| 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. |
