. Agresti, Categorical data analysis, pp.56-83, 2002.

. Agresti, Analysis of ordinal categorical data, pp.56-69, 2010.
DOI : 10.1002/9780470594001

R. M. Altman, Mixed Hidden Markov Models, Journal of the American Statistical Association, vol.102, issue.477, pp.201-210, 2007.
DOI : 10.1198/016214506000001086

J. A. Anderson, Regression and ordered categorical variables, Journal of the Royal Statistical Society. Series B (Methodological), vol.92, pp.1-30, 1984.
DOI : 10.2307/2346654

D. Barthélémy and Y. Caraglio, Plant Architecture: A Dynamic, Multilevel and Comprehensive Approach to Plant Form, Structure and Ontogeny, Annals of Botany, vol.99, issue.3, pp.375-407, 2007.
DOI : 10.1093/aob/mcl260

T. Bergstrom and M. Bagnoli, Log-concave probability and its applications, Economic theory, vol.26, issue.40, pp.445-469, 2005.

J. Burridge, A note on maximum likelihood estimation for regression models using grouped data, Journal of the Royal Statistical Society. Series B (Methodological), vol.40, pp.41-45, 1981.

Y. Chaubert-pereira, C. Caraglio, Y. Lavergne, and . Guédon, Identifying ontogenetic, environmental and individual components of forest tree growth, Annals of Botany, vol.104, issue.5, pp.883-896, 2009.
DOI : 10.1093/aob/mcp189

URL : https://hal.archives-ouvertes.fr/hal-00423945

G. A. Churchill, Stochastic models for heterogeneous DNA sequences, Bulletin of Mathematical Biology, vol.45, issue.1, pp.79-94, 1989.
DOI : 10.1007/BF02458837

I. B. Collings and T. Rydén, A new maximum likelihood gradient algorithm for on-line hidden Markov model identification, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), pp.2261-2264, 1998.
DOI : 10.1109/ICASSP.1998.681599

D. R. Cox, Regression Models and Life-Tables, Journal of the Royal Statistical Society. Series B (Methodological), pp.187-220, 1972.
DOI : 10.1007/978-1-4612-4380-9_37

G. Debreu, Review of rd luce, individual choice behavior: A theoretical analysis, American Economic Review, vol.50, issue.46, pp.186-188, 1960.

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 (Methodological), pp.1-38, 1977.

A. J. Dobson, An introduction to generalized linear models. CRC Pr I Llc, pp.34-131, 2002.

M. Doran and D. J. Newell, Manipulation in treatment of low back pain: a multicentre study., BMJ, vol.2, issue.5964, pp.161-208, 1975.
DOI : 10.1136/bmj.2.5964.161

L. Fahrmeir and G. Tutz, Multivariate statistical modelling based on generalized linear models, pp.36-58, 2001.

J. D. Ferguson, Variable duration models for speech, Proc. Symposium on the application of hidden Markov models to text and speech, pp.143-179, 1980.

S. Frühwirth-schnatter, Finite mixture and Markov switching models, p.107, 2006.

L. E. Gatsuk, O. V. Smirnova, L. I. Vorontzova, L. B. Zaugolnova, and L. A. Zhukova, Age States of Plants of Various Growth Forms: A Review, The Journal of Ecology, vol.68, issue.2, pp.675-696, 1980.
DOI : 10.2307/2259429

C. Godin and Y. Caraglio, A Multiscale Model of Plant Topological Structures, Journal of Theoretical Biology, vol.191, issue.1, pp.1-46, 1998.
DOI : 10.1006/jtbi.1997.0561

URL : https://hal.archives-ouvertes.fr/hal-00827484

. Guédon, Review of several stochastic speech unit models, Computer Speech & Language, vol.6, issue.4, pp.377-402, 1992.
DOI : 10.1016/0885-2308(92)90030-8

Y. Guédon, Estimating Hidden Semi-Markov Chains From Discrete Sequences, Journal of Computational and Graphical Statistics, vol.12, issue.3, pp.604-639, 2003.
DOI : 10.1198/1061860032030

