A Component Analysis Approach Towards Multisubject Multivariate Longitudinal Data Analysis

Abstract

Longitudinal research is performed to study a phenomenon as it is evolving over time. Usually, this is done by measuring variables at carefully chosen measurement occasions. This chapter aims at giving an overview of currently available component analysis approaches to the analysis of longitudinally collected multivariate data from more than one subject. The data is analyzed by studying the mutual linear relationships between the variables and looking for a smaller set of (latent) variables that meaningfully summarize the observed data. Attention will be paid to counterpart models in the structural equation modeling (SEM) approach. As will be pointed out, the component analysis approach is less problematic than the SEM approach for a particular kind of data. To enlighten the differences between the two approaches, the two are shortly compared in the next section. Subsequently, models for three types of longitudinal data will be treated. The discussion is started from the fairly simple analysis of multivariate time series obtained from a single subject. Then, we turn into the more complex analysis of multisubject multivariate time series. The use of Simultaneous Component Analysis to analyze this kind of data is discussed and illustrated by means of an empirical example. Then, we turn into the analysis of multisubject multivariate growth data by the Tucker3 model, and illustrate its use by means of an empirical data example.KeywordsStructural Equation ModelingComponent ScoreMultivariate Time SeriesAlternate Little SquareStructural Equation Modeling ApproachThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.