Metric structures in ordinal data

摘要: Abstract Under appropriate conditions, data merely about the ordering of objects—or separations between objects—is sometimes sufficient to fix positions those objects on an essentially numerical scale. This paper uses both mathematical and “Monte Carlo” results establish clarify possibility thus extracting metric information from purely ordinal for two multidimensional cases: (a) analysis proximities, in which one is given a single rank order all n(n−1) 2 pairs n with respect psychological similarity or “proximity”; (b) nonmetric factor analysis, different individual each m attributes. As (and m) increase, are found determine spatial representation more nearly within general transformation, case affine analysis. Extensions these other cases also considered.