title: The K-INDSCAL Model for Heterogeneous Three-Way Dissimilarity Data.
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.
authors: Department of Communication and Social Research, Sapienza University of Rome, Via Salaria, 113, 00198, Rome, Italy. laura.bocci@uniroma1.it.
authors: Laura
authors: L
authors: Bocci
authors: Department of Statistical Sciences, Sapienza University of Rome, P.le Aldo Moro, 5, 00185, Rome, Italy.
authors: Maurizio
authors: M
authors: Vichi
keywords: INDSCAL; heterogeneous dissimilarities data; mixture of INDSCAL models; three-way dissimilarity data