Dependent Data in Social Sciences Research

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.

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 establish MFIT 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!

The detection of distinctive developmental trajectories is of great importance in criminological research. The methodology of growth curve and finite mixture modeling provides the opportunity to examine different developments of offending. With latent growth curve models (LGM) (Meredith and Tisak, Psychometrika 55:107–122, 1990) the structural equation methodology offers a strategy to examine intra- and interindividual developmental processes of delinquent behavior. There might, however, not be a single but a mixture of populations underlying the growth curves which refers to unobserved heterogeneity in the longitudinal data. Growth mixture models (GMM) introduced by Muthén and Shedden (Biometrics 55:463–469, 1999) can consider unobserved heterogeneity when estimating growth curves. GMM distinguish between continuous variables which represent the growth curve model and categorical variables which refer to subgroups that have a common development in the growth process. The models are usually based on single-phase data which associate any event with a specific period. Panel data, however, often contain several relevant phases. In this context, stage-sequential growth mixture models with multiphase longitudinal data become increasingly important. Kim and Kim (Structural Equation Modeling: A Multidisciplinary Journal 19:293–319, 2012) investigated and discussed three distinctive types of stage-sequential growth mixture models: traditional piecewise GMM, discontinuous piecewise GMM, and sequential process GMM. These models will be applied here to examine different stages of delinquent trajectories within the time range of adolescence and young adulthood using data from the German panel study Crime in the Modern City (CrimoC, Boers et al., Monatsschrift für Kriminologie und Strafrechtsreform 3:183–202, 2014). Methodological and substantive differences between single-phase and multi-phase models are discussed as well as recommendations for future applications.