Studies in the robustness of multidimensional scaling: euclidean models and simulation studies

This series of papers is devoted to the investigation ot the extent to which the accuracy oi operation of multidimensional scaling can be put onto a quantitative footing. In thls third and final paper, four probabilistic models for the generation of euclidean-distance-like dissimilarity function are proposed; these models reflect some of the ways in which dissimilarities actually arise. and allow such effects as dependence between dissimilarities to be studied. Using these models. simulation experiments are carried out to assess the response of both classical and ordinal (non-metric) scaling to errors, with procrustes statistics being used to measure accuracy of recovery. A further scaling method. leait bquarer scaling. is discussed briefly and shown to display empirically a useful combination of properties. as is a technique used to preprocess the dissimilarity matrix.