Additive structure in qualitative data: An alternating least squares method with optimal scaling features

A method is developed to investigate the additive structure of data that (a) may be measured at the nominal, ordinal or cardinal levels, (b) may be obtained from either a discrete or continuous source, (c) may have known degrees of imprecision, or (d) may be obtained in unbalanced designs. The method also permits experimental variables to be measured at the ordinal level. It is shown that the method is convergent, and includes several previously proposed methods as special cases. Both Monte Carlo and empirical evaluations indicate that the method is robust.This research was supported in part by grant MH-10006 from the National Institute of Mental Health to the Psychometric Laboratory of the University of North Carolina. We wish to thank Thomas S. Wallsten for comments on an earlier draft of this paper. Copies of the paper and of ADDALS, a program to perform the analyses discussed herein, may be obtained from the second author.