The simultaneous maximization of congruence for two or more matrices under orthogonal rotation

While a rotation procedure currently exists to maximize simultaneously Tucker's coefficient of congruence between corresponding factors of two factor matrices under orthogonal rotation of one factor matrix, only approximate solutions are known for the generalized case where two or more matrices are rotated. A generalization and modification of the existing rotation procedure to simultaneously maximize the congruence is described. An example using four data matrices, comparing the generalized congruence maximization procedure with alternative rotation procedures, is presented. The results show a marked improvement of the obtained congruence using the generalized congruence maximization procedure compared to other procedures, without a significant loss of success with respect to the least squares criterion. A computer program written by the author to perform the rotations is briefly discussed.