. Guédon, Hidden hybrid Markov/semi-Markov chains, Computational Statistics & Data Analysis, vol.49, issue.3, pp.663-688, 2005.
DOI : 10.1016/j.csda.2004.05.033

Y. Guedon and C. Cocozza-thivent, Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme, Computer Speech & Language, vol.4, issue.2, pp.167-192, 1990.
DOI : 10.1016/0885-2308(90)90003-O

Y. Guédon, D. Barthélémy, Y. Caraglio, and E. Costes, Pattern Analysis in Branching and Axillary Flowering Sequences, Journal of Theoretical Biology, vol.212, issue.4, pp.481-520, 2001.
DOI : 10.1006/jtbi.2001.2392

Y. Guedon, Y. Caraglio, P. Heuret, E. Lebarbier, and C. Meredieu, Analysing growth components in trees, Journal of Theorical Biology, pp.418-447, 2007.

H. Han, C. Coutand, H. Cochard, C. Trottier, and P. Lauri, Effects of shoot bending on lateral fate and hydraulics: invariant and changing traits across five apple genotypes, Journal of experimental botany, issue.13 11, pp.583537-3547, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01189253

R. Hastie, J. Tibshirani, J. Friedman, and . Franklin, The elements of statistical learning: data mining, inference and prediction. The Mathematical Intelligencer, pp.83-85, 2005.

P. Heuret, D. Barthélémy, Y. Guédon, X. Coulmier, and J. Tancre, Synchronization of growth, branching and flowering processes in the South American tropical tree Cecropia obtusa (Cecropiaceae), American Journal of Botany, vol.89, issue.7, pp.1180-1187, 2002.
DOI : 10.3732/ajb.89.7.1180

URL : https://hal.archives-ouvertes.fr/hal-00827469

L. Baillaud, Structures répétitives spatiales et spatio-temporelles des plantes, Phytomorphology, vol.49, pp.377-404, 1999.

E. Läärä and J. N. Matthews, The Equivalence of Two Models for Ordinal Data, Biometrika, vol.72, issue.1, pp.206-207, 1985.
DOI : 10.2307/2336352

P. Lauri and E. Terouanne, The influence of shoot growth on the pattern of axillary development on the long shoots of young apple trees (malus domestica borkh.). International journal of plant sciences, pp.283-296, 1998.

S. E. Levinson, Continuously variable duration hidden Markov models for automatic speech recognition, Computer Speech & Language, vol.1, issue.1, pp.29-45, 1986.
DOI : 10.1016/S0885-2308(86)80009-2

T. Lim, W. Loh, and Y. Shih, A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms, Machine Learning, vol.40, issue.3, pp.203-228, 2000.
DOI : 10.1023/A:1007608224229

R. D. Luce, Individual choice behavior, p.127, 1959.

J. Marschak, Binary-choice constraints and random utility indicators, Proceedings of a Symposium on Mathematical Methods in the Social Sciences, p.127, 1960.
DOI : 10.1007/978-94-010-9276-0_9

G. N. Masters, A rasch model for partial credit scoring, Psychometrika, vol.47, issue.2, pp.149-174, 1982.
DOI : 10.1007/BF02296272

A. E. Maxwell, Analysing qualitative data, p.73, 1961.

P. Mccullagh, A class of parametric models for the analysis of square contingency tables with ordered categories, Biometrika, vol.65, issue.2, pp.413-418, 1978.
DOI : 10.1093/biomet/65.2.413

P. Mccullagh, Regression models for ordinal data, Journal of the Royal Statistical Society. Series B (Methodological), pp.109-142, 1980.

. Mcfadden, Conditional logit analysis of qualitative choice behavior, p.38, 1973.

. Mcfadden, Conditional logit analysis of qualitative choice analysis, Frontiers in Econometrics, vol.12, issue.119, pp.105-142, 1974.

