Most analysts would respond, “a mixed model,” but have you ever heard of latent growth curves? How about latent trajectories, latent curves, growth curves, or time paths, which are other names for the same approach?
One of those tricky, but necessary, concepts in statistics is the difference between crossed and nested factors.
As a reminder, a factor is any categorical independent variable. In experiments, or any randomized designs, these factors are often manipulated. Experimental manipulations (like Treatment vs. Control) are factors.
Observational categorical predictors, such as gender, time point, poverty status, etc., are also factors. Whether the factor is observational or manipulated won’t affect the analysis, but it will affect the conclusions you draw from the results.