Sensitivity in metric scaling and analysis of distance.

Assessing the sensitivity or sampling variability of multivariate ordination methods is essential if inferences are to be drawn from the analysis, but such assessment has to date been notably absent in many applications of multidimensional scaling (MDS). The only available technique seems to be the one by DeLeeuw and Meulman who proposed a special jackknife in a general MDS setting, but this method does not appear to have been widely used to date. A possible reason for this is that it is perceived to be computationally daunting. However, if attention is focused on classical metric scaling (principal coordinate analysis) then known analytical results can be used and the apparent computational complexity disappears. The purpose of this article is to set out these results, to indicate their use in more general analysis of distance, and to illustrate the methodology on some biometric examples.