A New Three-mode Principal Component Analysis to Estimate Tendencies of Individual Which Exist Independently on Stimuli

Abstract

In this study, we proposed a new analytical method for three-mode data to explain the individual differences that exist independently in changes of stimuli. Three-mode data, such as semantic differential data, is widely used in such fields as psychology, marketing studies, or Kansei engineering. We assumed that the response of an individual to a stimulus is determined by component scores consisting of the sum of the scores of the stimulus and tendencies of the person. We introduced a new component model that consists of a loading matrix, stimuli scores, and individual tendencies, and we minimized it with the alternating least squares algorithm. The results of simulation studies and the analysis of two data sets illustrate the validities and utilities of the method.