FITTING A DISTANCE MODEL TO HOMOGENEOUS SUBSETS OF VARIABLES - POINTS-OF-VIEW ANALYSIS OF CATEGORICAL-DATA

An approach is presented for analyzing a heterogeneous set of categori cal variables assumed to form a limited number of homogeneous subsets. The variables generate a particular set of proximities between the ob jects in the data matrix, and the objective of the analysis is to repr esent the objects in low-dimensional Euclidean spaces, where the dista nces approximate these proximities. A least squares loss function is m inimized that involves three major components: a) the partitioning of the heterogeneous variables into homogeneous subsets; b) the optimal q uantification of the categories of the variables, and c) the represent ation of the objects through multiple multidimensional scaling tasks p erformed simultaneously. An important aspect from an algorithmic point of view is in the use of majorization. The use of the procedure is de monstrated by a typical example of possible application, i.e., the ana lysis of categorical data obtained in a free-sort task. The results of points of view analysis are contrasted with a standard homogeneity an alysis, and the stability is studied through a Jackknife analysis.