R. Booth, G. Hobert, and P. , Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.1, pp.265-285, 1999.
DOI : 10.1111/1467-9868.00176

M. Davidian and D. Giltinan, Nonlinear Models for repeated Measures Data, 1995.

B. Delyon, M. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm, Ann. Statist, vol.27, issue.1, pp.94-128, 1999.

A. Dempster, N. Laird, . Rubin, and . Db, Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Stat. Soc. Ser. B, vol.39, pp.1-38, 1977.

A. Gelman and D. Rubin, Inference from Iterative Simulation Using Multiple Sequences, Statistical Science, vol.7, issue.4, pp.457-511, 1992.
DOI : 10.1214/ss/1177011136

E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004.
DOI : 10.1051/ps:2004007

E. Kuhn and M. Lavielle, Maximum likelihood estimation in nonlinear mixed effects models, Computational Statistics & Data Analysis, vol.49, issue.4, pp.1020-1038, 2005.
DOI : 10.1016/j.csda.2004.07.002

M. Lindstrom and D. Bates, Nonlinear Mixed Effects Models for Repeated Measures Data, Biometrics, vol.46, issue.3, pp.673-687, 1990.
DOI : 10.2307/2532087

T. Louis, Finding the observed information matrix when using the EM algorithm, 1982.

J. Pinheiro and D. Bates, Mixed-effects Models in S and S-PLUS, 1995.
DOI : 10.1007/978-1-4419-0318-1

J. Pinheiro and D. Bates, Approximations to the log-likelihood function in the nonlinear mixed effects model, J. Comput. Graph. Statist, vol.4, pp.12-35, 1995.

C. Robert and G. Casella, Monte Carlo Statistical methods, 2004.

L. Sheiner and S. Beal, Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: Routine clinical pharmacokinetic data, Journal of Pharmacokinetics and Biopharmaceutics, vol.39, issue.6, 1980.
DOI : 10.1007/BF01060053

S. Walker, An EM Algorithm for Nonlinear Random Effects Models, Biometrics, vol.52, issue.3, pp.934-944, 1996.
DOI : 10.2307/2533054

J. Wang, EM algorithms for nonlinear mixed effects models, Computational Statistics & Data Analysis, vol.51, issue.6, pp.3244-3256, 2007.
DOI : 10.1016/j.csda.2006.11.022

G. Wei and M. Tanner, A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, vol.51, issue.411, pp.699-704, 1990.
DOI : 10.1214/aos/1176346060

G. E. Battese and B. P. Bonyhady, Estimation of Household Expenditure Functions:An Application of a Class of Heteroscedastic Regression Models, Economic Record, vol.47, issue.2, pp.80-85, 1981.
DOI : 10.2307/1401241

A. Blasco, M. Piles, and L. Varona, A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits, Genetics Selection Evolution, vol.35, issue.1, pp.21-41, 2003.
DOI : 10.1186/1297-9686-35-1-21
URL : https://hal.archives-ouvertes.fr/hal-00894433

G. E. Box and W. J. Hill, Correcting Inhomogeneity of Variance with Power Transformation Weighting, Technometrics, vol.7, issue.1, pp.385-389, 1974.
DOI : 10.1021/ie50605a025

W. J. Brown, D. Draper, H. Golstein, and J. Rasbash, Bayesian and likelihood methods for fitting multilevel models with complex level-1 variation, Computational Statistics & Data Analysis, vol.39, issue.2, pp.203-225, 2002.
DOI : 10.1016/S0167-9473(01)00058-5

O. Cappé, A. Guillin, J. M. Marin, and C. P. Robert, Population Monte Carlo, Journal of Computational and Graphical Statistics, vol.13, issue.4, pp.907-929, 2004.
DOI : 10.1198/106186004X12803

M. Davidian and J. Carroll, Variance Function Estimation, Journal of the American Statistical Association, vol.10, issue.11, pp.1079-1091, 1987.
DOI : 10.1080/01621459.1987.10478543

M. Davidian and D. M. Giltinan, Nonlinear mixed models for repeated Measures Data, 1995.

B. Delyon, M. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm, Annals of Statistics, vol.27, pp.94-128, 1999.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B, vol.39, pp.1-38, 1977.

