Three way factorial data analysis and randomization tests

In experimental data analysis beside the variables of direct interest we often have information on the structure of the experiment given by categorical variables, supposed to influence that principal ones, playing a dissymetric role. In this contest we consider a three-way data matrix (handled in two way form) (n subjects x p response variables x k occasions) and we study the structure between the three modes by means of Principal Component Analysis with Instrumental Variables (PCAIV). By Randomization tests we prove the significance of the predictors.