Covariates and latents in growth modelling.
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Date
2014
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Abstract
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.
Description
Ph. D. University of KwaZulu-Natal, Pietermaritzburg 2014.
Keywords
Analysis of variance., Latent variables., Latent structure analysis., Theses--Statistics.