Blockwise simple component analysis via rotation, constraints or penalties, with an application to product × attribute × panelist data. (July 2018) - Kiers, Henk A.L.; Timmerman, Marieke E.; Ceulemans, Eva
Highlights: Three methods for summarizing sensory profile data are compared. These methods focus both on product characteristics and panelist behavior. Sparse Group Component Analysis performed relatively poorly here. Blockwise Simplimax and Blockwise Zero Constrained CA performed well. Blockwise Simplimax also identifies idiosyncratic panelist behavior. Abstract: Sensory profiling data consisting of judgements on a number of products with respect to a number of attributes by a number of panelists can be summarized in various ways. Besides finding components describing the main product features, there is an interest in individual panelist behavior. Earlier methods identify this by means of separate PCAs, Procrustes analyses, or three-way component methods, but these give only global comparisons of panelists. In the present paper, methods that can distinguish panelist behavior related to separate attributes, are described. These methods model the data in such a way that blocks of loadings pertaining to the attributes are either small or large. At the same time, one can zoom in on the loadings for panelists within each block of loadings associated with an attribute to inspect differences in panelist behavior. Two types of methods have been proposed for this earlier (rotation to simple blocks and penalizing blocks of loadings), and a third one is proposed in the present paper (constraining blocks of loadings to zero). The new approach is compared here to the other two methods. It is found that the rotation and constraints approaches work about equally well and better than the penalty approach. However, the rotation approach offers richer panelist behavior information, as is illustrated by the analysis of empirical data. It is also shown how, in this example, the reliability of idiosyncratic panelist behavior indicators can be evaluated.