Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure

SIMPLIMAX is proposed as a procedure for oblique rotation of a factor loadings matrix to simple structure. The distinguishing feature of this method is that it rotates the loading matrix so that after rotation the m smallest elements have a minimal sum of squares (where m is specified in advance). In the present paper, the SIMPLIMAX method is generalized to handle three-way arrays: Three-way SIMPLIMAX finds oblique simple structure rotations of the core matrix that results from a three-mode factor analysis. Specifically, three-way SIMPLIMAX minimizes the sum of the m smallest elements of the rotated core array. An algorithm for three-way SIMPLIMAX is presented, the performance of the algorithm is discussed, some applications are shown, and it is indicated how the method can be used to serve additional purposes. Also, it is shown how the method can be used for rotation of solutions of N-mode factor analysis, and for rotation over a subset of the modes of an N-mode core array. (C) 1998 Elsevier Science B.V. All rights reserved.