EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT BERNAARDS AND JENNRICH GRADIENT PROJECTION ALGORITHMS AND SOFTWARE FOR ARBITRARY ROTATION CRITERIA IN FACTOR ANALYSIS

Almost all modern rotation of factor loadings is based on optimizing a criterion, for example, the quartimax criterion for quartimax rotation. Recent advancements in numer-ical methods have led to general orthogonal and oblique algorithms for optimizing essen-tially any rotation criterion. All that is required for a specific application is a definition of the criterion and its gradient. The authors present the implementations of gradient projec-tion algorithms, both orthogonal and oblique, as well as a catalogue of rotation criteria and corresponding gradients. Software for these is downloadable and free; a specific ver-sion is given for each of the computing environments used most by statisticians. Exam-ples of rotation methods are presented by applying them to a loading matrix from Wehmeyer and Palmer