In this article, we pursue two points of discussion. First, a new illustration is presented of the person-oriented tenet according to which it can be hazardous to generalize to the individual results that are based on the analysis of aggregated data. Second, it is illustrated that taking into account serial dependence information can result in not only a more detailed and richer but also a different description of covariation in multivariate time series. To capture serial dependence, lagged variables can be created, that is, variables that contain the original information but shifted by one or more observation points. When these points are placed along units such as days, the relation between the original and the lagged variables can be interpreted as the relation of the original observations to those from one or several days before. Original and lagged variables can be used in P-technique factor analysis and in structural modeling. Using a data example from the development of alcoholism, it is shown that analysis at the level of the individual can lead to different results than analysis that is based on aggregated raw data. It is also shown that taking lagged variables into account can shed new light on time series.