Unfolding Models for Asymmetric Dissimilarity Data With External Information Based on Path Structures

This article contains asymmetric dissimilarity data which is observed in various situations. In asymmetric dissimilarity data, dissimilarity from subject i to j and from subject j to i are not the same necessarily. Asymmetric multidimensional scaling (AMDS) is a visualization method for describing the asymmetric relations between subjects, given asymmetric dissimilarity data for subjects. It is sure that AMDS is a useful tool for interpreting the asymmetric relation, however, existing AMDS cannot be considered for the external information, even if the external information of the same subjects for the asymmetric dissimilarity data is given. If the estimated coordinates can be interpreted from the loading matrix for the external information like principal component analysis (PCA), the AMDS become more useful. This is because we can interpret the relation between the estimated asymmetries and the factors of the external information on the low dimensions. In this article, we proposed new AMDS with external information. In addition to that, the proposed method can consider the path structure for variables like SEM.