The K-INDSCAL Model for Heterogeneous Three-Way Dissimilarity Data |
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Authors: | Laura Bocci Maurizio Vichi |
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Affiliation: | (1) CEPS/INSTEAD Research Institute, B.P. 48, L-4501 Differdange, Luxembourg;(2) University of Nancy 2, Nancy Cedex, France;(3) CEMAFI – University of Nice Sophia Antipolis, Nice, France;; |
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Abstract: | A weighted Euclidean distance model for analyzing three-way dissimilarity data (stimuli by stimuli by subjects) for heterogeneous subjects is proposed. First, it is shown that INDSCAL may fail to identify a common space representative of the observed data structure in presence of heterogeneity. A new model that removes the rotational invariance of the classical multidimensional scaling problem and specifies K common homogeneous spaces is proposed. The model, called mixture INDSCAL in K classes, or briefly K-INDSCAL, still includes individual saliencies. However, the large number of parameters in K-INDSCAL may produce instability of the estimates and therefore a parsimonious model will also be discussed. The parameters of the model are estimated in a least-squares fitting context and an efficient coordinate descent algorithm is given. The usefulness of K-INDSCAL is demonstrated by both artificial and real data analyses. |
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