Distance stability analysis in multidimensional scaling using the jackknife method

Stability or sensitivity analysis is an important topic in data analysis that has received little attention in the application of multidimensional scaling (MDS), for which the only available approaches are given in terms of a coordinate-based analytical jackknife methodology. Although in MDS the prime interest is in assessing the stability of the points in the configuration, this methodology may be influenced by imprecisions resulting from the inherently necessary Procrustes method. This paper proposes an analytical distance-based jackknife procedure to study stability and cross-validation in MDS in terms of the jackknife distances, which is not influenced by the Procrustes method. For each object, the corresponding jackknife estimated points are considered as naturally clustered points, and stability and cross-validation are analysed in terms of the MDS distances arising from the jackknife procedure, on the basis of a weighted cluster-MDS algorithm. A jackknife-relevant configuration is also proposed for cross-validation in terms of coordinates, in a cluster-MDS framework.