Subject Variations in Sorting Data: Revisiting the Points-of-View Model

Cultural consensus analysis (CCA) of similarity data involves analyzing the matrix of inter-subject correlations with Factor Analysis. If the pattern of correlations can be explained by a single dominant factor, one can assume that the subjects grouped the items according to a shared mental model - a cultural consensus - and their responses can safely be merged in subsequent stages of analysis. In the negative case where no consensus exists and the pattern of correlations contains more than one factor, we argue that a logical extension of CCA is the Points-of-View approach of Tucker and Messick. Each "point of view" (PoV) is an idealized or prototypal mode of organizing the items, obtained by rotating the factors to simple structure. The distinct organization present in each PoV can be made explicit by considering it as a matrix of item proximities, suitable for clustering or multidimensional scaling. To account for each subject's data, these idealized modes are combined in proportions given by the subject's factor loadings. Following a canonical application of CCA, subjects sorted a list of animal names. The Points-of-View model accommodated the variations among subjects, while clarifying the distinct mental models forming the extremes of their variation.