A GENERALIZATION OF GIPSCAL FOR THE ANALYSIS OF NONSYMMETRIC DATA

Graphical representation of nonsymmetric relationships data has usuall y proceeded via separate displays for the symmetric and the skew-symme tric parts of a data matrix. DEDICOM avoids splitting the data into sy mmetric and skew-symmetric parts, but lacks a graphical representation of the results. Chino's GIPSCAL combines features of both models, but may have a poor goodness-of-fit compared to DEDICOM. We simplify and generalize Chino's method in such a way that it fits the data better. We develop an alternating least squares algorithm for the resulting me thod, called Generalized GIPSCAL, and adjust it to handle GIPSCAL as w ell. In addition, we show that Generalized GIPSCAL is a constrained va riant of DEDICOM and derive necessary and sufficient conditions for eq uivalence of the two models. Because these conditions are rather mild, we expect that in many practical cases DEDICOM and Generalized GIPSCA L are (nearly) equivalent, and hence that the graphical representation from Generalized GIPSCAL can be used to display the DEDICOM results g raphically. Such a representation is given for an illustration. Finall y, we show Generalized GIPSCAL to be a generalization of another metho d for joint representation of the symmetric and skew-symmetric parts o f a data matrix.