A general parametric model of similarity and subjective difference

The field of multidimensional scaling is dominated by models that lack inherent parameters. Correcting parameters have been introduced, e.g. INDSCAL, to increase power of prediction. Although a nonparametirc model with correcting parameters may exhibit a very good fit to data, a parametric model is intrinsically superior. The general parametric model proposed here yields measures of both absolute and relative subjective differences (dissimilarity) in addition to similarity. It is basically unidimensioanal. Rules for combining values of attributes into a single multidimensional value may be applied either to the input or to the output of the model. One of the resulting functions is a generalization of the Eisler-Ekman similarity function. A special case of another function is identical to the Minkowski class of distance functions (including INDSCAL). The model is not limited to pairwise relations. It yields unitary measures for any number of objects.