Consider adapting a non-parametric curve fitting approach to the longitudinal analysis. Rice [4] suggests modeling an individual's behavior as a combination of an average curve plus an individual curve. That is, the predicted performance for an individual comes from the sum of the average curve and the individual's curve: Yi (t) = µ (t) + fi (t) + ?, where Yi (t) is the performance of individual i at age t. He suggests a "two-step" process to do this:
(a) take a robust average of all of the smoothed curves for the individuals;
(b) subtract this average smoothed curve from the individual data points and smooth the residuals.