Generalized joint Procrustes analysis

In this paper, we propose a generalized version of Adachi’s (Psychometrika 74:667–683, <CitationRef CitationID="CR1">2009</CitationRef>) Joint Procrustes Analysis (GJPA), in order to transform the principal component score and loading matrices obtained for multiple data sets of the same size. The transformation is made so that multiple score and loading matrices are optimally matched to two unknown target matrices, respectively, without affecting the fit of the score and loading matrices to data sets, and without any constraint imposed on the transformation, except for its being nonsingular. The resulting transformed score and loading matrices can reasonably be compared across data sets. A simulation study is performed for assessing an alternate least-squares algorithm for GJPA. Additional procedures for interpreting GJPA solutions are also presented and they are illustrated with a real data example. Finally, GJPA is reconsidered in the contexts of three-way data analysis and canonical correlation analysis. Copyright Springer-Verlag Berlin Heidelberg 2013