Techniques for oblique factor rotation of two or more loading matrices to a mixture of simple structure and optimal agreement

Three techniques are proposed for oblique rotation of two or more loading matrices to a mixture of simple structure and optimal agreement. The three techniques, consensus direct oblimin, consensus promin and consensus simple target rotation, are compared to existing techniques and to each other, using artificial and real data. When agreement between solutions can be expected, the new techniques appear to be more useful than oblique rotation of each of the loading matrices separately. Consensus direct oblimin achieved the best results in terms of 'agreement between simple structures'; consensus promin was the technique that best recovered the underlying simple loading matrix; and consensus simple target rotation seemed to give an interesting compromise between agreement and simple structure, focusing a little more on simplicity than consensus direct oblimin.