Technical Report, SFB 475: Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2000,52
In a previous paper Kunert and Qannari (1999) discussed a simple alternative to Generalized Procrustes Analysis to analyze data derived from a sensory profiling study. After simple pre-treatments of the individual data matrices, they propose to merge the data sets together and undergo Principal Components Analysis of the matrix thus formed. On the basis of two data sets, it was shown that the results slightly differ from those obtained by means of Generalized Procrustes Analysis. In this paper we give a mathematical justification to this approach by relating it to a statistical regression model. Furthermore, we obtain additional information from this method concerning the dimensions used by the assessors as well as the contribution of each assessor to the determination of these dimensions. This information may be useful to characterize the performance of the assessors and single out those assessors who downweight or overweight some dimensions. In particular, those assessors who overweight the last dimensions should arouse suspicion regarding their performance as, in general, the last dimensions in a principal components analysis are deemed to reflect random fluctuations.