Fitting a simplex symmetrically

A method for fitting a perfect 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 an iterative algorithm for fitting a quasi-simplex. Some empirical results are included.This work was done while the author held a Visiting Research Fellowship at the Educational Testing Service. The gracious hospitality of this institution, as well as its scenic surroundings, are beyond praise. An earlier version of this paper (ETS Research Bulletin RB-68-31) was reviewed by Drs. Karl G. Jöreskog and Bruce Bloxom who contributed to its improvement. For a critical reading of the final draft, I owe thanks to Miss Ming-Mei Wang.