Factorial rotation to simple structure and maximum similarity

When the regression of factored variates on variates defining subpopulations (or experimental groups) is (a) nonlinear or (b) heteroscedastic, an existing solution to the problem of factorial invariance does not apply. This paper presents an approach which can be used in place of the existing solution and derives a method for obtaining maximally similar orthogonal simple structure factor pattern matrices across subpopulations. The method is applied to data from three experimental groups.The writer wishes to express his gratitude to Professor Paul Horst for his many helpful suggestions in the development presented here. Credit is also due to William Meredith and Michael Browne for their helpful comments. The study was supported in part by Office of Naval Research Contract Nonr-477(33) and USPHS Research Grant MH00743-08 (Principal Investigator: Paul Horst).