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A two-level group-specific curve model is such that the mean response of eachmember of a group is a separate smooth function of a predictor of interest. Thethree-level extension is such that one grouping variable is nested withinanother one, and higher level extensions are analogous. Streamlined variationalinference for higher level group-specific curve models is a challengingproblem. We confront it by systematically working through two-level and thenthree-level cases and making use of the higher level sparse matrixinfrastructure laid down in Nolan and Wand (2018). A motivation is analysis ofdata from ultrasound technology for which three-level group-specific curvemodels are appropriate. Whilst extension to the number of levels exceedingthree is not covered explicitly, the pattern established by our systematicapproach sheds light on what is required for even higher level group-specificcurve models.

Streamlined Variational Inference for Higher Level Group-Specific Curve Models