This paper provides a coherent framework for studying longitudinal manifold-valued data. We introduce a Bayesian mixed-effects model which allows to estimate both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and inter-individual variability. We prove the existence of the maximum a posteriori estimate and its asymptotic consistency under reasonable assumptions. Due to the non-linearity of the proposed model, we use a stochastic version of Expectation-Maximization algorithm to estimate the model parameters. Our simulations show that our model is not noise-sensitive and succeed in explaining various paths of progression.