Exploratory analysis of longitudinal data using principal component methodology

Longitudinal data analysis (LDA) is commonly used in many scientific fields and characterized as the analysis of repeated measurements over a series of time points. As with other methodologies, LDAs can take the form of confirmatory data analysis (CDA) or exploratory data analysis (EDA). Although most recent work on LDA has taken the form of CDA, LDA deserves to be examined more often and more thoroughly using the EDA approach, partly because of the deficiencies of CDA methods for certain kinds of LD, and also because some kinds of exploratory methodology have not been well developed for LDA. In longitudinal data analysis covariates are often available. Unfortunately, in exploratory LDA contexts relatively little work has been done to take covariates into consideration, especially time-varying covariates.;The basic plan of the study divides the research into two parts: simulation studies where the goal will be to recover underlying longitudinal profiles that are known; and real data applications with the new exploratory method.;Given the results of the simulation studies based on the new approach, comparisons are made with results derived using conventional non-linear mixed effect models. These comparisons suggest that the proposed methods are effective for reducing random noise; they also show that the new methods can yield small numbers of (possibly interpretable) derived patterns. It is shown that under the various simulation conditions, the new methods can recover true profiles to a large extent; moreover, at least one version of the new methods do this more effectively in all cases than do model-based methods. Applications based on real data are shown to be reasonable and interpretable, when based on the new methods.;This dissertation proposes new methods that aim to effectively reduce 'white noise' and improve the chances of detecting underlying true patterns. The basic method involves time-based pre-smoothing and principal component analysis that can be seen as another kind of 'smoothing' method. Both kinds of smoothing entail 'borrowing strength' from correlated points in time, or related profiles. Another goal is to develop ways to examine effects of both time-varying and fixed covariates in the context of ELDA.