Comparing generalized procrustes analysis and statis

We consider a model for sensory profiling data including translation, rotation and scaling. We compare two methods to calculate an overall consensus from several data matrices: Generalized Procrustes Analysis (GPA) and STATIS (Structuration des Tableaux à Trois Indices de la Statistique). These methods are briefly illustrated and explained under our model. A series of simulations to compare their performance has been carried out. We found significant differences in performance depending on the variance of random errors and on the dimensionality of the true underlying consensus. Therefore, we investigated on the dimensionality of the calculated group averages. We found both methods gave too many dimensions compared to the true consensus. This finding is supported by some theoretical considerations. Finally we propose a combined approach which takes advantage of both methods and which gave better results in the simulations.