A generalization of the interpoint distance model

Coombs and Kao have conjectured that, given the distances between a set of points representing persons and another representing objects, factor analytic methods can be used to recover the locations of the persons and objects. In the present paper it is proved that the conjecture applies, with some qualifications, to squared distances rather than distances themselves. Possible applications to scaling and to inventory responses are discussed.Most of the work that resulted in this paper was done while the authors were affiliated with Educational Testing Service. Portions of this paper were presented at the APA convention, St. Louis, 1962.