3-MODE ORTHOMAX ROTATION

Factor analysis and principal components analysis (PCA) are often foll owed by an orthomax rotation to rotate a loading matrix to simple stru cture. The simple structure is usually defined in terms of the simplic ity of the columns of the loading matrix. In Three-made PCA, rotationa l freedom of the so called core (a three-way array relating components for the three different modes) can be used similarly to find a simple structure of the core. Simple structure of the core can be defined wi th respect to ail three modes simultaneously, possibly with different emphases on the different modes. The present paper provides a fully fl exible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally, this appr oach relies on repeated (two-way) orthomax applied to supermatrices co ntaining the frontal, lateral or horizontal slabs, respectively. The p rocedure is illustrated by means of a number of exemplary analyses. As a by-product, application of the Three-mode Orthomax procedures to tw o-way arrays is shown to reveal interesting relations with and interpr etations of existing two-way simple structure rotation techniques.