. Mcfadden, The Choice Theory Approach to Market Research, Marketing Science, vol.5, issue.4, pp.275-297, 1986.
DOI : 10.1287/mksc.5.4.275

D. Mcfadden, Modelling the choice of residential location Institute of Transportation Studies, pp.82-85, 1978.

B. Morawitz and G. Tutz, Alternative parameterizations in business tendency surveys, ZOR Zeitschrift f???r Operations Research Methods and Models of Operations Research, vol.15, issue.2, pp.143-156, 1990.
DOI : 10.1007/BF01415977

J. A. Nelder and R. W. Wedderburn, Generalized linear models, Journal of the Royal Statistical Society. Series A (General), vol.28, pp.370-384, 1972.

B. Nicolini, F. Chanson, and . Bonne, Stem Growth and Epicormic Branch Formation in Understorey Beech Trees (Fagus sylvatica L.), Annals of Botany, vol.87, issue.6, pp.737-750, 2001.
DOI : 10.1006/anbo.2001.1398

J. Peyhardi, E. Costes, Y. Caraglio, P. Lauri, C. Trottier et al., Integrative models for analyzing jointly shoot growth and branching patterns, 7th International Workshop on Functional Structural Plant Models, p.118, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01269303

J. Peyhardi, C. Trottier, and Y. Guédon, A unifying framework for specifying generalized linear models for categorical data, 28th International Workshop on Statistical Modeling, p.117, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00808270

J. W. Pratt, Concavity of the Log Likelihood, Journal of the American Statistical Association, vol.46, issue.373, pp.103-106, 1981.
DOI : 10.1080/01621459.1981.10477613

L. R. Rabiner, A tutorial on hidden markov models and selected applications in speech recognition, Proceedings of the IEEE, pp.257-286, 1989.

M. Renton, Y. Guédon, C. Godin, and E. Costes, Similarities and gradients in growth unit branching patterns during ontogeny in 'Fuji' apple trees: a stochastic approach, Journal of Experimental Botany, vol.57, issue.12, pp.3131-3143, 2006.
DOI : 10.1093/jxb/erl075

URL : https://hal.archives-ouvertes.fr/hal-00120198

M. Russell and R. Moore, Explicit modelling of state occupancy in hidden Markov models for automatic speech recognition, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.5-8, 1985.
DOI : 10.1109/ICASSP.1985.1168477

T. A. Steeves and I. M. Sussex, Patterns in plant development, p.19, 1989.
DOI : 10.1017/CBO9780511626227

O. Taugourdeau, F. Chaubert-pereira, S. Sabatier, and Y. Guédon, Deciphering the developmental plasticity of walnut saplings in relation to climatic factors and light environment, Journal of Experimental Botany, vol.62, issue.15, pp.625283-5296, 2011.
DOI : 10.1093/jxb/err115

URL : https://hal.archives-ouvertes.fr/hal-00828855

R. Turner, Direct maximization of the likelihood of a hidden Markov model, Computational Statistics & Data Analysis, vol.52, issue.9, pp.4147-4160, 2008.
DOI : 10.1016/j.csda.2008.01.029

G. Tutz, Compound Regression Models for Ordered Categorical Data, Biometrical Journal, vol.67, issue.3, pp.259-272, 1989.
DOI : 10.1002/bimj.4710310302

G. Tutz, Sequential item response models with an ordered response, British Journal of Mathematical and Statistical Psychology, vol.43, issue.1, pp.39-55, 1990.
DOI : 10.1111/j.2044-8317.1990.tb00925.x

G. Tutz, Sequential models in categorical regression, Computational Statistics & Data Analysis, vol.11, issue.3, pp.275-295, 1991.
DOI : 10.1016/0167-9473(91)90086-H

G. Tutz, Regression for categorical data, pp.83-103, 2012.
DOI : 10.1017/CBO9780511842061

R. W. Wedderburn, On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models, Biometrika, vol.63, issue.1, pp.27-32, 1976.
DOI : 10.1093/biomet/63.1.27

J. White, The Plant as a Metapopulation, Annual Review of Ecology and Systematics, vol.10, issue.1, pp.109-145, 1979.
DOI : 10.1146/annurev.es.10.110179.000545

Q. Zhang and E. H. Ip, Generalized linear model for partially ordered data, Statistics in Medicine, vol.24, issue.5, pp.95-96, 2012.
DOI : 10.1002/sim.4318