M. Duval and C. Robert-granié, SAEM-MCMC: some criteria, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00189580

R. F. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol.50, issue.4, pp.987-1008, 1982.
DOI : 10.2307/1912773

J. L. Foulley, M. San-cristobal, D. Gianola, and S. Im, Marginal likelihood and Bayesian approaches to the analysis of heterogeneous residual variances in mixed linear Gaussian models, Computational Statistics & Data Analysis, vol.13, issue.3, pp.291-305, 1992.
DOI : 10.1016/0167-9473(92)90137-5

J. L. Foulley and R. L. Quaas, Heterogeneous variances in Gaussian linear mixed models, Genetics Selection Evolution, vol.27, issue.3, pp.211-228, 1995.
DOI : 10.1186/1297-9686-27-3-211
URL : https://hal.archives-ouvertes.fr/hal-00894091

A. Gelman and D. B. Rubin, Inference from Iterative Simulation Using Multiple Sequences, Statistical Science, vol.7, issue.4, pp.457-511, 1992.
DOI : 10.1214/ss/1177011136

H. Goldstein, Multilevel models in educational and social research, 1987.

F. Jaffrézic, G. Marot, S. Degrelle, and I. Hue, A structural mixed model for variances in differential gene expression studies, Genetical Research, vol.89, issue.01, pp.19-25, 2007.
DOI : 10.1017/S0016672307008646

R. I. Jenrich and M. D. Schulter, Unbalanced Repeated-Measures Models with Structured Covariance Matrices, Biometrics, vol.42, issue.4, pp.805-820, 1986.
DOI : 10.2307/2530695

G. G. Judge, W. E. Griffiths, C. Hill, R. Lutkepohl, and H. , The theory and practice of econometrics, 1985.

E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004.
DOI : 10.1051/ps:2004007

Y. Lee and J. A. Nelder, Double hierarchical generalized linear models (with discussion), Journal of the Royal Statistical Society: Series C (Applied Statistics), vol.28, issue.2, pp.139-180, 2006.
DOI : 10.1111/1467-9868.00327

X. Lin, J. Ray, and S. D. Harlow, Linear Mixed Models with Heterogeneous within-Cluster Variances, Biometrics, vol.53, issue.3, pp.910-923, 1997.
DOI : 10.2307/2533552

M. Lindstrom and D. Bates, Nonlinear Mixed Effects Models for Repeated Measures Data, Biometrics, vol.46, issue.3, pp.673-687, 1990.
DOI : 10.2307/2532087

R. Littell, G. Milliken, W. Stroup, and R. Wolfinger, SAS for Mixed Models, 2006.

R. J. Little and D. B. Rubin, Statistical analysis with missing data, 1977.
DOI : 10.1002/9781119013563

T. A. Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society: Series B, vol.44, pp.226-233, 1982.

J. Lu, C. , D. Zhou, and W. , Quasi-likelihood estimation for GLM with random scales, Journal of Statistical Planning and Inference, vol.136, issue.2, pp.401-429, 2006.
DOI : 10.1016/j.jspi.2004.06.028

C. Meza, F. Jaffrézic, and J. L. Foulley, REML Estimation of Variance Parameters in Nonlinear Mixed Effects Models Using the SAEM Algorithm, Biometrical Journal, vol.85, issue.6, pp.876-888, 2007.
DOI : 10.1002/bimj.200610348

S. Mignon-grasteau, M. Piles, L. Varona, and J. P. Poivey, Genetic analysis of growth curve parameters for male and female chickens resulting from selection on shape of growth curve., Journal of Animal Science, vol.78, issue.10, pp.2532-2531, 2000.
DOI : 10.2527/2000.78102515x

