Nonmetric linear biplots

A methodology is developed for constructing linear biplots for a class of n onmetric multidimensional scaling methods for multivariate data. The nonlin ear transformations of nonmetric scaling manifest themselves in irregularly spaced calibration markers. Two approaches are examined, one based on Proc rustean embedding, the other on a modification of the popular regression me thod. The widespread use of an unmodified regression method in association with nonlinear transformations is questioned. An example is given. The meth odology presented here could potentially be developed to give an optimal re presention of a matrix in fewer geometric dimensions than its rank.