Contributions to Modeling the Dynamic Association Structure in Longitudinal Data Sets.

Statistics;Statistics and Numeric Data;Science;Statistics

Goldstick, Jason E.Zucker, Robert A. ;

University of Michigan

关键词: Statistics;    Statistics and Numeric Data;    Science;    Statistics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/77719/jasoneg_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This dissertation considers several modeling problems involvingclustered longitudinal data. Interest focuses on the associationstructure rather than the means and, in particular, on its change overtime.Concentration on this non-stationary, or ``dynamic;;;; aspect of theassociation structure is motivated by applications involving the studyof 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 approachto 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 quantifiedby the log odds ratio, although analogous models may be formulated for continuous variables. The first method we present uses penalizedmaximum likelihood to estimate the log odds ratio trajectorysemi-parametrically as a smooth function of time in the bivariate case. Asecond method, appropriate for any number of variables, is proposed that allowsfor the pairwise log odds ratio trajectories to be estimated in isolation. Byusing a composite, conditional likelihood approach we no longerneed to model means or dependencies of secondary interest.We next consider the setting where the longitudinal data areobserved in clusters (e.g. siblings). The children in a family areexposed to events that occur at specific calendar times, and also areinfluenced by developmental processes that depend are age-specific. Sincethe children in different families have different birth spacings,these two influences are offset to varying degrees in differentfamilies, prompting us to ask whether both age and time are modulatingthe association structure and can we disaggregate these effects? Existingmethods for such data only account for a single timing variable, effectively marginalizing over the other. We present a modelingframework for jointly estimating how age and time distinctly affect theassociation structure and extensive empirical results are presented to clarifyour ability to decompose these effects.Difficult computationalproblems arise, requiring the development of new estimators andcomputing techniques.