Nonparametric longitudinal regression model to analyze shape data using the Procrustes rotation

Shape, as an intrinsic concept, can be considered as a source of information in some statistical analysis contexts. For instance, one of the important topics in morphology is to study the shape changes along time. From a topological viewpoint, shape data are points on a particular manifold and so to construct a longitudinal model for treating shape variation is not as trivial as thought. Unlike using the common parametric models to do such a task, we invoke Procrustes analysis in the context of a nonparametric framework and propose a simple, yet useful, model to deal with shape changes. After conveying the problem into the nonparametric regression model, we utilize the weighted least squares method to estimates the related parameters. Also, we illustrate implementing this new model in simulation studies and analyzing two biological data sets. Our proposed model shows its superiority while compared with other counterpart models.