  We adapt the interactive spline model of Wahba to growth curves with
covariates. The smoothing spline formulation permits a non-parametric
representation of the growth curves. In the limit when the discretization error
is small relative to the estimation error, the resulting growth curve estimates
often depend only weakly on the number and locations of the knots. The
smoothness parameter is determined from the data by minimizing an empirical
estimate of the expected error. We show that the risk estimate of Craven and
Wahba is a weighted goodness of fit estimate. A modified loss estimate is
given, where $\sigma^2$ is replaced by its unbiased estimate.