J. Pan and R. Thompson, Quasi-Monte Carlo estimation in generalized linear mixed models, Computational Statistics & Data Analysis, vol.51, issue.12, pp.5765-5775, 2006.
DOI : 10.1016/j.csda.2006.10.003

J. C. Pinheiro and D. M. Bates, Mixed-effects Models in S and S-PLUS, 2000.
DOI : 10.1007/978-1-4419-0318-1

R. F. Pothoff and S. N. Roy, A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, vol.51, issue.3-4, pp.313-326, 1964.
DOI : 10.1093/biomet/51.3-4.313

R. A. Rigby and D. M. Stasinopoulos, Generalized additive models for location, scale and shape (with discussion) Applied Statistics, pp.507-554, 2005.

C. P. Robert and G. Casella, Monte Carlo Statistical methods, 2004.

L. B. Sheiner and S. L. Beal, Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: Routine clinical pharmacokinetic data, Journal of Pharmacokinetics and Biopharmaceutics, vol.39, issue.6, pp.553-571, 1980.
DOI : 10.1007/BF01060053

R. A. Torres, Markov chain Monte Carlo methods for estimating the covariance structure of longitudinal data -an application to dairy cattle, 2001.

G. Verbeke and G. Molenberghs, Linear models for longitudinal data, 1999.

R. D. Wolfinger, Laplace's approximation for nonlinear mixed models, Biometrika, vol.80, issue.4, pp.791-795, 1993.
DOI : 10.1093/biomet/80.4.791

L. Tableau, 10 (respectivement 4.11) présente les valeurs du test de Wald pour le modèle [MG] (respectivement

. Concernant-le-modèle, seules les covariables " campagne " et " race " ont une effet significatif sur les paramètres ? 0 et ? 1 . Concernant la fonction de variance

. Concernant-le-modèle, les covariables ayant un effet significatif sont différentes de celles obtenus pour le modèle [MG] : il s'agit des interactions " saison de vêlage*campagne " , " saison de vêlage*race " , et des effets simples " saison de vêlage

B. Abramowitz, M. Stegun, and I. A. , Handbook of mathematical functions with formulas , graphs, and mathematical tables, 1964.

M. Aitkin, Modelling Variance Heterogeneity in Normal Regression Using GLIM, Applied Statistics, vol.36, issue.3, pp.332-339, 1987.
DOI : 10.2307/2347792

H. Akaike, Information theory and an extension of the maximum likelihood principle, Second International Symposium on Information Theory. Budapest: Akademiai Kiado, pp.267-281, 1973.

A. K. Ali and L. R. Schaeffer, ACCOUNTING FOR COVARIANCES AMONG TEST DAY MILK YIELDS IN DAIRY COWS, Canadian Journal of Animal Science, vol.67, issue.3, pp.637-644, 1987.
DOI : 10.4141/cjas87-067

A. K. Ali and G. E. Shook, An Optimum Transformation for Somatic Cell Concentration in Milk, Journal of Dairy Science, vol.63, issue.3, pp.487-490, 1990.
DOI : 10.3168/jds.S0022-0302(80)82959-6

M. Al-zaid and S. S. Yang, An approximate EM algorithm for nonlinear mixed effects models, Biometrical Journal, vol.7, pp.881-893, 2001.

S. L. Beal and L. B. Sheiner, Estimating population kinetics, CRC Critical Reviews in Biomedical Engineering, vol.8, pp.195-222, 1982.

S. L. Beal and L. B. Sheiner, Heteroscedastic Nonlinear Regression, Technometrics, vol.9, issue.3, pp.327-338, 1988.
DOI : 10.1080/00401706.1988.10488406

J. Berger, Statistical Decision Theory and Bayesian Analysis, 1985.
DOI : 10.1007/978-1-4757-4286-2

J. Berger, B. Liseo, and R. L. Wolpert, Integrated likelihood methods for eliminating nuisance parameters, Statistical Science, vol.14, pp.1-28, 1999.

