Imagine you had a longitudinal study which measured a dependent variable (DV) once a week for 20 weeks on 200 participants. Although I'm interested in general, typical DVs that I'm thinking of include job performance following hire or various well-being measures following a clinical psychology intervention.
I know that multilevel modelling can be used to model the relationship between time and the DV. You can also allow coefficients (e.g., intercepts, slopes, etc.) to vary between individuals and estimate the particular values for participants. But what if when visually inspecting the data you find that the relationship between time and the DV is any one of the following:
- different in functional form (perhaps some are linear and others are exponential or some have a discontinuity)
- different in error variance (some individuals are more volatile from one time point to the next)
- What would be a good way to approach modelling data like this?
- Specifically, what approaches are good at identifying different types of relationships, and categorising individuals with regards to their type?
- What implementations exist in R for such analyses?
- Are there any references on how to do this: textbook or actual application?