  In many applications, geodesic hierarchical models are adequate for the study
of temporal observations. We employ such a model derived for manifold-valued
data to Kendall's shape space. In particular, instead of the Sasaki metric, we
adapt a functional-based metric, which increases the computational efficiency
and does not require the implementation of the curvature tensor. We propose the
corresponding variational time discretization of geodesics and employ the
approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes
derived from an imaging study on osteoarthritis. Particularly, we perform
hypothesis test and estimate the mean trends.
