notebook, Mimeo, Cornell University, Ithaca, New York. 
  54. RAO C.R. ( 1971a), Estimation of variance components-Minque theory, Journal of Multivariate Analysis, 1, 257-275. Zbl0223.62086MR301869
  55. RAO C.R. ( 1971b), Minimum variance quadratic unbiased estimation of variance components, Journal of Multivariate Analysis, 1, 445-456. Zbl0259.62061MR301870
  56. RAO C.R. (1973), Linear Statistical Inference and its Applications, 2nd edition. Wiley, New-York. Zbl0137.36203MR346957
  57. RAO C.R. (1979), MIQE theory and its relation to ML and MML estimation of variance components, Sankhya B, 41, 138-153. Zbl0485.62066MR637672
  58. RAO C.R., KLEFFE J. (1988), Estimation of variance components and applications, North Holland series in statistics and probability, Elsevier, Amsterdam. Zbl0645.62073MR933559
  59. ROBINSON G.K. (1991), The estimation of random effects, Statistical Science, 6, 15-51. Zbl0955.62500MR1108815
  60. SAN CRISTOBAL M., ROBERT-GRANIE C. , FOULLEY J.L. (2002), Hétéroscédasticité et modèles linéaires mixtes : théorie et applications en génétique quantitative, Journal de la Société Française de Statistique, 143, 1-2, 155-165. 
  61. SEARLE S.R. (1979), Notes on variance component estimation. A detailed account of maximum likelihood and kindred methodology, Paper BU-673-M, Cornell University, Ithaca. MR640736
  62. SEARLE S.R. (1982), Matrix algebra useful for statistics, J. Wiley and Sons, New York. Zbl0555.62002MR670947
  63. SEARLE S.R. (1989), Variance components - some history and a summary account of estimation methods, Journal of Animal Breeding and Genetics, 106, 1-29. 
  64. SEARLE S.R., CASELLA G., Mc CULLOCH C.E. (1992), Variance components, J. Wiley and Sons, New-York. Zbl1108.62064MR1190470
  65. SELF S.G., LIANG K.Y. (1987), Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under non-standard conditions, Journal of the American Statistical Association, 82, 605-610. Zbl0639.62020MR898365
  66. STRAM D.O., LEE J.W. (1994), Variance components testing in the longitudinal mixed effects model, Biometrics, 50, 1171-1177. Zbl0826.62054
  67. STRAM D.O., LEE J.W. (1995), Correction to "Variance components testing in the longitudinal mixed effects model", Biometrics, 51, 1196. 
  68. SWEETING T.J. (1980), Uniform asymptotic normality of the maximum likelihood estimator, The Annals of Statistics, 8, 1375-1381. Zbl0447.62041MR594652
  69. THOMPSON W.A. (1962), The problem of negative estimates of variance components, Annals of Mathematical Statistics, 33, 273-289. Zbl0108.15902MR133912
  70. THOMPSON R. (1989), REML, Biometric Bulletin, 6, (3), 4-5. 
  71. THOMPSON R. (2002), A review of genetic parameter estimation, Proceedings of the 7th World Congress of Genetics applied to Livestock Production, Montpellier, France, 19-23 August 2002. 
  72. VAN DYK D.A. (2000), Fitting mixed-effects models using efficient EM-type algorithmes, Journal of Computational and Graphical Statistics, 9, 78-98. MR1826277
  73. VAN DYK D.A., MENG X.L. (2001), The art of data augmentation, Journal of Computational and Graphical Statistics, 10, 1-50. MR1936358
  74. VERBEKE G., MOLENBERGHS G. (2000), Linear mixed models for longitudinal data, Springer Verlag, New York. Zbl0956.62055MR1880596
  75. VERBYLA A.P., CULLIS B.R., KENWARD M.G., WELHAM S.J. (1999), The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion), Applied Statistics, 48, 269-311. Zbl0956.62062
  76. WELHAM S.J., THOMPSON R. (1997), A likelihood ratio test for fixed model ternis using residual maximum likelihood, Journal of the Royal Statistical Society B, 59, 701- 714. Zbl0889.62060MR1452034
  77. YATES F. (1934), The analysis of multiple classifications with unequal numbers in the different classes, Journal of the American Statistical Association, 29, 51-66. Zbl60.1165.03JFM60.1165.03

Citations in EuDML Documents

  1. Magali San Cristobal, Christèle Robert-Granié, Jean-Louis Foulley, Héteroscédasticité et modèles linéaires mixtes : théorie et applications en génétique quantitative
  2. Julie Latreille, Christiane Guinot, Christèle Robert-Granié, Isabelle Le Fur, Michel Tenenhaus, Jean-Louis Foulley, Étude des variations journalières de paramètres biophysiques de la peau à l'aide d'un modèle linéaire mixte pour mesures répétées
  3. Jean-Louis Foulley, Algorithme EM : théorie et application au modèle mixte

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.