G. J. Booth and P. J. Hobert, Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.1, pp.265-285, 1999.
DOI : 10.1111/1467-9868.00176

G. E. Box and D. R. Cox, An analysis of transformations, Journal of the Royal Statistical Society, Ser. B, vol.26, pp.211-252, 1964.

G. E. Box and W. J. Hill, Correcting Inhomogeneity of Variance with Power Transformation Weighting, Technometrics, vol.7, issue.1, pp.385-389, 1974.
DOI : 10.1021/ie50605a025

W. J. Browne, D. Draper, H. Goldstein, and J. Rasbash, Bayesian and likelihood methods for fitting multilevel models with complex level-1 variation, Computational Statistics & Data Analysis, vol.39, issue.2, pp.203-225, 2002.
DOI : 10.1016/S0167-9473(01)00058-5

G. Celeux and J. Diebolt, The SEM algorithm: a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem, Computational Statistics Quaterly, vol.2, pp.73-82, 1985.

J. J. Colleau, L. Bihan-duval, and E. , A Simulation Study of Selection Methods to Improve Mastitis Resistance of Dairy Cows, Journal of Dairy Science, vol.78, issue.3, pp.659-671, 1995.
DOI : 10.3168/jds.S0022-0302(95)76678-4

D. Concordet and O. G. Nunez, A simulated pseudo-maximum likelihood estimator for nonlinear mixed models, Computational Statistics & Data Analysis, vol.39, issue.2, pp.187-201, 2002.
DOI : 10.1016/S0167-9473(01)00052-4

R. D. Cook and S. Weisberg, Diagnostics for heteroscedasticity in regression, Biometrika, vol.70, issue.1, pp.1-10, 1983.
DOI : 10.1093/biomet/70.1.1

M. Davidian and J. Carroll, Variance Function Estimation, Journal of the American Statistical Association, vol.10, issue.11, pp.1079-1091, 1987.
DOI : 10.1080/01621459.1987.10478543

M. Davidian and A. R. Gallant, Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine, Journal of Pharmacokinetics and Biopharmaceutics, vol.11, issue.60, pp.529-556, 1992.
DOI : 10.1007/BF01061470

M. Davidian and D. M. Giltinan, Non linear models for repeated measurement data, 1995.

M. Davidian and D. M. Giltinan, Nonlinear models for repeated measurement data: An overview and update, Journal of Agricultural, Biological, and Environmental Statistics, vol.16, issue.4, pp.387-419, 2003.
DOI : 10.1198/1085711032697

P. J. Davis and P. Rabinowitz, Methods of numerical integration, 1984.

D. Boor and C. , A practical guide to splines, 1978.

B. Delyon, M. Lavielle, and E. Moulines, Convergence of a stochastic approximation version of the EM algorithm, Annals of Statistics, vol.27, pp.94-128, 1999.

E. Demidenko, Asymptotic properties of nonlinear mixed-effects models. In Modelling longitudinal and spatially correlated data : methods, Applications, and future directions, 1997.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, Ser. B, vol.39, pp.1-38, 1977.

S. Donnet and A. Samson, Estimation of parameters in incomplete data models defined by dynamical systems, Journal of Statistical Planning and Inference, vol.137, issue.9, pp.2815-2831, 2007.
DOI : 10.1016/j.jspi.2006.10.013
URL : https://hal.archives-ouvertes.fr/hal-00263507

S. Donnet and A. Samson, Parametric inference for mixed models defined by stochastic differential equations, ESAIM: Probability and Statistics, vol.12, pp.196-218, 2008.
DOI : 10.1051/ps:2007045
URL : https://hal.archives-ouvertes.fr/hal-00263515

M. Duval and C. Robert-granié, Criteria to calibrate the parameters of the SAEM- MCMC algorithm in maximum likelihood estimation for nonlinear mixed effects models, 2007.

M. Duval, C. Robert-granié, and J. L. Foulley, Estimation of heterogeneous variances in nonlinear mixed models via the SAEM-MCMC algorithm, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01193504

R. F. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol.50, issue.4, pp.987-1008, 1982.
DOI : 10.2307/1912773

J. L. Foulley, Including mean-variance relationships in heteroskedastic mixed linear models: theory and applications, 2004.

