Résumé
Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous between individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations between individuals, (iii) an individual component corresponding mainly to the local environment of each tree. In order to identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e. models that combine linear mixed models in a semi-markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) while the linear mixed models attached to each state of the underlying semi-Markov chain represent -in the corresponding growth phase- both the influence of time-varying climatic covariates (environmental component) as fixed effects, and inter-individual heterogeneity (individual component) as random effects. In this paper we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a MCEM-like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.