The point is that the inclusion criterium for the children is that
they have _at least_ measurments in each quarter, but some have
measurements every month or so. I thought lme would be a good
way to deal with this difference in the amount of information available.
I would recommend that you start with a spline model for the fixed
effects but use either a simple additive shift for the random effects
(random = ~1|Subject) or an additive shift and a shift in the time
trend (random = ~ age | Subject). You simply don't have enough data
to estimate 6 parameters from the data for each child.
Bad enough, this is for an PhD (luckily not mine) about growth
velocity. The medical Prof sees no problem, saying: when you
have two measurements you have a growth velocity for the timepoint
right between these measurements.
I think this is a bad approach and suggested to smooth the curves
before. The approach of using (random = ~ age | Subject) or,
as seen from looking at the log's, better (random = ~ age^0.15 | Subject),
works as expected, but gives fits which are sometimes as far as
3 cm from the real measurements (while the measurement error
is assumed to be about 0.5cm). These unusual decelerations are
exactly what the wannabe-PhD is interested in.
Finally, the argument with the "too little data" does not apply
to the set-up with with Berkeley Boys, with each one 31 measurements,
where a 7-parameters spline basis random effect wouldn't converge
within several hours.