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.