Covariates and latents in growth modelling.
The growth curve models are the natural models for the increment processes taking place gradually over time. When individuals are observed over time it is often apparent that they grow at different rates, even though they are clones and no differences in treatment or environment are present. Neverthless the classical growth curve model only deals with the average growth and does not account for individual differences, nor does it have room to accommodate covariates. Accordingly we strive to construct and investigate tractable models which incorporate both individual effects and covariates. The study was motivated by plantations of fast growing tree species, and the climatic and genetic factors that influence stem radial growth of juvenile Eucalyptus hybrids grown on the east coast of South Africa. Measurement of stem radius was conducted using dendrometres on eighteen sampled trees of two Eucalyptus hybrid clones (E. grandis χ E.urophylla, GU and E.grandis χ E. Camaldulensis, GC). Information on climatic data (temperature, rainfall, solar radiation, relative humidity and wind speed) was simultaneously collected from the study site. We explored various functional statistical models which are able to handle the growth, individual traits, and covariates. These models include partial least squares approaches, principal component regression, path models, fractional polynomial models, nonlinear mixed models and additive mixed models. Each one of these models has strengths and weaknesses. Application of these models is carried out by analysing the stem radial growth data. The partial least squares and principal component regression methods were used to identify the most important predictor for stem radial growth. Path models approach was then applied mainly to find some indirect effects of climatic factors. We further explored the tree specific effects that are unique to a particular tree under study by fitting a fractional polynomial model in the context of linear mixed effects model. The fitted fractional polynomial model showed that the relationship between stem radius and tree age is nonlinear. The performance of fractional polynomial models was compared with that of nonlinear mixed effects models. Using nonlinear mixed effects models some growth parameters like inflection points were estimated. Moreover, the fractional polynomial model fit was almost as good as the nonlinear growth curves. Consequently, the fractional polynomial model fit was extended to include the effects of all climatic variables. Furthermore, the parametric methods do not allow the data to decide the most suitable form of the functions. In order to capture the main features of the longitudinal profiles in a more flexible way, a semiparametric approach was adopted. Specifically, the additive mixed models were used to model the effect of tree age as well as the effect of each climatic factor.