TIME-SERIES ANALYSIS AND ITS RELATIONSHIP WITH LONGITUDINAL ANALYSIS

This paper discusses the relationship between longitudinal analysis of inter-individual (co-)variation and time series analysis of intra-ind ividual (co-)variation. To set the stage for this discussion, first a tutorial overview of modern techniques of multivariate time series ana lysis is given which highlights the central role of rate-space modelin g. Some increasingly general instances of the state-spuce model are pr esented, followed by a concise description of two recent applications involving nonlinear state-space modeling of oscillatory finger motion and nonlinear growth, respectively. We then consider the question unde r which conditions longitudinal factor analysis of inter-individual co variation will yield the same results as dynamic factor analysis of si ngle-subject time series data. The conditions concerned can be derived from ergodicity theory and turn out to be very restrictive. This impl ies that the results obtained in analyses of inter-individual variatio n (like the construction and validation of measurement scales) cannot be generalized to the assessment and prediction of individual developm ental processes (e. g., in single-subject conseling). A simple illustr ation with simulated data is given, to the best of our knowledge for t he first time, in which a factor analysis of inter-individual covariat ion yields a satisfactorily fitting solution that has no relationship whatsoever to the factor structures characterizing the intra-individua l covariation of each subject in the sample.