J. L. Foulley and D. A. Van-dyk, The PX-EM algorithm for fast stable fitting of Henderson's mixed model, Genetics Selection Evolution, vol.32, issue.2, pp.143-163, 2000.
DOI : 10.1186/1297-9686-32-2-143

A. Gelman, F. Bois, and L. M. Jiang, Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions, Journal of the American Statistical Association, vol.55, issue.436, pp.1400-1412, 1996.
DOI : 10.2307/2533402

H. Goldstein, J. Rasbash, M. Yang, and G. Woodhouse, A Multilevel Analysis of School Examination Results, Oxford Review of Education, vol.13, issue.4, pp.425-433, 1993.
DOI : 10.1080/0305498900160201

C. Gourieroux and A. Montfort, Statistique et modèlesmodèleséconométriques. Collection " Economie et statistiques avancées, ENSAE, vol.2, 1989.

A. C. Harvey, Estimating Regression Models with Multiplicative Heteroscedasticity, Econometrica, vol.44, issue.3, pp.461-465, 1976.
DOI : 10.2307/1913974

D. A. Harville, Bayesian inference for variance components using only error contrasts, Biometrika, vol.61, issue.2, pp.383-385, 1974.
DOI : 10.1093/biomet/61.2.383

D. A. Harville, Extension of the Gauss-Markov Theorem to Include the Estimation of Random Effects, The Annals of Statistics, vol.4, issue.2, pp.384-395, 1976.
DOI : 10.1214/aos/1176343414

D. Hedeker and R. J. Mermelstein, Mixed-effects regression models with heterogeneous variance: analyzing ecological momentary assessment data of smoking, 2007.

C. R. Henderson, Estimation of Variance and Covariance Components, Biometrics, vol.9, issue.2, pp.226-252, 1953.
DOI : 10.2307/3001853

C. R. Henderson, O. Kempthorne, S. R. Searle, V. Krosigk, and C. N. , The Estimation of Environmental and Genetic Trends from Records Subject to Culling, Biometrics, vol.15, issue.2, pp.192-218, 1959.
DOI : 10.2307/2527669

C. R. Henderson, Sire evaluation and genetic trends, Proceedings of the Animal Breeding and Genetics Symposium in Honor of Dr, pp.10-41, 1973.

S. Huet, E. Jolivet, and A. Messéan, La régression non-linéaire (méthodes et applications en biologie), 1992.

G. G. Judge, W. E. Griffiths, . Carter, R. Hill, H. Lutkepohl et al., The theory and practice of econometrics, 1985.

E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004.
DOI : 10.1051/ps:2004007

N. M. Laird and J. H. Ware, Random-Effects Models for Longitudinal Data, Biometrics, vol.38, issue.4, pp.963-974, 1982.
DOI : 10.2307/2529876

M. Lavielle and C. Meza, A parameter expansion version of the SAEM algorithm, Statistics and Computing, vol.99, issue.2, pp.121-130, 2007.
DOI : 10.1007/s11222-006-9007-6

F. Lescourret and J. B. Coulon, Modeling the Impact of Mastitis on Milk Production by Dairy Cows, Journal of Dairy Science, vol.77, issue.8, pp.2289-2301, 1994.
DOI : 10.3168/jds.S0022-0302(94)77172-1

X. Lin, J. Ray, and S. D. Harlow, Linear Mixed Models with Heterogeneous within-Cluster Variances, Biometrics, vol.53, issue.3, pp.910-923, 1997.
DOI : 10.2307/2533552

M. J. Lindstrom and D. M. Bates, Nonlinear Mixed Effects Models for Repeated Measures Data, Biometrics, vol.46, issue.3, pp.673-687, 1990.
DOI : 10.2307/2532087

