The orthogonal approximation of an oblique structure in factor analysis

A procedure is derived for obtaining an orthogonal transformation which most nearly transforms one given matrix into another given matrix, according to some least-squares criterion of fit. From this procedure, three analytic methods are derived for obtaining an orthogonal factor matrix which closely approximates a given oblique factor matrix. The case is considered of approximating a specified subset of oblique vectors by orthogonal vectors.Part of this research was carried out while the author was a psychometric fellow at the Educational Testing Service, Princeton, New Jersey.