Abstract. This chapter considers models of longitudinal data sets with longer time dimensions than were considered in earlier chapters. With many observations per subject, analysts have several options for introducing more complex dynamic model features that address questions of interest or that represent important tendencies of the data (or both). One option is based on the serial correlation structure; this chapter extends the basic structures that were introduced in Chapter 2. Another dynamic option is to allow parameters to vary over time. Moreover, for a data set with a long time dimension relative to the number of subjects, we have an opportunity to model the cross-sectional correlation, an important issue in many studies. The chapter also considers the Kalman filter approach, which allows the analyst to incorporate many of these features simultaneously. Throughout, the assumption of exogeneity of the explanatory variables is maintained. Chapter 6 considered lagged dependent variables as explanatory variables, another way of introducing dynamic features into the model.