R. Littell, G. Milliken, W. Stroup, R. Wolfinger, and O. Schabenberger, SAS for Mixed Models, 2006.

C. Liu, D. Rubin, and Y. Wu, Parameter expansion to accelerate EM: the PX-EM algorithm, Biometrika, vol.85, issue.4, pp.755-770, 1998.
DOI : 10.1093/biomet/85.4.755

C. E. Mcculloch, Maximum Likelihood Algorithms for Generalized Linear Mixed Models, Journal of the American Statistical Association, vol.86, issue.437, pp.162-169, 1997.
DOI : 10.1080/01621459.1997.10473613

F. Minvielle, La sélection animale. Collection " Que sais-je ?, 1998.

S. V. Morant and A. Gnanasakthy, ABSTRACT, Animal Production, vol.38, issue.02, pp.151-162, 1989.
DOI : 10.1038/216164a0

R. A. Mrode and G. J. Swanson, Genetic and statistical properties of somatic cell count and its suitability as an indirect means of reducing the incidence of mastitis in dairy cattle, Animal Breeding Abstract, vol.64, pp.847-857, 1996.

J. C. Pinheiro and D. M. Bates, Approximations to the log-likelihood function in the nonlinear mixed effects model, Journal of Computational and Graphical Statistics, vol.4, pp.12-35, 1995.

J. C. Pinheiro and D. M. Bates, Mixed-effects in S and S-Plus, 2000.

A. Racine-poon, A Bayesian Approach to Nonlinear Random Effects Models, Biometrics, vol.41, issue.4, pp.1015-1024, 1985.
DOI : 10.2307/2530972

R. Q. Ramos and . Pantula, Estimation of nonlinear random coefficient models, Statistics & Probability Letters, vol.24, issue.1, pp.49-56, 1995.
DOI : 10.1016/0167-7152(94)00147-Z

H. Robbins and S. Monroe, A Stochastic Approximation Method, The Annals of Mathematical Statistics, vol.22, issue.3, pp.400-407, 1951.
DOI : 10.1214/aoms/1177729586

C. Robert, L'analyse statistique bayésienne, 1992.

C. P. Robert and G. Casella, Monte Carlo Statistical methods, 2004.

C. Robert-granié, B. Bona¨?tibona¨?ti, D. Boichard, and A. Barbat, Accounting for variance heterogeneity in French dairy cattle genetic evaluation, Livestock Production Science, vol.60, issue.2-3, pp.343-357, 1999.
DOI : 10.1016/S0301-6226(99)00105-0

C. Robert-granié, J. L. Foulley, E. Meza, and R. Rupp, Statistical analysis of somatic cell scores via mixed model methodology for longitudinal data, Animal Research, vol.53, issue.4, pp.259-273, 2004.
DOI : 10.1051/animres:2004016

G. K. Robinson, That BLUP is a Good Thing: The Estimation of Random Effects, Statistical Science, vol.6, issue.1, pp.15-51, 1991.
DOI : 10.1214/ss/1177011926

S. L. Rodriguez-zas, D. Gianola, and G. E. Shook, Evaluation of models for somatic cell score lactation patterns in Holsteins, Livestock Production Science, vol.67, issue.1-2, pp.19-30, 2000.
DOI : 10.1016/S0301-6226(00)00193-7

A. J. Rook, J. France, and M. S. Dhanoa, On the mathematical description of lactation curves, The Journal of Agricultural Science, vol.49, issue.01, pp.97-102, 1993.
DOI : 10.1038/216164a0

P. Royston and D. G. Altman, Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling, Applied Statistics, vol.43, issue.3, pp.429-467, 1994.
DOI : 10.2307/2986270

R. Rupp and D. Boichard, Evaluation génétique des bovins laitiers sur les comptages de cellules somatiques pour l'amélioration de la résistance aux mammites, Rencontres Recherches Ruminants, vol.4, pp.211-214, 1997.

