Peter H. Schonemann
Fitting a simplex symmetrically
Psychometrika, 1970, 35, 1-21
A method for fitting a eprfect simplex (Guttman, 1954) is suggested which, in contrast to Kaiser's (1962) is independent of the order of the manifest variables. It is based on a procedure for scaling a set of points from their pairwise distances (Torgerson, 1958, Young & Householder, 1938) which is reviewed in compact notation in the Appendix.
The method is extended to fitting a quasisimplex. Some empirical results are included.
Appendix 1 contains a matrix formulation of the complete euclidean embedding problem, which can be traced back at least to Cayley (1841). Psychologists usually attribute it to Torgerson (1958). In matrix terms, it amounts to converting a matrix of squared euclidean distances into a scalar product matrix by pre- and postmultiplying it with a projector which annihilates (zeroes out) a vector of ones. Knowledge of this fact eventually contributed to finding the solution of the metric unfolding problem, which generalizes the metric embedding problem from the complete to the incomplete data case.