  A two-level group-specific curve model is such that the mean response of each
member of a group is a separate smooth function of a predictor of interest. The
three-level extension is such that one grouping variable is nested within
another one, and higher level extensions are analogous. Streamlined variational
inference for higher level group-specific curve models is a challenging
problem. We confront it by systematically working through two-level and then
three-level cases and making use of the higher level sparse matrix
infrastructure laid down in Nolan and Wand (2018). A motivation is analysis of
data from ultrasound technology for which three-level group-specific curve
models are appropriate. Whilst extension to the number of levels exceeding
three is not covered explicitly, the pattern established by our systematic
approach sheds light on what is required for even higher level group-specific
curve models.
