Reduced versus complete space configurations in total information analysis

Abstract

In most multidimensional analyses, the dimension reduction is a key concept and reduced space analysis is routinely used. Contrary to this traditional approach, total information analysis (TIA) (Nishisato and Clavel, Behaviormetrika 37:15-32, 2010) places its focal point on tapping every piece of information in data. The present paper is to demonstrate that the time-honored practice of reduced space analysis may have to be reconsidered as its grasp of data structure may be compromised by ignoring intricate details of data. The paper will present numerical examples to make our point. © 2012 Springer-Verlag Berlin Heidelberg.