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Controlling the Two Kinds of Error Rate in Selecting an Appropriate Asymmetric MDS Model

ASYMMAXSCAL is revisited first, which is a maximum likelihood asymmetric multidimensional scaling method recently proposed by Saburi and Chino (2008). It is proven that the likelihood ratio test statistic on the quasi-symmetry hypothesis proposed by Caussinus (1965) and that of a marginal homogeneity hypothesis suggested by Andersen (1980) are mutually independent statistically. A possible application of this theorem is indicated to asymmetric relational data in the context of asymmetric multidimensional scaling.