R. Rupp and D. Boichard, Genetic Parameters for Clinical Mastitis, Somatic Cell Score, Production, Udder Type Traits, and Milking Ease in First Lactation Holsteins, Journal of Dairy Science, vol.82, issue.10, pp.2198-2204, 1999.
DOI : 10.3168/jds.S0022-0302(99)75465-2

R. Rupp, Analyse génétique de la résistance aux mammites chez les ruminants laitiers, Thèse de doctorat. Institut National Agronomique, 2000.

D. Ruppert, M. P. Wand, and R. J. Carroll, Semiparametric Regression, 2003.
DOI : 10.1017/CBO9780511755453

S. Cristobal, M. Robert-granié, C. Foulley, and J. L. , Hétéroscédasticité et modèles linéaires mixtes : théorie et applications en génétique quantitative, pp.1-2, 2002.

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-646, 1978.
DOI : 10.1214/aos/1176344136

S. R. Searle, G. Casella, and C. E. Mcculloch, Variance components, 1992.
DOI : 10.1002/9780470316856

J. Seegers, J. L. Menard, O. Dejean, and M. Weber, Cell count evolution and clinical mastitis frequency in milk recording herds of the OPTILAIT area, p.279, 1997.

S. G. Self and K. Y. Liang, Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions, Journal of the American Statistical Association, vol.72, issue.398, pp.605-610, 1987.
DOI : 10.1080/01621459.1987.10478472

L. B. Sheiner, B. Rosenberg, and K. L. Melmon, Modelling of individual pharmacokinetics for computer-aided drug dosage, Computers and Biomedical Research, vol.5, issue.5, pp.441-459, 1972.
DOI : 10.1016/0010-4809(72)90051-1

A. F. Smith and G. O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, Journal of the Royal Statistical Society, Ser. B, vol.55, pp.3-23, 1993.

L. Tierney and J. Kadane, Accurate Approximations for Posterior Moments and Marginal Densities, Journal of the American Statistical Association, vol.31, issue.393, pp.82-86, 1986.
DOI : 10.1080/01621459.1974.10480130

R. A. Torres, MCMC methods for estimating the covariance structure of longitudinal data -An application to dairy cattle data, 2001.

G. Verbeke and G. Molenberghs, Linear Mixed Models for Longitudinal Data, 2000.
DOI : 10.1007/978-1-4612-2294-1_3

E. F. Vonesh, Non-linear models for the analysis of longitudinal data, Statistics in Medicine, vol.10, issue.14-15, pp.1929-1954, 1992.
DOI : 10.1002/sim.4780111413

E. G. Vonesh, H. Wang, L. Nie, and D. Majumdar, Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models, Journal of the American Statistical Association, vol.97, issue.457, pp.271-283, 2002.
DOI : 10.1198/016214502753479400

J. C. Wakefield, A. F. Smith, A. Racine-poon, and A. E. Gelfand, Bayesian Analysis of Linear and Non-Linear Population Models by Using the Gibbs Sampler, Applied Statistics, vol.43, issue.1, pp.201-221, 1994.
DOI : 10.2307/2986121

S. Walker, An EM Algorithm for Nonlinear Random Effects Models, Biometrics, vol.52, issue.3, pp.934-944, 1996.
DOI : 10.2307/2533054

J. Wang, EM algorithms for nonlinear mixed effects models, Computational Statistics & Data Analysis, vol.51, issue.6, pp.3244-3256, 2007.
DOI : 10.1016/j.csda.2006.11.022

G. C. Wei and M. A. Tanner, A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, vol.51, issue.411, pp.699-704, 1990.
DOI : 10.1214/aos/1176346060

G. R. Wiggans and G. E. Shook, A Lactation Measure of Somatic Cell Count, Journal of Dairy Science, vol.70, issue.12, pp.2666-2675, 1987.
DOI : 10.3168/jds.S0022-0302(87)80337-5

R. Wolfinger, Laplace's approximation for nonlinear mixed models, Biometrika, vol.80, issue.4, pp.791-795, 1993.
DOI : 10.1093/biomet/80.4.791

