Abstract
This thesis aims at proposing a new class of GLMs for a hierarchically-structured categorical response variable such as a partially-ordered variable for instance. A first step consisted of clarifying differences and commonalities between GLMs for nominal and ordinal response variables. On this basis we introduced a new specification of GLM for categorical response variable, weather ordinal or nominal, based on three components: the ratio of probabilities r, the cumulative distribution function F and the design matrix Z. This framework allowed us to define a new family of models for nominal data, similar to the cumulative, sequential and adjacent families of models for ordinal data. Then we defined the class of partitioned conditional GLMs (PCGLMs) using directed trees and (r,F,Z) specification. In our biological context, data takes the form of multivariate sequences associating a categorical response variable (type of axillary production) with explanatory variables (e.g. internode length). In the semi-Markov switching partitioned conditional generalized linear models (SMS-PCGLM) estimated on the basis of these sequences, the underlying semi-Markov chain represents both the succession and lengths of branching zones, while the PCGLMs represent the influence of growth explanatory variables on axillary productions within each branching zone. On the basis of these integrative statistical models, we showed that shoot growth influences specific branching events.