Relations between multidimensional scaling and three-mode factor analysis

A combination is achieved of two lines of psychometric interest: a) multidimensional scaling and b) factor analysis. This is accomplished with the use of three-mode factor analysis of scalar product matrices, one for each subject. Two of the modes are the groups of objects scaled and the third mode is the sample of subjects. Results are an object space, a person space, and a system for changing weights given to dimensions and of angles between dimensions in the object space for individuals located at different places in the person space. The development is illustrated with data from an adjective similarity study.Supported in part by the Personnel and Training Branch of the Office of Naval Research under Contract Number 00014-67-A-0305-0003. A number of very helpful comments were made by an anonymous editorial reviewer forPsychometrika.During 1970–71 at the L. L. Thurstone Psychometric Laboratory, University of North Carolina.