The observed dependency of longitudinal data

Abstract

It is well known that longitudinal data can deal with different concepts than cross-sectional data (see Baltes & Nesselroade, 1979; McArdle & Nesselroade, 2014). The key is in the observed dependency—that allows us to examine individual changes. Thus, all of the individual changes that can be examined are due to the longitudinal models (see McArdle, 2008) allowing dependencies among the observed scores at various time points. It is demonstrated here that the statistical power to detect changes is an explicit function of the positive dependencies and the timing of the observations. A lot of time is spent on the move to the latent curve model (LCM) from the basic regression structural model and the repeated measures model (RANOVA) because the latter seems standard in the field now. This LCM is introduced in this chapter as a principle that does have power to detect many more changes than the usual regression analysis but it comes along with several (to be discussed) assumptions. The four articles to follow in this volume are reviewed with longitudinal dependency in mind, and the highlights of each chapter are brought out. The chapter “Nonlinear Growth Curve Models” extends the LCM to handle serious forms of nonlinearity, and this is clearly prevalent in Psychology. The chapter “Stage- Sequential Growth Mixture Modeling” extends this work to include multistage models, Poisson relations, all in the context of a multiple mixture model. This is a fairly complex example. The chapter “General Growth Mixture Modeling: The Study of Developmental Pathways of Externalizing Behavior from Preschool Age to Adolescence” is a real-life example that includes LCMs for five mixture groups. The chapter “A Generalization of Nagin’s Finite Mixture Model” extends the mixture models further, mainly by adding a slope component. But what is also important in this regard is “measurement invariance” and how this can be crucial to understanding changes. Some elaboration of the early work on scales is further developed for selected items. The data to be considered here for LCM are a subset of the full set of data collected in the Cognition in the USA (CogUSA survey; McArdle & Fisher, 2015). These scales were chosen in a way that would be consistent with the principles of multiple factorial invariance over time (MFIT) but the result of the age-related changes over two waves was largely unknown and in need of establishment. Basically, we first try to establishMFIT over the two waves and then look for latent changes in these scales over age. Thus there are only eight scales to consider here (four cross-sectional scales by two longitudinal occasions), so there is still a lot of work to do!.