Contributions to Modeling the Dynamic Association Structure in Longitudinal Data Sets.
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Abstract
This dissertation considers several modeling problems involving
clustered longitudinal data. Interest focuses on the association
structure rather than the means and, in particular, on its change over
time. Concentration on this non-stationary, or ``dynamic'' aspect of the
association structure is motivated by applications involving the study
of behavioral traits in children observed from early childhood to adulthood.
To begin we consider cases where the longitudinal measurements
are comprised of multiple variables measured on an individual at each
time point. A natural approach
to characterizing the dynamic association structure in this setting is to
``regress" a univariate measure on time. Applications of this
framework include analyzing temporally dependent comorbidity patterns
among traits. In this section we consider binary associations quantified
by the log odds ratio, although analogous models may be formulated for
continuous variables. The first method we present uses penalized
maximum likelihood to estimate the log odds ratio trajectory
semi-parametrically as a smooth function of time in the bivariate case. A
second method, appropriate for any number of variables, is proposed that allows
for the pairwise log odds ratio trajectories to be estimated in isolation. By
using a composite, conditional likelihood approach we no longer
need to model means or dependencies of secondary interest.
We next consider the setting where the longitudinal data are
observed in clusters (e.g. siblings). The children in a family are
exposed to events that occur at specific calendar times, and also are
influenced by developmental processes that depend are age-specific. Since
the children in different families have different birth spacings,
these two influences are offset to varying degrees in different
families, prompting us to ask whether both age and time are modulating
the association structure and can we disaggregate these effects? Existing
methods for such data only account for a single timing variable, effectively
marginalizing over the other. We present a modeling
framework for jointly estimating how age and time distinctly affect the
association structure and extensive empirical results are presented to clarify
our ability to decompose these effects. Difficult computational
problems arise, requiring the development of new estimators and
computing techniques.Ph.D.StatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/77719/1/jasoneg_1.pd