R. D. Wolfinger, Heterogeneous Variance: Covariance Structures for Repeated Measures, Journal of Agricultural, Biological, and Environmental Statistics, vol.1, issue.2, pp.205-230, 1996.
DOI : 10.2307/1400366

P. D. Wood, Algebraic Model of the Lactation Curve in Cattle, Nature, vol.22, issue.5111, pp.164-165, 1967.
DOI : 10.1038/216164a0

C. F. Wu, On the Convergence Properties of the EM Algorithm, The Annals of Statistics, vol.11, issue.1, pp.95-103, 1983.
DOI : 10.1214/aos/1176346060

A. , F. De-koning, D. Boettcher, P. J. Bonnet, A. Buitenhuis et al., Analysis of the real EADGENE data set : Comparison of methods and guidelines for data normalization and selection of differentially expressed genes, Genetics Selection Evolution, vol.39, issue.6, pp.633-650, 2007.

P. A2-sorensen, A. Bonnet, B. Buitenhuis, R. Closset, S. Déjean et al., Analysis of the real EADGENE data set: Multivariate approaches and post analysis (Open Access publication), Genetics Selection Evolution, vol.39, issue.6, pp.651-668, 2007.
DOI : 10.1186/1297-9686-39-6-651

M. A3-watson, M. Perez-alegre, D. Baron, M. Delmas, C. Dovc et al., Analysis of a simulated microarray dataset: Comparison of methods for data normalisation and detection of differential expression (Open Access publication), Genetics Selection Evolution, vol.39, issue.6, pp.669-683, 2007.
DOI : 10.1186/1297-9686-39-6-669

A. , M. Delmas, C. Laurent, B. Robert-granié, and C. , A procedure based on partial sums of order statistics to detect differentially expressed genes, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00302355

A. , M. Robert-granié, and C. , Criteria to calibrate the parameters of the SAEM- MCMC algorithm in maximum likelihood estimation for nonlinear mixed effects models, 2007.

A. , M. Robert-granié, C. Foulley, and J. L. , Estimation of heterogeneous variances in nonlinear mixed models via the SAEM-MCMC algorithm, SoumisàSoumisà Statistical Modelling, 2008.

P. Communicationsàcommunicationsà-des-congrès-b1nozì-ere, M. Duval, L. Brossart, C. Courtial, and T. Hoch, Modélisation dynamique de l'absorption ruminale des acides gras volatils : influence du pH. 10ème rencontre recherche ruminants (3R), Décembre, pp.3-4, 2003.

M. B2-duval, S. Degrelle, C. Delmas, I. Hue, B. Laurent et al., A novel procedure to determine differentially expressed genes between several conditions. 4th Workshop on statistical analysis of post genomic data, 2006.

M. B3-duval, S. Degrelle, C. Delmas, I. Hue, B. Laurent et al., A novel procedure to determine differentially expressed genes between two conditions, 8th World Congress on Genetics Applied to Livestock Production, 2006.

M. B4-duval, S. Degrelle, C. Delmas, I. Hue, B. Laurent et al., A simple procedure to determine differentially expressed genes between several conditions, Statistique Mathématique et Applications " Novembre, pp.13-17, 2006.

C. Granié, Gene profile clustering, selection of predictive genes using random forests and a stochastic algorithm, regulatory networks in a transcriptomic kinetics on bovine mastitis. EADGENE " Data Analysis Workshop, 2006.

C. B6-delmas, C. Robert-granié, M. Duval, K. Lê-cao, M. San-cristobal et al., Two new procedures to detect differentially expressed genes. EADGENE " Data Analysis Workshop, 2006.

M. B7-duval and C. Robert-granié, Modèles non linéaires mixtes : SAEM-MCMC en pratique . 39èmes journées de la Société Française de Statistique, Juin, pp.11-15, 2007.

M. B8-duval, C. Robert-granié, and J. L. Foulley, Heterogeneous variances in nonlinear mixed effects models via the SAEM-MCMC algorithm, 24th International Biometric Conference, 2008.